9"""Z3 is a high performance theorem prover developed at Microsoft Research.
11Z3 is used in many applications such as: software/hardware verification and testing,
12constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13and geometrical problems.
16Please send feedback, comments and/or corrections on the Issue tracker for
17https://github.com/Z3prover/z3.git. Your comments are very valuable.
38... x = BitVec('x', 32)
40... # the expression x + y is type incorrect
42... except Z3Exception as ex:
43... print("failed: %s" % ex)
49from .z3consts
import *
50from .z3printer
import *
51from fractions
import Fraction
56if sys.version_info.major >= 3:
57 from typing
import Iterable
67if sys.version_info.major < 3:
69 return isinstance(v, (int, long))
72 return isinstance(v, int)
84 major = ctypes.c_uint(0)
85 minor = ctypes.c_uint(0)
86 build = ctypes.c_uint(0)
87 rev = ctypes.c_uint(0)
89 return "%s.%s.%s" % (major.value, minor.value, build.value)
93 major = ctypes.c_uint(0)
94 minor = ctypes.c_uint(0)
95 build = ctypes.c_uint(0)
96 rev = ctypes.c_uint(0)
98 return (major.value, minor.value, build.value, rev.value)
107 raise Z3Exception(msg)
111 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
115 """Log interaction to a file. This function must be invoked immediately after init(). """
120 """Append user-defined string to interaction log. """
125 """Convert an integer or string into a Z3 symbol."""
133 """Convert a Z3 symbol back into a Python object. """
146 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
148 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
149 return [arg
for arg
in args[0]]
160 if isinstance(args, (set, AstVector, tuple)):
161 return [arg
for arg
in args]
169 if isinstance(val, bool):
170 return "true" if val
else "false"
181 """A Context manages all other Z3 objects, global configuration options, etc.
183 Z3Py uses a default global context. For most applications this is sufficient.
184 An application may use multiple Z3 contexts. Objects created in one context
185 cannot be used in another one. However, several objects may be "translated" from
186 one context to another. It is not safe to access Z3 objects from multiple threads.
187 The only exception is the method `interrupt()` that can be used to interrupt() a long
189 The initialization method receives global configuration options for the new context.
194 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
213 if Z3_del_context
is not None and self.
owner:
219 """Return a reference to the actual C pointer to the Z3 context."""
223 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
225 This method can be invoked from a thread different from the one executing the
226 interruptible procedure.
231 """Return the global parameter description set."""
240 """Return a reference to the global Z3 context.
243 >>> x.ctx == main_ctx()
248 >>> x2 = Real('x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
274 >>> set_param(precision=10)
277 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
281 if not set_pp_option(k, v):
296 """Reset all global (or module) parameters.
302 """Alias for 'set_param' for backward compatibility.
308 """Return the value of a Z3 global (or module) parameter
310 >>> get_param('nlsat.reorder')
313 ptr = (ctypes.c_char_p * 1)()
315 r = z3core._to_pystr(ptr[0])
317 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
329 """Superclass for all Z3 objects that have support for pretty printing."""
335 in_html = in_html_mode()
338 set_html_mode(in_html)
343 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
351 if self.
ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
359 return obj_to_string(self)
362 return obj_to_string(self)
365 return self.
eq(other)
378 elif is_eq(self)
and self.num_args() == 2:
379 return self.arg(0).
eq(self.arg(1))
381 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
384 """Return a string representing the AST node in s-expression notation.
387 >>> ((x + 1)*x).sexpr()
393 """Return a pointer to the corresponding C Z3_ast object."""
397 """Return unique identifier for object. It can be used for hash-tables and maps."""
401 """Return a reference to the C context where this AST node is stored."""
402 return self.
ctx.ref()
405 """Return `True` if `self` and `other` are structurally identical.
412 >>> n1 = simplify(n1)
413 >>> n2 = simplify(n2)
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
428 >>> # Nodes in different contexts can't be mixed.
429 >>> # However, we can translate nodes from one context to another.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
443 >>> n1 = simplify(Int('x') + 1)
444 >>> n2 = simplify(2 + Int('x') - 1)
445 >>> n1.hash() == n2.hash()
452 """Return `True` if `a` is an AST node.
456 >>> is_ast(IntVal(10))
460 >>> is_ast(BoolSort())
462 >>> is_ast(Function('f', IntSort(), IntSort()))
469 return isinstance(a, AstRef)
473 """Return `True` if `a` and `b` are structurally identical AST nodes.
483 >>> eq(simplify(x + 1), simplify(1 + x))
517 _args = (FuncDecl * sz)()
519 _args[i] = args[i].as_func_decl()
527 _args[i] = args[i].as_ast()
535 _args[i] = args[i].as_ast()
543 elif k == Z3_FUNC_DECL_AST:
560 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
569 """Return the Z3 internal kind of a sort.
570 This method can be used to test if `self` is one of the Z3 builtin sorts.
573 >>> b.kind() == Z3_BOOL_SORT
575 >>> b.kind() == Z3_INT_SORT
577 >>> A = ArraySort(IntSort(), IntSort())
578 >>> A.kind() == Z3_ARRAY_SORT
580 >>> A.kind() == Z3_INT_SORT
586 """Return `True` if `self` is a subsort of `other`.
588 >>> IntSort().subsort(RealSort())
594 """Try to cast `val` as an element of sort `self`.
596 This method is used in Z3Py to convert Python objects such as integers,
597 floats, longs and strings into Z3 expressions.
600 >>> RealSort().cast(x)
609 """Return the name (string) of sort `self`.
611 >>> BoolSort().name()
613 >>> ArraySort(IntSort(), IntSort()).name()
619 """Return `True` if `self` and `other` are the same Z3 sort.
622 >>> p.sort() == BoolSort()
624 >>> p.sort() == IntSort()
632 """Return `True` if `self` and `other` are not the same Z3 sort.
635 >>> p.sort() != BoolSort()
637 >>> p.sort() != IntSort()
644 return AstRef.__hash__(self)
648 """Return `True` if `s` is a Z3 sort.
650 >>> is_sort(IntSort())
652 >>> is_sort(Int('x'))
654 >>> is_expr(Int('x'))
657 return isinstance(s, SortRef)
662 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
664 if k == Z3_BOOL_SORT:
666 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
668 elif k == Z3_BV_SORT:
670 elif k == Z3_ARRAY_SORT:
672 elif k == Z3_DATATYPE_SORT:
674 elif k == Z3_FINITE_DOMAIN_SORT:
676 elif k == Z3_FLOATING_POINT_SORT:
678 elif k == Z3_ROUNDING_MODE_SORT:
680 elif k == Z3_RE_SORT:
682 elif k == Z3_SEQ_SORT:
684 elif k == Z3_CHAR_SORT:
686 elif k == Z3_TYPE_VAR:
696 """Create a new uninterpreted sort named `name`.
698 If `ctx=None`, then the new sort is declared in the global Z3Py context.
700 >>> A = DeclareSort('A')
701 >>> a = Const('a', A)
702 >>> b = Const('b', A)
714 """Type variable reference"""
724 """Create a new type variable named `name`.
726 If `ctx=None`, then the new sort is declared in the global Z3Py context.
741 """Function declaration. Every constant and function have an associated declaration.
743 The declaration assigns a name, a sort (i.e., type), and for function
744 the sort (i.e., type) of each of its arguments. Note that, in Z3,
745 a constant is a function with 0 arguments.
758 """Return the name of the function declaration `self`.
760 >>> f = Function('f', IntSort(), IntSort())
763 >>> isinstance(f.name(), str)
769 """Return the number of arguments of a function declaration.
770 If `self` is a constant, then `self.arity()` is 0.
772 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
779 """Return the sort of the argument `i` of a function declaration.
780 This method assumes that `0 <= i < self.arity()`.
782 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
791 """Return the sort of the range of a function declaration.
792 For constants, this is the sort of the constant.
794 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
801 """Return the internal kind of a function declaration.
802 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
805 >>> d = (x + 1).decl()
806 >>> d.kind() == Z3_OP_ADD
808 >>> d.kind() == Z3_OP_MUL
816 result = [
None for i
in range(n)]
819 if k == Z3_PARAMETER_INT:
821 elif k == Z3_PARAMETER_DOUBLE:
823 elif k == Z3_PARAMETER_RATIONAL:
825 elif k == Z3_PARAMETER_SYMBOL:
827 elif k == Z3_PARAMETER_SORT:
829 elif k == Z3_PARAMETER_AST:
831 elif k == Z3_PARAMETER_FUNC_DECL:
838 """Create a Z3 application expression using the function `self`, and the given arguments.
840 The arguments must be Z3 expressions. This method assumes that
841 the sorts of the elements in `args` match the sorts of the
842 domain. Limited coercion is supported. For example, if
843 args[0] is a Python integer, and the function expects a Z3
844 integer, then the argument is automatically converted into a
847 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
857 _args = (Ast * num)()
862 tmp = self.
domain(i).cast(args[i])
864 _args[i] = tmp.as_ast()
869 """Return `True` if `a` is a Z3 function declaration.
871 >>> f = Function('f', IntSort(), IntSort())
878 return isinstance(a, FuncDeclRef)
882 """Create a new Z3 uninterpreted function with the given sorts.
884 >>> f = Function('f', IntSort(), IntSort())
890 _z3_assert(len(sig) > 0,
"At least two arguments expected")
895 dom = (Sort * arity)()
896 for i
in range(arity):
905 """Create a new fresh Z3 uninterpreted function with the given sorts.
909 _z3_assert(len(sig) > 0,
"At least two arguments expected")
914 dom = (z3.Sort * arity)()
915 for i
in range(arity):
928 """Create a new Z3 recursive with the given sorts."""
931 _z3_assert(len(sig) > 0,
"At least two arguments expected")
936 dom = (Sort * arity)()
937 for i
in range(arity):
946 """Set the body of a recursive function.
947 Recursive definitions can be simplified if they are applied to ground
950 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
951 >>> n = Int('n', ctx)
952 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
955 >>> s = Solver(ctx=ctx)
956 >>> s.add(fac(n) < 3)
959 >>> s.model().eval(fac(5))
969 _args[i] = args[i].ast
980 """Constraints, formulas and terms are expressions in Z3.
982 Expressions are ASTs. Every expression has a sort.
983 There are three main kinds of expressions:
984 function applications, quantifiers and bounded variables.
985 A constant is a function application with 0 arguments.
986 For quantifier free problems, all expressions are
987 function applications.
997 """Return the sort of expression `self`.
1009 """Shorthand for `self.sort().kind()`.
1011 >>> a = Array('a', IntSort(), IntSort())
1012 >>> a.sort_kind() == Z3_ARRAY_SORT
1014 >>> a.sort_kind() == Z3_INT_SORT
1017 return self.
sort().kind()
1020 """Return a Z3 expression that represents the constraint `self == other`.
1022 If `other` is `None`, then this method simply returns `False`.
1038 return AstRef.__hash__(self)
1041 """Return a Z3 expression that represents the constraint `self != other`.
1043 If `other` is `None`, then this method simply returns `True`.
1062 """Return the Z3 function declaration associated with a Z3 application.
1064 >>> f = Function('f', IntSort(), IntSort())
1077 """Return the number of arguments of a Z3 application.
1081 >>> (a + b).num_args()
1083 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1093 """Return argument `idx` of the application `self`.
1095 This method assumes that `self` is a function application with at least `idx+1` arguments.
1099 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1114 """Return a list containing the children of the given expression
1118 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1124 return [self.
arg(i)
for i
in range(self.
num_args())]
1138 """inverse function to the serialize method on ExprRef.
1139 It is made available to make it easier for users to serialize expressions back and forth between
1140 strings. Solvers can be serialized using the 'sexpr()' method.
1144 if len(s.assertions()) != 1:
1145 raise Z3Exception(
"single assertion expected")
1146 fml = s.assertions()[0]
1147 if fml.num_args() != 1:
1148 raise Z3Exception(
"dummy function 'F' expected")
1152 if isinstance(a, Pattern):
1156 if k == Z3_QUANTIFIER_AST:
1159 if sk == Z3_BOOL_SORT:
1161 if sk == Z3_INT_SORT:
1162 if k == Z3_NUMERAL_AST:
1165 if sk == Z3_REAL_SORT:
1166 if k == Z3_NUMERAL_AST:
1171 if sk == Z3_BV_SORT:
1172 if k == Z3_NUMERAL_AST:
1176 if sk == Z3_ARRAY_SORT:
1178 if sk == Z3_DATATYPE_SORT:
1180 if sk == Z3_FLOATING_POINT_SORT:
1184 return FPRef(a, ctx)
1185 if sk == Z3_FINITE_DOMAIN_SORT:
1186 if k == Z3_NUMERAL_AST:
1190 if sk == Z3_ROUNDING_MODE_SORT:
1192 if sk == Z3_SEQ_SORT:
1194 if sk == Z3_CHAR_SORT:
1196 if sk == Z3_RE_SORT:
1197 return ReRef(a, ctx)
1214 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1224 if isinstance(a, str)
and isinstance(b, SeqRef):
1226 if isinstance(b, str)
and isinstance(a, SeqRef):
1228 if isinstance(a, float)
and isinstance(b, ArithRef):
1230 if isinstance(b, float)
and isinstance(a, ArithRef):
1243 for element
in sequence:
1244 result = func(result, element)
1255 alist = [
_py2expr(a, ctx)
for a
in alist]
1256 s =
_reduce(_coerce_expr_merge, alist,
None)
1257 return [s.cast(a)
for a
in alist]
1261 """Return `True` if `a` is a Z3 expression.
1268 >>> is_expr(IntSort())
1272 >>> is_expr(IntVal(1))
1275 >>> is_expr(ForAll(x, x >= 0))
1277 >>> is_expr(FPVal(1.0))
1280 return isinstance(a, ExprRef)
1284 """Return `True` if `a` is a Z3 function application.
1286 Note that, constants are function applications with 0 arguments.
1293 >>> is_app(IntSort())
1297 >>> is_app(IntVal(1))
1300 >>> is_app(ForAll(x, x >= 0))
1303 if not isinstance(a, ExprRef):
1306 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1310 """Return `True` if `a` is Z3 constant/variable expression.
1319 >>> is_const(IntVal(1))
1322 >>> is_const(ForAll(x, x >= 0))
1325 return is_app(a)
and a.num_args() == 0
1329 """Return `True` if `a` is variable.
1331 Z3 uses de-Bruijn indices for representing bound variables in
1339 >>> f = Function('f', IntSort(), IntSort())
1340 >>> # Z3 replaces x with bound variables when ForAll is executed.
1341 >>> q = ForAll(x, f(x) == x)
1347 >>> is_var(b.arg(1))
1354 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1362 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1363 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1364 >>> q = ForAll([x, y], f(x, y) == x + y)
1366 f(Var(1), Var(0)) == Var(1) + Var(0)
1370 >>> v1 = b.arg(0).arg(0)
1371 >>> v2 = b.arg(0).arg(1)
1376 >>> get_var_index(v1)
1378 >>> get_var_index(v2)
1387 """Return `True` if `a` is an application of the given kind `k`.
1391 >>> is_app_of(n, Z3_OP_ADD)
1393 >>> is_app_of(n, Z3_OP_MUL)
1396 return is_app(a)
and a.decl().kind() == k
1399def If(a, b, c, ctx=None):
1400 """Create a Z3 if-then-else expression.
1404 >>> max = If(x > y, x, y)
1410 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1411 return Cond(a, b, c, ctx)
1418 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1423 """Create a Z3 distinct expression.
1430 >>> Distinct(x, y, z)
1432 >>> simplify(Distinct(x, y, z))
1434 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1435 And(Not(x == y), Not(x == z), Not(y == z))
1440 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1449 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1450 args[0] = a.as_ast()
1451 args[1] = b.as_ast()
1452 return f(a.ctx.ref(), 2, args)
1456 """Create a constant of the given sort.
1458 >>> Const('x', IntSort())
1462 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1468 """Create several constants of the given sort.
1470 `names` is a string containing the names of all constants to be created.
1471 Blank spaces separate the names of different constants.
1473 >>> x, y, z = Consts('x y z', IntSort())
1477 if isinstance(names, str):
1478 names = names.split(
" ")
1479 return [
Const(name, sort)
for name
in names]
1483 """Create a fresh constant of a specified sort"""
1489 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1490 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1493 >>> Var(0, IntSort())
1495 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1505 Create a real free variable. Free variables are used to create quantified formulas.
1506 They are also used to create polynomials.
1516 Create a list of Real free variables.
1517 The variables have ids: 0, 1, ..., n-1
1519 >>> x0, x1, x2, x3 = RealVarVector(4)
1523 return [
RealVar(i, ctx)
for i
in range(n)]
1536 """Try to cast `val` as a Boolean.
1538 >>> x = BoolSort().cast(True)
1548 if isinstance(val, bool):
1552 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1554 if not self.
eq(val.sort()):
1555 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1559 return isinstance(other, ArithSortRef)
1569 """All Boolean expressions are instances of this class."""
1575 if isinstance(other, BoolRef):
1576 other =
If(other, 1, 0)
1577 return If(self, 1, 0) + other
1586 """Create the Z3 expression `self * other`.
1588 if isinstance(other, int)
and other == 1:
1589 return If(self, 1, 0)
1590 if isinstance(other, int)
and other == 0:
1592 if isinstance(other, BoolRef):
1593 other =
If(other, 1, 0)
1594 return If(self, other, 0)
1597 return And(self, other)
1600 return Or(self, other)
1603 return Xor(self, other)
1612 """Return `True` if `a` is a Z3 Boolean expression.
1618 >>> is_bool(And(p, q))
1626 return isinstance(a, BoolRef)
1630 """Return `True` if `a` is the Z3 true expression.
1635 >>> is_true(simplify(p == p))
1640 >>> # True is a Python Boolean expression
1648 """Return `True` if `a` is the Z3 false expression.
1655 >>> is_false(BoolVal(False))
1662 """Return `True` if `a` is a Z3 and expression.
1664 >>> p, q = Bools('p q')
1665 >>> is_and(And(p, q))
1667 >>> is_and(Or(p, q))
1674 """Return `True` if `a` is a Z3 or expression.
1676 >>> p, q = Bools('p q')
1679 >>> is_or(And(p, q))
1686 """Return `True` if `a` is a Z3 implication expression.
1688 >>> p, q = Bools('p q')
1689 >>> is_implies(Implies(p, q))
1691 >>> is_implies(And(p, q))
1698 """Return `True` if `a` is a Z3 not expression.
1710 """Return `True` if `a` is a Z3 equality expression.
1712 >>> x, y = Ints('x y')
1720 """Return `True` if `a` is a Z3 distinct expression.
1722 >>> x, y, z = Ints('x y z')
1723 >>> is_distinct(x == y)
1725 >>> is_distinct(Distinct(x, y, z))
1732 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1736 >>> p = Const('p', BoolSort())
1739 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1742 >>> is_bool(r(0, 1))
1750 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1754 >>> is_true(BoolVal(True))
1758 >>> is_false(BoolVal(False))
1769 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1781 """Return a tuple of Boolean constants.
1783 `names` is a single string containing all names separated by blank spaces.
1784 If `ctx=None`, then the global context is used.
1786 >>> p, q, r = Bools('p q r')
1787 >>> And(p, Or(q, r))
1791 if isinstance(names, str):
1792 names = names.split(
" ")
1793 return [
Bool(name, ctx)
for name
in names]
1797 """Return a list of Boolean constants of size `sz`.
1799 The constants are named using the given prefix.
1800 If `ctx=None`, then the global context is used.
1802 >>> P = BoolVector('p', 3)
1806 And(p__0, p__1, p__2)
1808 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1812 """Return a fresh Boolean constant in the given context using the given prefix.
1814 If `ctx=None`, then the global context is used.
1816 >>> b1 = FreshBool()
1817 >>> b2 = FreshBool()
1826 """Create a Z3 implies expression.
1828 >>> p, q = Bools('p q')
1840 """Create a Z3 Xor expression.
1842 >>> p, q = Bools('p q')
1845 >>> simplify(Xor(p, q))
1856 """Create a Z3 not expression or probe.
1861 >>> simplify(Not(Not(p)))
1882 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1890 """Create a Z3 and-expression or and-probe.
1892 >>> p, q, r = Bools('p q r')
1895 >>> P = BoolVector('p', 5)
1897 And(p__0, p__1, p__2, p__3, p__4)
1901 last_arg = args[len(args) - 1]
1902 if isinstance(last_arg, Context):
1903 ctx = args[len(args) - 1]
1904 args = args[:len(args) - 1]
1905 elif len(args) == 1
and isinstance(args[0], AstVector):
1907 args = [a
for a
in args[0]]
1913 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1923 """Create a Z3 or-expression or or-probe.
1925 >>> p, q, r = Bools('p q r')
1928 >>> P = BoolVector('p', 5)
1930 Or(p__0, p__1, p__2, p__3, p__4)
1934 last_arg = args[len(args) - 1]
1935 if isinstance(last_arg, Context):
1936 ctx = args[len(args) - 1]
1937 args = args[:len(args) - 1]
1938 elif len(args) == 1
and isinstance(args[0], AstVector):
1940 args = [a
for a
in args[0]]
1946 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1962 """Patterns are hints for quantifier instantiation.
1974 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
1976 >>> f = Function('f', IntSort(), IntSort())
1978 >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
1980 ForAll(x, f(x) == 0)
1981 >>> q.num_patterns()
1983 >>> is_pattern(q.pattern(0))
1988 return isinstance(a, PatternRef)
1992 """Create a Z3 multi-pattern using the given expressions `*args`
1994 >>> f = Function('f', IntSort(), IntSort())
1995 >>> g = Function('g', IntSort(), IntSort())
1997 >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
1999 ForAll(x, f(x) != g(x))
2000 >>> q.num_patterns()
2002 >>> is_pattern(q.pattern(0))
2005 MultiPattern(f(Var(0)), g(Var(0)))
2008 _z3_assert(len(args) > 0,
"At least one argument expected")
2029 """Universally and Existentially quantified formulas."""
2038 """Return the Boolean sort or sort of Lambda."""
2044 """Return `True` if `self` is a universal quantifier.
2046 >>> f = Function('f', IntSort(), IntSort())
2048 >>> q = ForAll(x, f(x) == 0)
2051 >>> q = Exists(x, f(x) != 0)
2058 """Return `True` if `self` is an existential quantifier.
2060 >>> f = Function('f', IntSort(), IntSort())
2062 >>> q = ForAll(x, f(x) == 0)
2065 >>> q = Exists(x, f(x) != 0)
2072 """Return `True` if `self` is a lambda expression.
2074 >>> f = Function('f', IntSort(), IntSort())
2076 >>> q = Lambda(x, f(x))
2079 >>> q = Exists(x, f(x) != 0)
2086 """Return the Z3 expression `self[arg]`.
2093 """Return the weight annotation of `self`.
2095 >>> f = Function('f', IntSort(), IntSort())
2097 >>> q = ForAll(x, f(x) == 0)
2100 >>> q = ForAll(x, f(x) == 0, weight=10)
2107 """Return the skolem id of `self`.
2112 """Return the quantifier id of `self`.
2117 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2119 >>> f = Function('f', IntSort(), IntSort())
2120 >>> g = Function('g', IntSort(), IntSort())
2122 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2123 >>> q.num_patterns()
2129 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2131 >>> f = Function('f', IntSort(), IntSort())
2132 >>> g = Function('g', IntSort(), IntSort())
2134 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2135 >>> q.num_patterns()
2147 """Return the number of no-patterns."""
2151 """Return a no-pattern."""
2157 """Return the expression being quantified.
2159 >>> f = Function('f', IntSort(), IntSort())
2161 >>> q = ForAll(x, f(x) == 0)
2168 """Return the number of variables bounded by this quantifier.
2170 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2173 >>> q = ForAll([x, y], f(x, y) >= x)
2180 """Return a string representing a name used when displaying the quantifier.
2182 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2185 >>> q = ForAll([x, y], f(x, y) >= x)
2196 """Return the sort of a bound variable.
2198 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2201 >>> q = ForAll([x, y], f(x, y) >= x)
2212 """Return a list containing a single element self.body()
2214 >>> f = Function('f', IntSort(), IntSort())
2216 >>> q = ForAll(x, f(x) == 0)
2220 return [self.
body()]
2224 """Return `True` if `a` is a Z3 quantifier.
2226 >>> f = Function('f', IntSort(), IntSort())
2228 >>> q = ForAll(x, f(x) == 0)
2229 >>> is_quantifier(q)
2231 >>> is_quantifier(f(x))
2234 return isinstance(a, QuantifierRef)
2237def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2242 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2253 _vs = (Ast * num_vars)()
2254 for i
in range(num_vars):
2256 _vs[i] = vs[i].as_ast()
2258 num_pats = len(patterns)
2259 _pats = (Pattern * num_pats)()
2260 for i
in range(num_pats):
2261 _pats[i] = patterns[i].ast
2268 num_no_pats, _no_pats,
2269 body.as_ast()), ctx)
2272def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2273 """Create a Z3 forall formula.
2275 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2277 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2280 >>> ForAll([x, y], f(x, y) >= x)
2281 ForAll([x, y], f(x, y) >= x)
2282 >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2283 ForAll([x, y], f(x, y) >= x)
2284 >>> ForAll([x, y], f(x, y) >= x, weight=10)
2285 ForAll([x, y], f(x, y) >= x)
2287 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2290def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2291 """Create a Z3 exists formula.
2293 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2296 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2299 >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
2301 Exists([x, y], f(x, y) >= x)
2302 >>> is_quantifier(q)
2304 >>> r = Tactic('nnf')(q).as_expr()
2305 >>> is_quantifier(r)
2308 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2312 """Create a Z3 lambda expression.
2314 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2315 >>> mem0 = Array('mem0', IntSort(), IntSort())
2316 >>> lo, hi, e, i = Ints('lo hi e i')
2317 >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
2319 Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
2325 _vs = (Ast * num_vars)()
2326 for i
in range(num_vars):
2328 _vs[i] = vs[i].as_ast()
2339 """Real and Integer sorts."""
2342 """Return `True` if `self` is of the sort Real.
2347 >>> (x + 1).is_real()
2353 return self.
kind() == Z3_REAL_SORT
2356 """Return `True` if `self` is of the sort Integer.
2361 >>> (x + 1).is_int()
2367 return self.
kind() == Z3_INT_SORT
2373 """Return `True` if `self` is a subsort of `other`."""
2377 """Try to cast `val` as an Integer or Real.
2379 >>> IntSort().cast(10)
2381 >>> is_int(IntSort().cast(10))
2385 >>> RealSort().cast(10)
2387 >>> is_real(RealSort().cast(10))
2396 if val_s.is_int()
and self.
is_real():
2398 if val_s.is_bool()
and self.
is_int():
2399 return If(val, 1, 0)
2400 if val_s.is_bool()
and self.
is_real():
2403 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2410 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2415 """Return `True` if s is an arithmetical sort (type).
2417 >>> is_arith_sort(IntSort())
2419 >>> is_arith_sort(RealSort())
2421 >>> is_arith_sort(BoolSort())
2423 >>> n = Int('x') + 1
2424 >>> is_arith_sort(n.sort())
2427 return isinstance(s, ArithSortRef)
2431 """Integer and Real expressions."""
2434 """Return the sort (type) of the arithmetical expression `self`.
2438 >>> (Real('x') + 1).sort()
2444 """Return `True` if `self` is an integer expression.
2449 >>> (x + 1).is_int()
2452 >>> (x + y).is_int()
2458 """Return `True` if `self` is an real expression.
2463 >>> (x + 1).is_real()
2469 """Create the Z3 expression `self + other`.
2482 """Create the Z3 expression `other + self`.
2492 """Create the Z3 expression `self * other`.
2501 if isinstance(other, BoolRef):
2502 return If(other, self, 0)
2507 """Create the Z3 expression `other * self`.
2517 """Create the Z3 expression `self - other`.
2530 """Create the Z3 expression `other - self`.
2540 """Create the Z3 expression `self**other` (** is the power operator).
2547 >>> simplify(IntVal(2)**8)
2554 """Create the Z3 expression `other**self` (** is the power operator).
2561 >>> simplify(2**IntVal(8))
2568 """Create the Z3 expression `other/self`.
2591 """Create the Z3 expression `other/self`."""
2595 """Create the Z3 expression `other/self`.
2612 """Create the Z3 expression `other/self`."""
2616 """Create the Z3 expression `other%self`.
2622 >>> simplify(IntVal(10) % IntVal(3))
2627 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2631 """Create the Z3 expression `other%self`.
2639 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2643 """Return an expression representing `-self`.
2663 """Create the Z3 expression `other <= self`.
2665 >>> x, y = Ints('x y')
2676 """Create the Z3 expression `other < self`.
2678 >>> x, y = Ints('x y')
2689 """Create the Z3 expression `other > self`.
2691 >>> x, y = Ints('x y')
2702 """Create the Z3 expression `other >= self`.
2704 >>> x, y = Ints('x y')
2716 """Return `True` if `a` is an arithmetical expression.
2725 >>> is_arith(IntVal(1))
2733 return isinstance(a, ArithRef)
2737 """Return `True` if `a` is an integer expression.
2744 >>> is_int(IntVal(1))
2756 """Return `True` if `a` is a real expression.
2768 >>> is_real(RealVal(1))
2783 """Return `True` if `a` is an integer value of sort Int.
2785 >>> is_int_value(IntVal(1))
2789 >>> is_int_value(Int('x'))
2791 >>> n = Int('x') + 1
2796 >>> is_int_value(n.arg(1))
2798 >>> is_int_value(RealVal("1/3"))
2800 >>> is_int_value(RealVal(1))
2807 """Return `True` if `a` is rational value of sort Real.
2809 >>> is_rational_value(RealVal(1))
2811 >>> is_rational_value(RealVal("3/5"))
2813 >>> is_rational_value(IntVal(1))
2815 >>> is_rational_value(1)
2817 >>> n = Real('x') + 1
2820 >>> is_rational_value(n.arg(1))
2822 >>> is_rational_value(Real('x'))
2829 """Return `True` if `a` is an algebraic value of sort Real.
2831 >>> is_algebraic_value(RealVal("3/5"))
2833 >>> n = simplify(Sqrt(2))
2836 >>> is_algebraic_value(n)
2843 """Return `True` if `a` is an expression of the form b + c.
2845 >>> x, y = Ints('x y')
2855 """Return `True` if `a` is an expression of the form b * c.
2857 >>> x, y = Ints('x y')
2867 """Return `True` if `a` is an expression of the form b - c.
2869 >>> x, y = Ints('x y')
2879 """Return `True` if `a` is an expression of the form b / c.
2881 >>> x, y = Reals('x y')
2886 >>> x, y = Ints('x y')
2896 """Return `True` if `a` is an expression of the form b div c.
2898 >>> x, y = Ints('x y')
2908 """Return `True` if `a` is an expression of the form b % c.
2910 >>> x, y = Ints('x y')
2920 """Return `True` if `a` is an expression of the form b <= c.
2922 >>> x, y = Ints('x y')
2932 """Return `True` if `a` is an expression of the form b < c.
2934 >>> x, y = Ints('x y')
2944 """Return `True` if `a` is an expression of the form b >= c.
2946 >>> x, y = Ints('x y')
2956 """Return `True` if `a` is an expression of the form b > c.
2958 >>> x, y = Ints('x y')
2968 """Return `True` if `a` is an expression of the form IsInt(b).
2971 >>> is_is_int(IsInt(x))
2980 """Return `True` if `a` is an expression of the form ToReal(b).
2995 """Return `True` if `a` is an expression of the form ToInt(b).
3010 """Integer values."""
3013 """Return a Z3 integer numeral as a Python long (bignum) numeral.
3026 """Return a Z3 integer numeral as a Python string.
3034 """Return a Z3 integer numeral as a Python binary string.
3036 >>> v.as_binary_string()
3043 """Rational values."""
3046 """ Return the numerator of a Z3 rational numeral.
3048 >>> is_rational_value(RealVal("3/5"))
3050 >>> n = RealVal("3/5")
3053 >>> is_rational_value(Q(3,5))
3055 >>> Q(3,5).numerator()
3061 """ Return the denominator of a Z3 rational numeral.
3063 >>> is_rational_value(Q(3,5))
3072 """ Return the numerator as a Python long.
3074 >>> v = RealVal(10000000000)
3079 >>> v.numerator_as_long() + 1 == 10000000001
3085 """ Return the denominator as a Python long.
3087 >>> v = RealVal("1/3")
3090 >>> v.denominator_as_long()
3109 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3111 >>> v = RealVal("1/5")
3114 >>> v = RealVal("1/3")
3121 """Return a Z3 rational numeral as a Python string.
3130 """Return a Z3 rational as a Python Fraction object.
3132 >>> v = RealVal("1/5")
3140 """Algebraic irrational values."""
3143 """Return a Z3 rational number that approximates the algebraic number `self`.
3144 The result `r` is such that |r - self| <= 1/10^precision
3146 >>> x = simplify(Sqrt(2))
3148 6838717160008073720548335/4835703278458516698824704
3155 """Return a string representation of the algebraic number `self` in decimal notation
3156 using `prec` decimal places.
3158 >>> x = simplify(Sqrt(2))
3159 >>> x.as_decimal(10)
3161 >>> x.as_decimal(20)
3162 '1.41421356237309504880?'
3174 if isinstance(a, bool):
3178 if isinstance(a, float):
3180 if isinstance(a, str):
3185 _z3_assert(
False,
"Python bool, int, long or float expected")
3189 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3193 >>> x = Const('x', IntSort())
3196 >>> x.sort() == IntSort()
3198 >>> x.sort() == BoolSort()
3206 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3210 >>> x = Const('x', RealSort())
3215 >>> x.sort() == RealSort()
3223 if isinstance(val, float):
3224 return str(int(val))
3225 elif isinstance(val, bool):
3235 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3247 """Return a Z3 real value.
3249 `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
3250 If `ctx=None`, then the global context is used.
3254 >>> RealVal(1).sort()
3266 """Return a Z3 rational a/b.
3268 If `ctx=None`, then the global context is used.
3272 >>> RatVal(3,5).sort()
3276 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3277 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3281def Q(a, b, ctx=None):
3282 """Return a Z3 rational a/b.
3284 If `ctx=None`, then the global context is used.
3295 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3308 """Return a tuple of Integer constants.
3310 >>> x, y, z = Ints('x y z')
3315 if isinstance(names, str):
3316 names = names.split(
" ")
3317 return [
Int(name, ctx)
for name
in names]
3321 """Return a list of integer constants of size `sz`.
3323 >>> X = IntVector('x', 3)
3330 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3334 """Return a fresh integer constant in the given context using the given prefix.
3348 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3361 """Return a tuple of real constants.
3363 >>> x, y, z = Reals('x y z')
3366 >>> Sum(x, y, z).sort()
3370 if isinstance(names, str):
3371 names = names.split(
" ")
3372 return [
Real(name, ctx)
for name
in names]
3376 """Return a list of real constants of size `sz`.
3378 >>> X = RealVector('x', 3)
3387 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3391 """Return a fresh real constant in the given context using the given prefix.
3405 """ Return the Z3 expression ToReal(a).
3417 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3423 """ Return the Z3 expression ToInt(a).
3435 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3441 """ Return the Z3 predicate IsInt(a).
3444 >>> IsInt(x + "1/2")
3446 >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
3448 >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
3452 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3458 """ Return a Z3 expression which represents the square root of a.
3471 """ Return a Z3 expression which represents the cubic root of a.
3490 """Bit-vector sort."""
3493 """Return the size (number of bits) of the bit-vector sort `self`.
3495 >>> b = BitVecSort(32)
3505 """Try to cast `val` as a Bit-Vector.
3507 >>> b = BitVecSort(32)
3510 >>> b.cast(10).sexpr()
3523 """Return True if `s` is a Z3 bit-vector sort.
3525 >>> is_bv_sort(BitVecSort(32))
3527 >>> is_bv_sort(IntSort())
3530 return isinstance(s, BitVecSortRef)
3534 """Bit-vector expressions."""
3537 """Return the sort of the bit-vector expression `self`.
3539 >>> x = BitVec('x', 32)
3542 >>> x.sort() == BitVecSort(32)
3548 """Return the number of bits of the bit-vector expression `self`.
3550 >>> x = BitVec('x', 32)
3553 >>> Concat(x, x).size()
3559 """Create the Z3 expression `self + other`.
3561 >>> x = BitVec('x', 32)
3562 >>> y = BitVec('y', 32)
3572 """Create the Z3 expression `other + self`.
3574 >>> x = BitVec('x', 32)
3582 """Create the Z3 expression `self * other`.
3584 >>> x = BitVec('x', 32)
3585 >>> y = BitVec('y', 32)
3595 """Create the Z3 expression `other * self`.
3597 >>> x = BitVec('x', 32)
3605 """Create the Z3 expression `self - other`.
3607 >>> x = BitVec('x', 32)
3608 >>> y = BitVec('y', 32)
3618 """Create the Z3 expression `other - self`.
3620 >>> x = BitVec('x', 32)
3628 """Create the Z3 expression bitwise-or `self | other`.
3630 >>> x = BitVec('x', 32)
3631 >>> y = BitVec('y', 32)
3641 """Create the Z3 expression bitwise-or `other | self`.
3643 >>> x = BitVec('x', 32)
3651 """Create the Z3 expression bitwise-and `self & other`.
3653 >>> x = BitVec('x', 32)
3654 >>> y = BitVec('y', 32)
3664 """Create the Z3 expression bitwise-or `other & self`.
3666 >>> x = BitVec('x', 32)
3674 """Create the Z3 expression bitwise-xor `self ^ other`.
3676 >>> x = BitVec('x', 32)
3677 >>> y = BitVec('y', 32)
3687 """Create the Z3 expression bitwise-xor `other ^ self`.
3689 >>> x = BitVec('x', 32)
3699 >>> x = BitVec('x', 32)
3706 """Return an expression representing `-self`.
3708 >>> x = BitVec('x', 32)
3717 """Create the Z3 expression bitwise-not `~self`.
3719 >>> x = BitVec('x', 32)
3728 """Create the Z3 expression (signed) division `self / other`.
3730 Use the function UDiv() for unsigned division.
3732 >>> x = BitVec('x', 32)
3733 >>> y = BitVec('y', 32)
3740 >>> UDiv(x, y).sexpr()
3747 """Create the Z3 expression (signed) division `self / other`."""
3751 """Create the Z3 expression (signed) division `other / self`.
3753 Use the function UDiv() for unsigned division.
3755 >>> x = BitVec('x', 32)
3758 >>> (10 / x).sexpr()
3759 '(bvsdiv #x0000000a x)'
3760 >>> UDiv(10, x).sexpr()
3761 '(bvudiv #x0000000a x)'
3767 """Create the Z3 expression (signed) division `other / self`."""
3771 """Create the Z3 expression (signed) mod `self % other`.
3773 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3775 >>> x = BitVec('x', 32)
3776 >>> y = BitVec('y', 32)
3783 >>> URem(x, y).sexpr()
3785 >>> SRem(x, y).sexpr()
3792 """Create the Z3 expression (signed) mod `other % self`.
3794 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3796 >>> x = BitVec('x', 32)
3799 >>> (10 % x).sexpr()
3800 '(bvsmod #x0000000a x)'
3801 >>> URem(10, x).sexpr()
3802 '(bvurem #x0000000a x)'
3803 >>> SRem(10, x).sexpr()
3804 '(bvsrem #x0000000a x)'
3810 """Create the Z3 expression (signed) `other <= self`.
3812 Use the function ULE() for unsigned less than or equal to.
3814 >>> x, y = BitVecs('x y', 32)
3817 >>> (x <= y).sexpr()
3819 >>> ULE(x, y).sexpr()
3826 """Create the Z3 expression (signed) `other < self`.
3828 Use the function ULT() for unsigned less than.
3830 >>> x, y = BitVecs('x y', 32)
3835 >>> ULT(x, y).sexpr()
3842 """Create the Z3 expression (signed) `other > self`.
3844 Use the function UGT() for unsigned greater than.
3846 >>> x, y = BitVecs('x y', 32)
3851 >>> UGT(x, y).sexpr()
3858 """Create the Z3 expression (signed) `other >= self`.
3860 Use the function UGE() for unsigned greater than or equal to.
3862 >>> x, y = BitVecs('x y', 32)
3865 >>> (x >= y).sexpr()
3867 >>> UGE(x, y).sexpr()
3874 """Create the Z3 expression (arithmetical) right shift `self >> other`
3876 Use the function LShR() for the right logical shift
3878 >>> x, y = BitVecs('x y', 32)
3881 >>> (x >> y).sexpr()
3883 >>> LShR(x, y).sexpr()
3887 >>> BitVecVal(4, 3).as_signed_long()
3889 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
3891 >>> simplify(BitVecVal(4, 3) >> 1)
3893 >>> simplify(LShR(BitVecVal(4, 3), 1))
3895 >>> simplify(BitVecVal(2, 3) >> 1)
3897 >>> simplify(LShR(BitVecVal(2, 3), 1))
3904 """Create the Z3 expression left shift `self << other`
3906 >>> x, y = BitVecs('x y', 32)
3909 >>> (x << y).sexpr()
3911 >>> simplify(BitVecVal(2, 3) << 1)
3918 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3920 Use the function LShR() for the right logical shift
3922 >>> x = BitVec('x', 32)
3925 >>> (10 >> x).sexpr()
3926 '(bvashr #x0000000a x)'
3932 """Create the Z3 expression left shift `other << self`.
3934 Use the function LShR() for the right logical shift
3936 >>> x = BitVec('x', 32)
3939 >>> (10 << x).sexpr()
3940 '(bvshl #x0000000a x)'
3947 """Bit-vector values."""
3950 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3952 >>> v = BitVecVal(0xbadc0de, 32)
3955 >>> print("0x%.8x" % v.as_long())
3961 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3962 The most significant bit is assumed to be the sign.
3964 >>> BitVecVal(4, 3).as_signed_long()
3966 >>> BitVecVal(7, 3).as_signed_long()
3968 >>> BitVecVal(3, 3).as_signed_long()
3970 >>> BitVecVal(2**32 - 1, 32).as_signed_long()
3972 >>> BitVecVal(2**64 - 1, 64).as_signed_long()
3977 if val >= 2**(sz - 1):
3979 if val < -2**(sz - 1):
3991 """Return `True` if `a` is a Z3 bit-vector expression.
3993 >>> b = BitVec('b', 32)
4001 return isinstance(a, BitVecRef)
4005 """Return `True` if `a` is a Z3 bit-vector numeral value.
4007 >>> b = BitVec('b', 32)
4010 >>> b = BitVecVal(10, 32)
4020 """Return the Z3 expression BV2Int(a).
4022 >>> b = BitVec('b', 3)
4023 >>> BV2Int(b).sort()
4028 >>> x > BV2Int(b, is_signed=False)
4030 >>> x > BV2Int(b, is_signed=True)
4031 x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
4032 >>> solve(x > BV2Int(b), b == 1, x < 3)
4036 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4043 """Return the z3 expression Int2BV(a, num_bits).
4044 It is a bit-vector of width num_bits and represents the
4045 modulo of a by 2^num_bits
4052 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4054 >>> Byte = BitVecSort(8)
4055 >>> Word = BitVecSort(16)
4058 >>> x = Const('x', Byte)
4059 >>> eq(x, BitVec('x', 8))
4067 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4069 >>> v = BitVecVal(10, 32)
4072 >>> print("0x%.8x" % v.as_long())
4084 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4085 If `ctx=None`, then the global context is used.
4087 >>> x = BitVec('x', 16)
4094 >>> word = BitVecSort(16)
4095 >>> x2 = BitVec('x', word)
4099 if isinstance(bv, BitVecSortRef):
4108 """Return a tuple of bit-vector constants of size bv.
4110 >>> x, y, z = BitVecs('x y z', 16)
4117 >>> Product(x, y, z)
4119 >>> simplify(Product(x, y, z))
4123 if isinstance(names, str):
4124 names = names.split(
" ")
4125 return [
BitVec(name, bv, ctx)
for name
in names]
4129 """Create a Z3 bit-vector concatenation expression.
4131 >>> v = BitVecVal(1, 4)
4132 >>> Concat(v, v+1, v)
4133 Concat(Concat(1, 1 + 1), 1)
4134 >>> simplify(Concat(v, v+1, v))
4136 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
4142 _z3_assert(sz >= 2,
"At least two arguments expected.")
4149 if is_seq(args[0])
or isinstance(args[0], str):
4152 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4155 v[i] = args[i].as_ast()
4160 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4163 v[i] = args[i].as_ast()
4167 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4169 for i
in range(sz - 1):
4175 """Create a Z3 bit-vector extraction expression.
4176 Extract is overloaded to also work on sequence extraction.
4177 The functions SubString and SubSeq are redirected to Extract.
4178 For this case, the arguments are reinterpreted as:
4179 high - is a sequence (string)
4181 a - is the length to be extracted
4183 >>> x = BitVec('x', 8)
4184 >>> Extract(6, 2, x)
4186 >>> Extract(6, 2, x).sort()
4188 >>> simplify(Extract(StringVal("abcd"),2,1))
4191 if isinstance(high, str):
4198 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4200 "First and second arguments must be non negative integers")
4201 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4207 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4211 """Create the Z3 expression (unsigned) `other <= self`.
4213 Use the operator <= for signed less than or equal to.
4215 >>> x, y = BitVecs('x y', 32)
4218 >>> (x <= y).sexpr()
4220 >>> ULE(x, y).sexpr()
4229 """Create the Z3 expression (unsigned) `other < self`.
4231 Use the operator < for signed less than.
4233 >>> x, y = BitVecs('x y', 32)
4238 >>> ULT(x, y).sexpr()
4247 """Create the Z3 expression (unsigned) `other >= self`.
4249 Use the operator >= for signed greater than or equal to.
4251 >>> x, y = BitVecs('x y', 32)
4254 >>> (x >= y).sexpr()
4256 >>> UGE(x, y).sexpr()
4265 """Create the Z3 expression (unsigned) `other > self`.
4267 Use the operator > for signed greater than.
4269 >>> x, y = BitVecs('x y', 32)
4274 >>> UGT(x, y).sexpr()
4283 """Create the Z3 expression (unsigned) division `self / other`.
4285 Use the operator / for signed division.
4287 >>> x = BitVec('x', 32)
4288 >>> y = BitVec('y', 32)
4291 >>> UDiv(x, y).sort()
4295 >>> UDiv(x, y).sexpr()
4304 """Create the Z3 expression (unsigned) remainder `self % other`.
4306 Use the operator % for signed modulus, and SRem() for signed remainder.
4308 >>> x = BitVec('x', 32)
4309 >>> y = BitVec('y', 32)
4312 >>> URem(x, y).sort()
4316 >>> URem(x, y).sexpr()
4325 """Create the Z3 expression signed remainder.
4327 Use the operator % for signed modulus, and URem() for unsigned remainder.
4329 >>> x = BitVec('x', 32)
4330 >>> y = BitVec('y', 32)
4333 >>> SRem(x, y).sort()
4337 >>> SRem(x, y).sexpr()
4346 """Create the Z3 expression logical right shift.
4348 Use the operator >> for the arithmetical right shift.
4350 >>> x, y = BitVecs('x y', 32)
4353 >>> (x >> y).sexpr()
4355 >>> LShR(x, y).sexpr()
4359 >>> BitVecVal(4, 3).as_signed_long()
4361 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
4363 >>> simplify(BitVecVal(4, 3) >> 1)
4365 >>> simplify(LShR(BitVecVal(4, 3), 1))
4367 >>> simplify(BitVecVal(2, 3) >> 1)
4369 >>> simplify(LShR(BitVecVal(2, 3), 1))
4378 """Return an expression representing `a` rotated to the left `b` times.
4380 >>> a, b = BitVecs('a b', 16)
4381 >>> RotateLeft(a, b)
4383 >>> simplify(RotateLeft(a, 0))
4385 >>> simplify(RotateLeft(a, 16))
4394 """Return an expression representing `a` rotated to the right `b` times.
4396 >>> a, b = BitVecs('a b', 16)
4397 >>> RotateRight(a, b)
4399 >>> simplify(RotateRight(a, 0))
4401 >>> simplify(RotateRight(a, 16))
4410 """Return a bit-vector expression with `n` extra sign-bits.
4412 >>> x = BitVec('x', 16)
4413 >>> n = SignExt(8, x)
4420 >>> v0 = BitVecVal(2, 2)
4425 >>> v = simplify(SignExt(6, v0))
4430 >>> print("%.x" % v.as_long())
4435 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4440 """Return a bit-vector expression with `n` extra zero-bits.
4442 >>> x = BitVec('x', 16)
4443 >>> n = ZeroExt(8, x)
4450 >>> v0 = BitVecVal(2, 2)
4455 >>> v = simplify(ZeroExt(6, v0))
4463 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4468 """Return an expression representing `n` copies of `a`.
4470 >>> x = BitVec('x', 8)
4471 >>> n = RepeatBitVec(4, x)
4476 >>> v0 = BitVecVal(10, 4)
4477 >>> print("%.x" % v0.as_long())
4479 >>> v = simplify(RepeatBitVec(4, v0))
4482 >>> print("%.x" % v.as_long())
4487 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4492 """Return the reduction-and expression of `a`."""
4494 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4499 """Return the reduction-or expression of `a`."""
4501 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4506 """A predicate the determines that bit-vector addition does not overflow"""
4513 """A predicate the determines that signed bit-vector addition does not underflow"""
4520 """A predicate the determines that bit-vector subtraction does not overflow"""
4527 """A predicate the determines that bit-vector subtraction does not underflow"""
4534 """A predicate the determines that bit-vector signed division does not overflow"""
4541 """A predicate the determines that bit-vector unary negation does not overflow"""
4543 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4548 """A predicate the determines that bit-vector multiplication does not overflow"""
4555 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4571 """Return the domain of the array sort `self`.
4573 >>> A = ArraySort(IntSort(), BoolSort())
4580 """Return the domain of the array sort `self`.
4585 """Return the range of the array sort `self`.
4587 >>> A = ArraySort(IntSort(), BoolSort())
4595 """Array expressions. """
4598 """Return the array sort of the array expression `self`.
4600 >>> a = Array('a', IntSort(), BoolSort())
4607 """Shorthand for `self.sort().domain()`.
4609 >>> a = Array('a', IntSort(), BoolSort())
4616 """Shorthand for self.sort().domain_n(i)`."""
4620 """Shorthand for `self.sort().range()`.
4622 >>> a = Array('a', IntSort(), BoolSort())
4629 """Return the Z3 expression `self[arg]`.
4631 >>> a = Array('a', IntSort(), BoolSort())
4645 if isinstance(arg, tuple):
4646 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4649 arg = ar.sort().domain().cast(arg)
4658 """Return `True` if `a` is a Z3 array expression.
4660 >>> a = Array('a', IntSort(), IntSort())
4663 >>> is_array(Store(a, 0, 1))
4668 return isinstance(a, ArrayRef)
4672 """Return `True` if `a` is a Z3 constant array.
4674 >>> a = K(IntSort(), 10)
4675 >>> is_const_array(a)
4677 >>> a = Array('a', IntSort(), IntSort())
4678 >>> is_const_array(a)
4685 """Return `True` if `a` is a Z3 constant array.
4687 >>> a = K(IntSort(), 10)
4690 >>> a = Array('a', IntSort(), IntSort())
4698 """Return `True` if `a` is a Z3 map array expression.
4700 >>> f = Function('f', IntSort(), IntSort())
4701 >>> b = Array('b', IntSort(), IntSort())
4714 """Return `True` if `a` is a Z3 default array expression.
4715 >>> d = Default(K(IntSort(), 10))
4719 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4723 """Return the function declaration associated with a Z3 map array expression.
4725 >>> f = Function('f', IntSort(), IntSort())
4726 >>> b = Array('b', IntSort(), IntSort())
4728 >>> eq(f, get_map_func(a))
4732 >>> get_map_func(a)(0)
4747 """Return the Z3 array sort with the given domain and range sorts.
4749 >>> A = ArraySort(IntSort(), BoolSort())
4756 >>> AA = ArraySort(IntSort(), A)
4758 Array(Int, Array(Int, Bool))
4762 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4763 arity = len(sig) - 1
4769 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4773 dom = (Sort * arity)()
4774 for i
in range(arity):
4780 """Return an array constant named `name` with the given domain and range sorts.
4782 >>> a = Array('a', IntSort(), IntSort())
4794 """Return a Z3 store array expression.
4796 >>> a = Array('a', IntSort(), IntSort())
4797 >>> i, v = Ints('i v')
4798 >>> s = Update(a, i, v)
4801 >>> prove(s[i] == v)
4804 >>> prove(Implies(i != j, s[j] == a[j]))
4812 raise Z3Exception(
"array update requires index and value arguments")
4816 i = a.sort().domain().cast(i)
4817 v = a.sort().range().cast(v)
4819 v = a.sort().range().cast(args[-1])
4820 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4826 """ Return a default value for array expression.
4827 >>> b = K(IntSort(), 1)
4828 >>> prove(Default(b) == 1)
4837 """Return a Z3 store array expression.
4839 >>> a = Array('a', IntSort(), IntSort())
4840 >>> i, v = Ints('i v')
4841 >>> s = Store(a, i, v)
4844 >>> prove(s[i] == v)
4847 >>> prove(Implies(i != j, s[j] == a[j]))
4854 """Return a Z3 select array expression.
4856 >>> a = Array('a', IntSort(), IntSort())
4860 >>> eq(Select(a, i), a[i])
4870 """Return a Z3 map array expression.
4872 >>> f = Function('f', IntSort(), IntSort(), IntSort())
4873 >>> a1 = Array('a1', IntSort(), IntSort())
4874 >>> a2 = Array('a2', IntSort(), IntSort())
4875 >>> b = Map(f, a1, a2)
4878 >>> prove(b[0] == f(a1[0], a2[0]))
4883 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4886 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4893 """Return a Z3 constant array expression.
4895 >>> a = K(IntSort(), 10)
4915 """Return extensionality index for one-dimensional arrays.
4916 >> a, b = Consts('a b', SetSort(IntSort()))
4933 """Return `True` if `a` is a Z3 array select application.
4935 >>> a = Array('a', IntSort(), IntSort())
4946 """Return `True` if `a` is a Z3 array store application.
4948 >>> a = Array('a', IntSort(), IntSort())
4951 >>> is_store(Store(a, 0, 1))
4964 """ Create a set sort over element sort s"""
4969 """Create the empty set
4970 >>> EmptySet(IntSort())
4978 """Create the full set
4979 >>> FullSet(IntSort())
4987 """ Take the union of sets
4988 >>> a = Const('a', SetSort(IntSort()))
4989 >>> b = Const('b', SetSort(IntSort()))
5000 """ Take the union of sets
5001 >>> a = Const('a', SetSort(IntSort()))
5002 >>> b = Const('b', SetSort(IntSort()))
5003 >>> SetIntersect(a, b)
5013 """ Add element e to set s
5014 >>> a = Const('a', SetSort(IntSort()))
5024 """ Remove element e to set s
5025 >>> a = Const('a', SetSort(IntSort()))
5035 """ The complement of set s
5036 >>> a = Const('a', SetSort(IntSort()))
5037 >>> SetComplement(a)
5045 """ The set difference of a and b
5046 >>> a = Const('a', SetSort(IntSort()))
5047 >>> b = Const('b', SetSort(IntSort()))
5048 >>> SetDifference(a, b)
5056 """ Check if e is a member of set s
5057 >>> a = Const('a', SetSort(IntSort()))
5067 """ Check if a is a subset of b
5068 >>> a = Const('a', SetSort(IntSort()))
5069 >>> b = Const('b', SetSort(IntSort()))
5084 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5085 if not isinstance(acc, tuple):
5089 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5093 """Helper class for declaring Z3 datatypes.
5095 >>> List = Datatype('List')
5096 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5097 >>> List.declare('nil')
5098 >>> List = List.create()
5099 >>> # List is now a Z3 declaration
5102 >>> List.cons(10, List.nil)
5104 >>> List.cons(10, List.nil).sort()
5106 >>> cons = List.cons
5110 >>> n = cons(1, cons(0, nil))
5112 cons(1, cons(0, nil))
5113 >>> simplify(cdr(n))
5115 >>> simplify(car(n))
5131 _z3_assert(isinstance(name, str),
"String expected")
5132 _z3_assert(isinstance(rec_name, str),
"String expected")
5135 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5140 """Declare constructor named `name` with the given accessors `args`.
5141 Each accessor is a pair `(name, sort)`, where `name` is a string and `sort` a Z3 sort
5142 or a reference to the datatypes being declared.
5144 In the following example `List.declare('cons', ('car', IntSort()), ('cdr', List))`
5145 declares the constructor named `cons` that builds a new List using an integer and a List.
5146 It also declares the accessors `car` and `cdr`. The accessor `car` extracts the integer
5147 of a `cons` cell, and `cdr` the list of a `cons` cell. After all constructors were declared,
5148 we use the method create() to create the actual datatype in Z3.
5150 >>> List = Datatype('List')
5151 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5152 >>> List.declare('nil')
5153 >>> List = List.create()
5156 _z3_assert(isinstance(name, str),
"String expected")
5157 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5164 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5166 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5168 >>> List = Datatype('List')
5169 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5170 >>> List.declare('nil')
5171 >>> List = List.create()
5174 >>> List.cons(10, List.nil)
5181 """Auxiliary object used to create Z3 datatypes."""
5188 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5193 """Auxiliary object used to create Z3 datatypes."""
5200 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5205 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5207 In the following example we define a Tree-List using two mutually recursive datatypes.
5209 >>> TreeList = Datatype('TreeList')
5210 >>> Tree = Datatype('Tree')
5211 >>> # Tree has two constructors: leaf and node
5212 >>> Tree.declare('leaf', ('val', IntSort()))
5213 >>> # a node contains a list of trees
5214 >>> Tree.declare('node', ('children', TreeList))
5215 >>> TreeList.declare('nil')
5216 >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
5217 >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
5218 >>> Tree.val(Tree.leaf(10))
5220 >>> simplify(Tree.val(Tree.leaf(10)))
5222 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5224 node(cons(leaf(10), cons(leaf(20), nil)))
5225 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5226 >>> simplify(n2 == n1)
5228 >>> simplify(TreeList.car(Tree.children(n2)) == n1)
5233 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5234 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5235 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5236 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5239 names = (Symbol * num)()
5240 out = (Sort * num)()
5241 clists = (ConstructorList * num)()
5243 for i
in range(num):
5246 num_cs = len(d.constructors)
5247 cs = (Constructor * num_cs)()
5248 for j
in range(num_cs):
5249 c = d.constructors[j]
5254 fnames = (Symbol * num_fs)()
5255 sorts = (Sort * num_fs)()
5256 refs = (ctypes.c_uint * num_fs)()
5257 for k
in range(num_fs):
5261 if isinstance(ftype, Datatype):
5264 ds.count(ftype) == 1,
5265 "One and only one occurrence of each datatype is expected",
5268 refs[k] = ds.index(ftype)
5272 sorts[k] = ftype.ast
5281 for i
in range(num):
5283 num_cs = dref.num_constructors()
5284 for j
in range(num_cs):
5285 cref = dref.constructor(j)
5286 cref_name = cref.name()
5287 cref_arity = cref.arity()
5288 if cref.arity() == 0:
5290 setattr(dref, cref_name, cref)
5291 rref = dref.recognizer(j)
5292 setattr(dref,
"is_" + cref_name, rref)
5293 for k
in range(cref_arity):
5294 aref = dref.accessor(j, k)
5295 setattr(dref, aref.name(), aref)
5297 return tuple(result)
5301 """Datatype sorts."""
5304 """Return the number of constructors in the given Z3 datatype.
5306 >>> List = Datatype('List')
5307 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5308 >>> List.declare('nil')
5309 >>> List = List.create()
5310 >>> # List is now a Z3 declaration
5311 >>> List.num_constructors()
5317 """Return a constructor of the datatype `self`.
5319 >>> List = Datatype('List')
5320 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5321 >>> List.declare('nil')
5322 >>> List = List.create()
5323 >>> # List is now a Z3 declaration
5324 >>> List.num_constructors()
5326 >>> List.constructor(0)
5328 >>> List.constructor(1)
5336 """In Z3, each constructor has an associated recognizer predicate.
5338 If the constructor is named `name`, then the recognizer `is_name`.
5340 >>> List = Datatype('List')
5341 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5342 >>> List.declare('nil')
5343 >>> List = List.create()
5344 >>> # List is now a Z3 declaration
5345 >>> List.num_constructors()
5347 >>> List.recognizer(0)
5349 >>> List.recognizer(1)
5351 >>> simplify(List.is_nil(List.cons(10, List.nil)))
5353 >>> simplify(List.is_cons(List.cons(10, List.nil)))
5355 >>> l = Const('l', List)
5356 >>> simplify(List.is_cons(l))
5364 """In Z3, each constructor has 0 or more accessor.
5365 The number of accessors is equal to the arity of the constructor.
5367 >>> List = Datatype('List')
5368 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5369 >>> List.declare('nil')
5370 >>> List = List.create()
5371 >>> List.num_constructors()
5373 >>> List.constructor(0)
5375 >>> num_accs = List.constructor(0).arity()
5378 >>> List.accessor(0, 0)
5380 >>> List.accessor(0, 1)
5382 >>> List.constructor(1)
5384 >>> num_accs = List.constructor(1).arity()
5398 """Datatype expressions."""
5401 """Return the datatype sort of the datatype expression `self`."""
5405 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5410 """Create a named tuple sort base on a set of underlying sorts
5412 >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
5415 projects = [(
"project%d" % i, sorts[i])
for i
in range(len(sorts))]
5416 tuple.declare(name, *projects)
5417 tuple = tuple.create()
5418 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5422 """Create a named tagged union sort base on a set of underlying sorts
5424 >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
5427 for i
in range(len(sorts)):
5428 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5430 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5434 """Return a new enumeration sort named `name` containing the given values.
5436 The result is a pair (sort, list of constants).
5438 >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
5441 _z3_assert(isinstance(name, str),
"Name must be a string")
5442 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Enumeration sort values must be strings")
5443 _z3_assert(len(values) > 0,
"At least one value expected")
5446 _val_names = (Symbol * num)()
5447 for i
in range(num):
5448 _val_names[i] =
to_symbol(values[i], ctx)
5449 _values = (FuncDecl * num)()
5450 _testers = (FuncDecl * num)()
5454 for i
in range(num):
5456 V = [a()
for a
in V]
5467 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5469 Consider using the function `args2params` to create instances of this object.
5484 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5488 """Set parameter name with value val."""
5490 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5492 if isinstance(val, bool):
5496 elif isinstance(val, float):
5498 elif isinstance(val, str):
5508 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5513 """Convert python arguments into a Z3_params object.
5514 A ':' is added to the keywords, and '_' is replaced with '-'
5516 >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
5517 (params model true relevancy 2 elim_and true)
5520 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5536 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5540 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5546 return ParamsDescrsRef(self.
descr, self.
ctx)
5549 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5553 """Return the size of in the parameter description `self`.
5558 """Return the size of in the parameter description `self`.
5563 """Return the i-th parameter name in the parameter description `self`.
5568 """Return the kind of the parameter named `n`.
5573 """Return the documentation string of the parameter named `n`.
5594 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5596 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5597 A goal has a solution if one of its subgoals has a solution.
5598 A goal is unsatisfiable if all subgoals are unsatisfiable.
5601 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5604 "If goal is different from None, then ctx must be also different from None")
5607 if self.
goal is None:
5612 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5616 """Return the depth of the goal `self`.
5617 The depth corresponds to the number of tactics applied to `self`.
5619 >>> x, y = Ints('x y')
5621 >>> g.add(x == 0, y >= x + 1)
5624 >>> r = Then('simplify', 'solve-eqs')(g)
5625 >>> # r has 1 subgoal
5634 """Return `True` if `self` contains the `False` constraints.
5636 >>> x, y = Ints('x y')
5638 >>> g.inconsistent()
5640 >>> g.add(x == 0, x == 1)
5643 >>> g.inconsistent()
5645 >>> g2 = Tactic('propagate-values')(g)[0]
5646 >>> g2.inconsistent()
5652 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5655 >>> g.prec() == Z3_GOAL_PRECISE
5657 >>> x, y = Ints('x y')
5658 >>> g.add(x == y + 1)
5659 >>> g.prec() == Z3_GOAL_PRECISE
5661 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5664 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5665 >>> g2.prec() == Z3_GOAL_PRECISE
5667 >>> g2.prec() == Z3_GOAL_UNDER
5673 """Alias for `prec()`.
5676 >>> g.precision() == Z3_GOAL_PRECISE
5682 """Return the number of constraints in the goal `self`.
5687 >>> x, y = Ints('x y')
5688 >>> g.add(x == 0, y > x)
5695 """Return the number of constraints in the goal `self`.
5700 >>> x, y = Ints('x y')
5701 >>> g.add(x == 0, y > x)
5708 """Return a constraint in the goal `self`.
5711 >>> x, y = Ints('x y')
5712 >>> g.add(x == 0, y > x)
5721 """Return a constraint in the goal `self`.
5724 >>> x, y = Ints('x y')
5725 >>> g.add(x == 0, y > x)
5731 if arg >= len(self):
5733 return self.
get(arg)
5736 """Assert constraints into the goal.
5740 >>> g.assert_exprs(x > 0, x < 2)
5755 >>> g.append(x > 0, x < 2)
5766 >>> g.insert(x > 0, x < 2)
5777 >>> g.add(x > 0, x < 2)
5784 """Retrieve model from a satisfiable goal
5785 >>> a, b = Ints('a b')
5787 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5788 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5791 [Or(b == 0, b == 1), Not(0 <= b)]
5793 [Or(b == 0, b == 1), Not(1 <= b)]
5794 >>> # Remark: the subgoal r[0] is unsatisfiable
5795 >>> # Creating a solver for solving the second subgoal
5802 >>> # Model s.model() does not assign a value to `a`
5803 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5804 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5805 >>> r[1].convert_model(s.model())
5809 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5813 return obj_to_string(self)
5816 """Return a textual representation of the s-expression representing the goal."""
5820 """Return a textual representation of the goal in DIMACS format."""
5824 """Copy goal `self` to context `target`.
5832 >>> g2 = g.translate(c2)
5835 >>> g.ctx == main_ctx()
5839 >>> g2.ctx == main_ctx()
5843 _z3_assert(isinstance(target, Context),
"target must be a context")
5853 """Return a new simplified goal.
5855 This method is essentially invoking the simplify tactic.
5859 >>> g.add(x + 1 >= 2)
5862 >>> g2 = g.simplify()
5865 >>> # g was not modified
5870 return t.apply(self, *arguments, **keywords)[0]
5873 """Return goal `self` as a single Z3 expression.
5892 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5902 """A collection (vector) of ASTs."""
5911 assert ctx
is not None
5916 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5920 """Return the size of the vector `self`.
5925 >>> A.push(Int('x'))
5926 >>> A.push(Int('x'))
5933 """Return the AST at position `i`.
5936 >>> A.push(Int('x') + 1)
5937 >>> A.push(Int('y'))
5944 if isinstance(i, int):
5952 elif isinstance(i, slice):
5954 for ii
in range(*i.indices(self.
__len__())):
5962 """Update AST at position `i`.
5965 >>> A.push(Int('x') + 1)
5966 >>> A.push(Int('y'))
5978 """Add `v` in the end of the vector.
5983 >>> A.push(Int('x'))
5990 """Resize the vector to `sz` elements.
5996 >>> for i in range(10): A[i] = Int('x')
6003 """Return `True` if the vector contains `item`.
6026 """Copy vector `self` to context `other_ctx`.
6032 >>> B = A.translate(c2)
6048 return obj_to_string(self)
6051 """Return a textual representation of the s-expression representing the vector."""
6062 """A mapping from ASTs to ASTs."""
6071 assert ctx
is not None
6079 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6083 """Return the size of the map.
6089 >>> M[x] = IntVal(1)
6096 """Return `True` if the map contains key `key`.
6109 """Retrieve the value associated with key `key`.
6120 """Add/Update key `k` with value `v`.
6129 >>> M[x] = IntVal(1)
6139 """Remove the entry associated with key `k`.
6153 """Remove all entries from the map.
6158 >>> M[x+x] = IntVal(1)
6168 """Return an AstVector containing all keys in the map.
6173 >>> M[x+x] = IntVal(1)
6187 """Store the value of the interpretation of a function in a particular point."""
6198 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6202 """Return the number of arguments in the given entry.
6204 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6206 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6211 >>> f_i.num_entries()
6213 >>> e = f_i.entry(0)
6220 """Return the value of argument `idx`.
6222 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6224 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6229 >>> f_i.num_entries()
6231 >>> e = f_i.entry(0)
6242 ... except IndexError:
6243 ... print("index error")
6251 """Return the value of the function at point `self`.
6253 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6255 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6260 >>> f_i.num_entries()
6262 >>> e = f_i.entry(0)
6273 """Return entry `self` as a Python list.
6274 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6276 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6281 >>> f_i.num_entries()
6283 >>> e = f_i.entry(0)
6288 args.append(self.
value())
6296 """Stores the interpretation of a function in a Z3 model."""
6301 if self.
f is not None:
6305 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6310 Return the `else` value for a function interpretation.
6311 Return None if Z3 did not specify the `else` value for
6314 >>> f = Function('f', IntSort(), IntSort())
6316 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6322 >>> m[f].else_value()
6332 """Return the number of entries/points in the function interpretation `self`.
6334 >>> f = Function('f', IntSort(), IntSort())
6336 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6342 >>> m[f].num_entries()
6348 """Return the number of arguments for each entry in the function interpretation `self`.
6350 >>> f = Function('f', IntSort(), IntSort())
6352 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6362 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6364 >>> f = Function('f', IntSort(), IntSort())
6366 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6372 >>> m[f].num_entries()
6382 """Copy model 'self' to context 'other_ctx'.
6393 """Return the function interpretation as a Python list.
6394 >>> f = Function('f', IntSort(), IntSort())
6396 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6410 return obj_to_string(self)
6414 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6417 assert ctx
is not None
6423 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6427 return obj_to_string(self)
6430 """Return a textual representation of the s-expression representing the model."""
6433 def eval(self, t, model_completion=False):
6434 """Evaluate the expression `t` in the model `self`.
6435 If `model_completion` is enabled, then a default interpretation is automatically added
6436 for symbols that do not have an interpretation in the model `self`.
6440 >>> s.add(x > 0, x < 2)
6453 >>> m.eval(y, model_completion=True)
6455 >>> # Now, m contains an interpretation for y
6462 raise Z3Exception(
"failed to evaluate expression in the model")
6465 """Alias for `eval`.
6469 >>> s.add(x > 0, x < 2)
6473 >>> m.evaluate(x + 1)
6475 >>> m.evaluate(x == 1)
6478 >>> m.evaluate(y + x)
6482 >>> m.evaluate(y, model_completion=True)
6484 >>> # Now, m contains an interpretation for y
6485 >>> m.evaluate(y + x)
6488 return self.
eval(t, model_completion)
6491 """Return the number of constant and function declarations in the model `self`.
6493 >>> f = Function('f', IntSort(), IntSort())
6496 >>> s.add(x > 0, f(x) != x)
6505 return num_consts + num_funcs
6508 """Return the interpretation for a given declaration or constant.
6510 >>> f = Function('f', IntSort(), IntSort())
6513 >>> s.add(x > 0, x < 2, f(x) == 0)
6523 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6527 if decl.arity() == 0:
6529 if _r.value
is None:
6545 sz = fi.num_entries()
6549 e =
Store(e, fe.arg_value(0), fe.value())
6560 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6562 >>> A = DeclareSort('A')
6563 >>> a, b = Consts('a b', A)
6575 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6577 >>> A = DeclareSort('A')
6578 >>> B = DeclareSort('B')
6579 >>> a1, a2 = Consts('a1 a2', A)
6580 >>> b1, b2 = Consts('b1 b2', B)
6582 >>> s.add(a1 != a2, b1 != b2)
6598 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6600 >>> A = DeclareSort('A')
6601 >>> B = DeclareSort('B')
6602 >>> a1, a2 = Consts('a1 a2', A)
6603 >>> b1, b2 = Consts('b1 b2', B)
6605 >>> s.add(a1 != a2, b1 != b2)
6615 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6617 >>> A = DeclareSort('A')
6618 >>> a, b = Consts('a b', A)
6624 >>> m.get_universe(A)
6628 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6635 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6636 If `idx` is a declaration, then the actual interpretation is returned.
6638 The elements can be retrieved using position or the actual declaration.
6640 >>> f = Function('f', IntSort(), IntSort())
6643 >>> s.add(x > 0, x < 2, f(x) == 0)
6657 >>> for d in m: print("%s -> %s" % (d, m[d]))
6662 if idx >= len(self):
6665 if (idx < num_consts):
6669 if isinstance(idx, FuncDeclRef):
6673 if isinstance(idx, SortRef):
6676 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6680 """Return a list with all symbols that have an interpretation in the model `self`.
6681 >>> f = Function('f', IntSort(), IntSort())
6684 >>> s.add(x > 0, x < 2, f(x) == 0)
6699 """Update the interpretation of a constant"""
6702 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6706 for i
in range(value.num_entries()):
6711 v.push(e.arg_value(j))
6716 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6721 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6724 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6741 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6742 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6746 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6759 """Statistics for `Solver.check()`."""
6770 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6777 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6780 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6783 out.write(u(
"<tr>"))
6785 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6786 out.write(u(
"</table>"))
6787 return out.getvalue()
6792 """Return the number of statistical counters.
6795 >>> s = Then('simplify', 'nlsat').solver()
6799 >>> st = s.statistics()
6806 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6809 >>> s = Then('simplify', 'nlsat').solver()
6813 >>> st = s.statistics()
6817 ('nlsat propagations', 2)
6819 ('nlsat restarts', 1)
6821 if idx >= len(self):
6830 """Return the list of statistical counters.
6833 >>> s = Then('simplify', 'nlsat').solver()
6837 >>> st = s.statistics()
6842 """Return the value of a particular statistical counter.
6845 >>> s = Then('simplify', 'nlsat').solver()
6849 >>> st = s.statistics()
6850 >>> st.get_key_value('nlsat propagations')
6853 for idx
in range(len(self)):
6859 raise Z3Exception(
"unknown key")
6862 """Access the value of statistical using attributes.
6864 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6865 we should use '_' (e.g., 'nlsat_propagations').
6868 >>> s = Then('simplify', 'nlsat').solver()
6872 >>> st = s.statistics()
6873 >>> st.nlsat_propagations
6878 key = name.replace(
"_",
" ")
6882 raise AttributeError
6892 """Represents the result of a satisfiability check: sat, unsat, unknown.
6898 >>> isinstance(r, CheckSatResult)
6909 return isinstance(other, CheckSatResult)
and self.
r == other.r
6912 return not self.
__eq__(other)
6916 if self.
r == Z3_L_TRUE:
6918 elif self.
r == Z3_L_FALSE:
6919 return "<b>unsat</b>"
6921 return "<b>unknown</b>"
6923 if self.
r == Z3_L_TRUE:
6925 elif self.
r == Z3_L_FALSE:
6931 in_html = in_html_mode()
6934 set_html_mode(in_html)
6945 Solver API provides methods for implementing the main SMT 2.0 commands:
6946 push, pop, check, get-model, etc.
6949 def __init__(self, solver=None, ctx=None, logFile=None):
6950 assert solver
is None or ctx
is not None
6959 if logFile
is not None:
6960 self.
set(
"smtlib2_log", logFile)
6963 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
6974 """Set a configuration option.
6975 The method `help()` return a string containing all available options.
6978 >>> # The option MBQI can be set using three different approaches.
6979 >>> s.set(mbqi=True)
6980 >>> s.set('MBQI', True)
6981 >>> s.set(':mbqi', True)
6987 """Create a backtracking point.
7009 """Backtrack \\c num backtracking points.
7031 """Return the current number of backtracking points.
7049 """Remove all asserted constraints and backtracking points created using `push()`.
7063 """Assert constraints into the solver.
7067 >>> s.assert_exprs(x > 0, x < 2)
7074 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7082 """Assert constraints into the solver.
7086 >>> s.add(x > 0, x < 2)
7097 """Assert constraints into the solver.
7101 >>> s.append(x > 0, x < 2)
7108 """Assert constraints into the solver.
7112 >>> s.insert(x > 0, x < 2)
7119 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7121 If `p` is a string, it will be automatically converted into a Boolean constant.
7126 >>> s.set(unsat_core=True)
7127 >>> s.assert_and_track(x > 0, 'p1')
7128 >>> s.assert_and_track(x != 1, 'p2')
7129 >>> s.assert_and_track(x < 0, p3)
7130 >>> print(s.check())
7132 >>> c = s.unsat_core()
7142 if isinstance(p, str):
7144 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7149 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7155 >>> s.add(x > 0, x < 2)
7158 >>> s.model().eval(x)
7164 >>> s.add(2**x == 4)
7170 num = len(assumptions)
7171 _assumptions = (Ast * num)()
7172 for i
in range(num):
7173 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7178 """Return a model for the last `check()`.
7180 This function raises an exception if
7181 a model is not available (e.g., last `check()` returned unsat).
7185 >>> s.add(a + 2 == 0)
7194 raise Z3Exception(
"model is not available")
7197 """Import model converter from other into the current solver"""
7198 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7200 def interrupt(self):
7201 """Interrupt the execution of the solver object.
7202 Remarks: This ensures that the interrupt applies only
7203 to the given solver object and it applies only if it is running.
7205 Z3_solver_interrupt(self.ctx.ref(), self.solver)
7207 def unsat_core(self):
7208 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7210 These are the assumptions Z3 used in the unsatisfiability proof.
7211 Assumptions are available in Z3. They are used to extract unsatisfiable cores.
7212 They may be also used to "retract" assumptions. Note that, assumptions are not really
7213 "soft constraints", but they can be used to implement them.
7215 >>> p1, p2, p3 = Bools('p1 p2 p3')
7216 >>> x, y = Ints('x y')
7218 >>> s.add(Implies(p1, x > 0))
7219 >>> s.add(Implies(p2, y > x))
7220 >>> s.add(Implies(p2, y < 1))
7221 >>> s.add(Implies(p3, y > -3))
7222 >>> s.check(p1, p2, p3)
7224 >>> core = s.unsat_core()
7233 >>> # "Retracting" p2
7237 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7239 def consequences(self, assumptions, variables):
7240 """Determine fixed values for the variables based on the solver state and assumptions.
7242 >>> a, b, c, d = Bools('a b c d')
7243 >>> s.add(Implies(a,b), Implies(b, c))
7244 >>> s.consequences([a],[b,c,d])
7245 (sat, [Implies(a, b), Implies(a, c)])
7246 >>> s.consequences([Not(c),d],[a,b,c,d])
7247 (sat, [Implies(d, d), Implies(Not(c), Not(c)), Implies(Not(c), Not(b)), Implies(Not(c), Not(a))])
7249 if isinstance(assumptions, list):
7250 _asms = AstVector(None, self.ctx)
7251 for a in assumptions:
7254 if isinstance(variables, list):
7255 _vars = AstVector(None, self.ctx)
7259 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7260 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7261 consequences = AstVector(None, self.ctx)
7262 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7263 variables.vector, consequences.vector)
7264 sz = len(consequences)
7265 consequences = [consequences[i] for i in range(sz)]
7266 return CheckSatResult(r), consequences
7268 def from_file(self, filename):
7269 """Parse assertions from a file"""
7270 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7272 def from_string(self, s):
7273 """Parse assertions from a string"""
7274 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7276 def cube(self, vars=None):
7278 The method takes an optional set of variables that restrict which
7279 variables may be used as a starting point for cubing.
7280 If vars is not None, then the first case split is based on a variable in
7283 self.cube_vs = AstVector(None, self.ctx)
7284 if vars is not None:
7286 self.cube_vs.push(v)
7288 lvl = self.backtrack_level
7289 self.backtrack_level = 4000000000
7290 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7291 if (len(r) == 1 and is_false(r[0])):
7297 def cube_vars(self):
7298 """Access the set of variables that were touched by the most recently generated cube.
7299 This set of variables can be used as a starting point for additional cubes.
7300 The idea is that variables that appear in clauses that are reduced by the most recent
7301 cube are likely more useful to cube on."""
7305 t = _py2expr(t, self.ctx)
7306 """Retrieve congruence closure root of the term t relative to the current search state
7307 The function primarily works for SimpleSolver. Terms and variables that are
7308 eliminated during pre-processing are not visible to the congruence closure.
7310 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7313 t = _py2expr(t, self.ctx)
7314 """Retrieve congruence closure sibling of the term t relative to the current search state
7315 The function primarily works for SimpleSolver. Terms and variables that are
7316 eliminated during pre-processing are not visible to the congruence closure.
7318 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7321 """Return a proof for the last `check()`. Proof construction must be enabled."""
7322 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7324 def assertions(self):
7325 """Return an AST vector containing all added constraints.
7336 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7339 """Return an AST vector containing all currently inferred units.
7341 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7343 def non_units(self):
7344 """Return an AST vector containing all atomic formulas in solver state that are not units.
7346 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7348 def trail_levels(self):
7349 """Return trail and decision levels of the solver state after a check() call.
7351 trail = self.trail()
7352 levels = (ctypes.c_uint * len(trail))()
7353 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7354 return trail, levels
7356 def set_initial_value(self, var, value):
7357 """initialize the solver's state by setting the initial value of var to value
7360 value = s.cast(value)
7361 Z3_solver_set_initial_value(self.ctx.ref(), self.solver, var.ast, value.ast)
7364 """Return trail of the solver state after a check() call.
7366 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7368 def statistics(self):
7369 """Return statistics for the last `check()`.
7371 >>> s = SimpleSolver()
7376 >>> st = s.statistics()
7377 >>> st.get_key_value('final checks')
7384 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7386 def reason_unknown(self):
7387 """Return a string describing why the last `check()` returned `unknown`.
7390 >>> s = SimpleSolver()
7391 >>> s.add(2**x == 4)
7394 >>> s.reason_unknown()
7395 '(incomplete (theory arithmetic))'
7397 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7400 """Display a string describing all available options."""
7401 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7403 def param_descrs(self):
7404 """Return the parameter description set."""
7405 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7408 """Return a formatted string with all added constraints."""
7409 return obj_to_string(self)
7411 def translate(self, target):
7412 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7416 >>> s1 = Solver(ctx=c1)
7417 >>> s2 = s1.translate(c2)
7420 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7421 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7422 return Solver(solver, target)
7425 return self.translate(self.ctx)
7427 def __deepcopy__(self, memo={}):
7428 return self.translate(self.ctx)
7431 """Return a formatted string (in Lisp-like format) with all added constraints.
7432 We say the string is in s-expression format.
7440 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7442 def dimacs(self, include_names=True):
7443 """Return a textual representation of the solver in DIMACS format."""
7444 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7447 """return SMTLIB2 formatted benchmark for solver's assertions"""
7448 es = self.assertions()
7454 for i in range(sz1):
7455 v[i] = es[i].as_ast()
7457 e = es[sz1].as_ast()
7459 e = BoolVal(True, self.ctx).as_ast()
7460 return Z3_benchmark_to_smtlib_string(
7461 self.ctx.ref(), "benchmark generated from python API", "", "unknown", "", sz1, v, e,
7465def SolverFor(logic, ctx=None, logFile=None):
7466 """Create a solver customized for the given logic.
7468 The parameter `logic` is a string. It should be contains
7469 the name of a SMT-LIB logic.
7470 See http://www.smtlib.org/ for the name of all available logics.
7472 >>> s = SolverFor("QF_LIA")
7482 logic = to_symbol(logic)
7483 return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
7486def SimpleSolver(ctx=None, logFile=None):
7487 """Return a simple general purpose solver with limited amount of preprocessing.
7489 >>> s = SimpleSolver()
7496 return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
7498#########################################
7502#########################################
7505class Fixedpoint(Z3PPObject):
7506 """Fixedpoint API provides methods for solving with recursive predicates"""
7508 def __init__(self, fixedpoint=None, ctx=None):
7509 assert fixedpoint is None or ctx is not None
7510 self.ctx = _get_ctx(ctx)
7511 self.fixedpoint = None
7512 if fixedpoint is None:
7513 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7515 self.fixedpoint = fixedpoint
7516 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7519 def __deepcopy__(self, memo={}):
7520 return FixedPoint(self.fixedpoint, self.ctx)
7523 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7524 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7526 def set(self, *args, **keys):
7527 """Set a configuration option. The method `help()` return a string containing all available options.
7529 p = args2params(args, keys, self.ctx)
7530 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7533 """Display a string describing all available options."""
7534 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7536 def param_descrs(self):
7537 """Return the parameter description set."""
7538 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7540 def assert_exprs(self, *args):
7541 """Assert constraints as background axioms for the fixedpoint solver."""
7542 args = _get_args(args)
7543 s = BoolSort(self.ctx)
7545 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7547 f = self.abstract(f)
7548 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7551 arg = self.abstract(arg)
7552 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7554 def add(self, *args):
7555 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7556 self.assert_exprs(*args)
7558 def __iadd__(self, fml):
7562 def append(self, *args):
7563 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7564 self.assert_exprs(*args)
7566 def insert(self, *args):
7567 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7568 self.assert_exprs(*args)
7570 def add_rule(self, head, body=None, name=None):
7571 """Assert rules defining recursive predicates to the fixedpoint solver.
7574 >>> s = Fixedpoint()
7575 >>> s.register_relation(a.decl())
7576 >>> s.register_relation(b.decl())
7584 name = to_symbol(name, self.ctx)
7586 head = self.abstract(head)
7587 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7589 body = _get_args(body)
7590 f = self.abstract(Implies(And(body, self.ctx), head))
7591 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7593 def rule(self, head, body=None, name=None):
7594 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7595 self.add_rule(head, body, name)
7597 def fact(self, head, name=None):
7598 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7599 self.add_rule(head, None, name)
7601 def query(self, *query):
7602 """Query the fixedpoint engine whether formula is derivable.
7603 You can also pass an tuple or list of recursive predicates.
7605 query = _get_args(query)
7607 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7608 _decls = (FuncDecl * sz)()
7613 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7618 query = And(query, self.ctx)
7619 query = self.abstract(query, False)
7620 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7621 return CheckSatResult(r)
7623 def query_from_lvl(self, lvl, *query):
7624 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7626 query = _get_args(query)
7628 if sz >= 1 and isinstance(query[0], FuncDecl):
7629 _z3_assert(False, "unsupported")
7635 query = self.abstract(query, False)
7636 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7637 return CheckSatResult(r)
7639 def update_rule(self, head, body, name):
7643 name = to_symbol(name, self.ctx)
7644 body = _get_args(body)
7645 f = self.abstract(Implies(And(body, self.ctx), head))
7646 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7648 def get_answer(self):
7649 """Retrieve answer from last query call."""
7650 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7651 return _to_expr_ref(r, self.ctx)
7653 def get_ground_sat_answer(self):
7654 """Retrieve a ground cex from last query call."""
7655 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7656 return _to_expr_ref(r, self.ctx)
7658 def get_rules_along_trace(self):
7659 """retrieve rules along the counterexample trace"""
7660 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7662 def get_rule_names_along_trace(self):
7663 """retrieve rule names along the counterexample trace"""
7664 # this is a hack as I don't know how to return a list of symbols from C++;
7665 # obtain names as a single string separated by semicolons
7666 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7667 # split into individual names
7668 return names.split(";")
7670 def get_num_levels(self, predicate):
7671 """Retrieve number of levels used for predicate in PDR engine"""
7672 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7674 def get_cover_delta(self, level, predicate):
7675 """Retrieve properties known about predicate for the level'th unfolding.
7676 -1 is treated as the limit (infinity)
7678 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7679 return _to_expr_ref(r, self.ctx)
7681 def add_cover(self, level, predicate, property):
7682 """Add property to predicate for the level'th unfolding.
7683 -1 is treated as infinity (infinity)
7685 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7687 def register_relation(self, *relations):
7688 """Register relation as recursive"""
7689 relations = _get_args(relations)
7691 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7693 def set_predicate_representation(self, f, *representations):
7694 """Control how relation is represented"""
7695 representations = _get_args(representations)
7696 representations = [to_symbol(s) for s in representations]
7697 sz = len(representations)
7698 args = (Symbol * sz)()
7700 args[i] = representations[i]
7701 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7703 def parse_string(self, s):
7704 """Parse rules and queries from a string"""
7705 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7707 def parse_file(self, f):
7708 """Parse rules and queries from a file"""
7709 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7711 def get_rules(self):
7712 """retrieve rules that have been added to fixedpoint context"""
7713 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7715 def get_assertions(self):
7716 """retrieve assertions that have been added to fixedpoint context"""
7717 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7720 """Return a formatted string with all added rules and constraints."""
7724 """Return a formatted string (in Lisp-like format) with all added constraints.
7725 We say the string is in s-expression format.
7727 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7729 def to_string(self, queries):
7730 """Return a formatted string (in Lisp-like format) with all added constraints.
7731 We say the string is in s-expression format.
7732 Include also queries.
7734 args, len = _to_ast_array(queries)
7735 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7737 def statistics(self):
7738 """Return statistics for the last `query()`.
7740 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7742 def reason_unknown(self):
7743 """Return a string describing why the last `query()` returned `unknown`.
7745 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7747 def declare_var(self, *vars):
7748 """Add variable or several variables.
7749 The added variable or variables will be bound in the rules
7752 vars = _get_args(vars)
7756 def abstract(self, fml, is_forall=True):
7760 return ForAll(self.vars, fml)
7762 return Exists(self.vars, fml)
7765#########################################
7769#########################################
7771class FiniteDomainSortRef(SortRef):
7772 """Finite domain sort."""
7775 """Return the size of the finite domain sort"""
7776 r = (ctypes.c_ulonglong * 1)()
7777 if Z3_get_finite_domain_sort_size(self.ctx_ref(), self.ast, r):
7780 raise Z3Exception("Failed to retrieve finite domain sort size")
7783def FiniteDomainSort(name, sz, ctx=None):
7784 """Create a named finite domain sort of a given size sz"""
7785 if not isinstance(name, Symbol):
7786 name = to_symbol(name)
7788 return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
7791def is_finite_domain_sort(s):
7792 """Return True if `s` is a Z3 finite-domain sort.
7794 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7796 >>> is_finite_domain_sort(IntSort())
7799 return isinstance(s, FiniteDomainSortRef)
7802class FiniteDomainRef(ExprRef):
7803 """Finite-domain expressions."""
7806 """Return the sort of the finite-domain expression `self`."""
7807 return FiniteDomainSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
7809 def as_string(self):
7810 """Return a Z3 floating point expression as a Python string."""
7811 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
7814def is_finite_domain(a):
7815 """Return `True` if `a` is a Z3 finite-domain expression.
7817 >>> s = FiniteDomainSort('S', 100)
7818 >>> b = Const('b', s)
7819 >>> is_finite_domain(b)
7821 >>> is_finite_domain(Int('x'))
7824 return isinstance(a, FiniteDomainRef)
7827class FiniteDomainNumRef(FiniteDomainRef):
7828 """Integer values."""
7831 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7833 >>> s = FiniteDomainSort('S', 100)
7834 >>> v = FiniteDomainVal(3, s)
7840 return int(self.as_string())
7842 def as_string(self):
7843 """Return a Z3 finite-domain numeral as a Python string.
7845 >>> s = FiniteDomainSort('S', 100)
7846 >>> v = FiniteDomainVal(42, s)
7850 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
7853def FiniteDomainVal(val, sort, ctx=None):
7854 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7856 >>> s = FiniteDomainSort('S', 256)
7857 >>> FiniteDomainVal(255, s)
7859 >>> FiniteDomainVal('100', s)
7863 _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
7865 return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
7868def is_finite_domain_value(a):
7869 """Return `True` if `a` is a Z3 finite-domain value.
7871 >>> s = FiniteDomainSort('S', 100)
7872 >>> b = Const('b', s)
7873 >>> is_finite_domain_value(b)
7875 >>> b = FiniteDomainVal(10, s)
7878 >>> is_finite_domain_value(b)
7881 return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
7884#########################################
7888#########################################
7890class OptimizeObjective:
7891 def __init__(self, opt, value, is_max):
7894 self._is_max = is_max
7898 return _to_expr_ref(Z3_optimize_get_lower(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7902 return _to_expr_ref(Z3_optimize_get_upper(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7904 def lower_values(self):
7906 return AstVector(Z3_optimize_get_lower_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7908 def upper_values(self):
7910 return AstVector(Z3_optimize_get_upper_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7919 return "%s:%s" % (self._value, self._is_max)
7925def _global_on_model(ctx):
7926 (fn, mdl) = _on_models[ctx]
7930_on_model_eh = on_model_eh_type(_global_on_model)
7933class Optimize(Z3PPObject):
7934 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
7936 def __init__(self, optimize=None, ctx=None):
7937 self.ctx = _get_ctx(ctx)
7938 if optimize is None:
7939 self.optimize = Z3_mk_optimize(self.ctx.ref())
7941 self.optimize = optimize
7942 self._on_models_id = None
7943 Z3_optimize_inc_ref(self.ctx.ref(), self.optimize)
7945 def __deepcopy__(self, memo={}):
7946 return Optimize(self.optimize, self.ctx)
7949 if self.optimize is not None and self.ctx.ref() is not None and Z3_optimize_dec_ref is not None:
7950 Z3_optimize_dec_ref(self.ctx.ref(), self.optimize)
7951 if self._on_models_id is not None:
7952 del _on_models[self._on_models_id]
7954 def set(self, *args, **keys):
7955 """Set a configuration option.
7956 The method `help()` return a string containing all available options.
7958 p = args2params(args, keys, self.ctx)
7959 Z3_optimize_set_params(self.ctx.ref(), self.optimize, p.params)
7962 """Display a string describing all available options."""
7963 print(Z3_optimize_get_help(self.ctx.ref(), self.optimize))
7965 def param_descrs(self):
7966 """Return the parameter description set."""
7967 return ParamDescrsRef(Z3_optimize_get_param_descrs(self.ctx.ref(), self.optimize), self.ctx)
7969 def assert_exprs(self, *args):
7970 """Assert constraints as background axioms for the optimize solver."""
7971 args = _get_args(args)
7972 s = BoolSort(self.ctx)
7974 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7976 Z3_optimize_assert(self.ctx.ref(), self.optimize, f.as_ast())
7979 Z3_optimize_assert(self.ctx.ref(), self.optimize, arg.as_ast())
7981 def add(self, *args):
7982 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
7983 self.assert_exprs(*args)
7985 def __iadd__(self, fml):
7989 def assert_and_track(self, a, p):
7990 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7992 If `p` is a string, it will be automatically converted into a Boolean constant.
7997 >>> s.assert_and_track(x > 0, 'p1')
7998 >>> s.assert_and_track(x != 1, 'p2')
7999 >>> s.assert_and_track(x < 0, p3)
8000 >>> print(s.check())
8002 >>> c = s.unsat_core()
8012 if isinstance(p, str):
8013 p = Bool(p, self.ctx)
8014 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
8015 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
8016 Z3_optimize_assert_and_track(self.ctx.ref(), self.optimize, a.as_ast(), p.as_ast())
8018 def add_soft(self, arg, weight="1", id=None):
8019 """Add soft constraint with optional weight and optional identifier.
8020 If no weight is supplied, then the penalty for violating the soft constraint
8022 Soft constraints are grouped by identifiers. Soft constraints that are
8023 added without identifiers are grouped by default.
8026 weight = "%d" % weight
8027 elif isinstance(weight, float):
8028 weight = "%f" % weight
8029 if not isinstance(weight, str):
8030 raise Z3Exception("weight should be a string or an integer")
8033 id = to_symbol(id, self.ctx)
8036 v = Z3_optimize_assert_soft(self.ctx.ref(), self.optimize, a.as_ast(), weight, id)
8037 return OptimizeObjective(self, v, False)
8038 if sys.version_info.major >= 3 and isinstance(arg, Iterable):
8039 return [asoft(a) for a in arg]
8042 def set_initial_value(self, var, value):
8043 """initialize the solver's state by setting the initial value of var to value
8046 value = s.cast(value)
8047 Z3_optimize_set_initial_value(self.ctx.ref(), self.optimize, var.ast, value.ast)
8049 def maximize(self, arg):
8050 """Add objective function to maximize."""
8051 return OptimizeObjective(
8053 Z3_optimize_maximize(self.ctx.ref(), self.optimize, arg.as_ast()),
8057 def minimize(self, arg):
8058 """Add objective function to minimize."""
8059 return OptimizeObjective(
8061 Z3_optimize_minimize(self.ctx.ref(), self.optimize, arg.as_ast()),
8066 """create a backtracking point for added rules, facts and assertions"""
8067 Z3_optimize_push(self.ctx.ref(), self.optimize)
8070 """restore to previously created backtracking point"""
8071 Z3_optimize_pop(self.ctx.ref(), self.optimize)
8073 def check(self, *assumptions):
8074 """Check consistency and produce optimal values."""
8075 assumptions = _get_args(assumptions)
8076 num = len(assumptions)
8077 _assumptions = (Ast * num)()
8078 for i in range(num):
8079 _assumptions[i] = assumptions[i].as_ast()
8080 return CheckSatResult(Z3_optimize_check(self.ctx.ref(), self.optimize, num, _assumptions))
8082 def reason_unknown(self):
8083 """Return a string that describes why the last `check()` returned `unknown`."""
8084 return Z3_optimize_get_reason_unknown(self.ctx.ref(), self.optimize)
8087 """Return a model for the last check()."""
8089 return ModelRef(Z3_optimize_get_model(self.ctx.ref(), self.optimize), self.ctx)
8091 raise Z3Exception("model is not available")
8093 def unsat_core(self):
8094 return AstVector(Z3_optimize_get_unsat_core(self.ctx.ref(), self.optimize), self.ctx)
8096 def lower(self, obj):
8097 if not isinstance(obj, OptimizeObjective):
8098 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8101 def upper(self, obj):
8102 if not isinstance(obj, OptimizeObjective):
8103 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8106 def lower_values(self, obj):
8107 if not isinstance(obj, OptimizeObjective):
8108 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8109 return obj.lower_values()
8111 def upper_values(self, obj):
8112 if not isinstance(obj, OptimizeObjective):
8113 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8114 return obj.upper_values()
8116 def from_file(self, filename):
8117 """Parse assertions and objectives from a file"""
8118 Z3_optimize_from_file(self.ctx.ref(), self.optimize, filename)
8120 def from_string(self, s):
8121 """Parse assertions and objectives from a string"""
8122 Z3_optimize_from_string(self.ctx.ref(), self.optimize, s)
8124 def assertions(self):
8125 """Return an AST vector containing all added constraints."""
8126 return AstVector(Z3_optimize_get_assertions(self.ctx.ref(), self.optimize), self.ctx)
8128 def objectives(self):
8129 """returns set of objective functions"""
8130 return AstVector(Z3_optimize_get_objectives(self.ctx.ref(), self.optimize), self.ctx)
8133 """Return a formatted string with all added rules and constraints."""
8137 """Return a formatted string (in Lisp-like format) with all added constraints.
8138 We say the string is in s-expression format.
8140 return Z3_optimize_to_string(self.ctx.ref(), self.optimize)
8142 def statistics(self):
8143 """Return statistics for the last check`.
8145 return Statistics(Z3_optimize_get_statistics(self.ctx.ref(), self.optimize), self.ctx)
8147 def set_on_model(self, on_model):
8148 """Register a callback that is invoked with every incremental improvement to
8149 objective values. The callback takes a model as argument.
8150 The life-time of the model is limited to the callback so the
8151 model has to be (deep) copied if it is to be used after the callback
8153 id = len(_on_models) + 41
8154 mdl = Model(self.ctx)
8155 _on_models[id] = (on_model, mdl)
8156 self._on_models_id = id
8157 Z3_optimize_register_model_eh(
8158 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8162#########################################
8166#########################################
8167class ApplyResult(Z3PPObject):
8168 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8169 It also contains model and proof converters.
8172 def __init__(self, result, ctx):
8173 self.result = result
8175 Z3_apply_result_inc_ref(self.ctx.ref(), self.result)
8177 def __deepcopy__(self, memo={}):
8178 return ApplyResult(self.result, self.ctx)
8181 if self.ctx.ref() is not None and Z3_apply_result_dec_ref is not None:
8182 Z3_apply_result_dec_ref(self.ctx.ref(), self.result)
8185 """Return the number of subgoals in `self`.
8187 >>> a, b = Ints('a b')
8189 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8190 >>> t = Tactic('split-clause')
8194 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8197 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8201 return int(Z3_apply_result_get_num_subgoals(self.ctx.ref(), self.result))
8203 def __getitem__(self, idx):
8204 """Return one of the subgoals stored in ApplyResult object `self`.
8206 >>> a, b = Ints('a b')
8208 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8209 >>> t = Tactic('split-clause')
8212 [a == 0, Or(b == 0, b == 1), a > b]
8214 [a == 1, Or(b == 0, b == 1), a > b]
8216 if idx >= len(self):
8218 return Goal(goal=Z3_apply_result_get_subgoal(self.ctx.ref(), self.result, idx), ctx=self.ctx)
8221 return obj_to_string(self)
8224 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8225 return Z3_apply_result_to_string(self.ctx.ref(), self.result)
8228 """Return a Z3 expression consisting of all subgoals.
8233 >>> g.add(Or(x == 2, x == 3))
8234 >>> r = Tactic('simplify')(g)
8236 [[Not(x <= 1), Or(x == 2, x == 3)]]
8238 And(Not(x <= 1), Or(x == 2, x == 3))
8239 >>> r = Tactic('split-clause')(g)
8241 [[x > 1, x == 2], [x > 1, x == 3]]
8243 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8247 return BoolVal(False, self.ctx)
8249 return self[0].as_expr()
8251 return Or([self[i].as_expr() for i in range(len(self))])
8253#########################################
8257#########################################
8260 """Simplifiers act as pre-processing utilities for solvers.
8261 Build a custom simplifier and add it to a solve
r"""
8263 def __init__(self, simplifier, ctx=None):
8264 self.ctx = _get_ctx(ctx)
8265 self.simplifier = None
8266 if isinstance(simplifier, SimplifierObj):
8267 self.simplifier = simplifier
8268 elif isinstance(simplifier, list):
8269 simps = [Simplifier(s, ctx) for s in simplifier]
8270 self.simplifier = simps[0].simplifier
8271 for i in range(1, len(simps)):
8272 self.simplifier = Z3_simplifier_and_then(self.ctx.ref(), self.simplifier, simps[i].simplifier)
8273 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8277 _z3_assert(isinstance(simplifier, str), "simplifier name expected")
8279 self.simplifier = Z3_mk_simplifier(self.ctx.ref(), str(simplifier))
8281 raise Z3Exception("unknown simplifier '%s'" % simplifier)
8282 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8284 def __deepcopy__(self, memo={}):
8285 return Simplifier(self.simplifier, self.ctx)
8288 if self.simplifier is not None and self.ctx.ref() is not None and Z3_simplifier_dec_ref is not None:
8289 Z3_simplifier_dec_ref(self.ctx.ref(), self.simplifier)
8291 def using_params(self, *args, **keys):
8292 """Return a simplifier that uses the given configuration options"""
8293 p = args2params(args, keys, self.ctx)
8294 return Simplifier(Z3_simplifier_using_params(self.ctx.ref(), self.simplifier, p.params), self.ctx)
8296 def add(self, solver):
8297 """Return a solver that applies the simplification pre-processing specified by the simplifie
r"""
8298 return Solver(Z3_solver_add_simplifier(self.ctx.ref(), solver.solver, self.simplifier), self.ctx)
8301 """Display a string containing a description of the available options for the `self` simplifier."""
8302 print(Z3_simplifier_get_help(self.ctx.ref(), self.simplifier))
8304 def param_descrs(self):
8305 """Return the parameter description set."""
8306 return ParamDescrsRef(Z3_simplifier_get_param_descrs(self.ctx.ref(), self.simplifier), self.ctx)
8309#########################################
8313#########################################
8317 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8318 A Tactic can be converted into a Solver using the method solver().
8320 Several combinators are available for creating new tactics using the built-in ones:
8321 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8324 def __init__(self, tactic, ctx=None):
8325 self.ctx = _get_ctx(ctx)
8327 if isinstance(tactic, TacticObj):
8328 self.tactic = tactic
8331 _z3_assert(isinstance(tactic, str), "tactic name expected")
8333 self.tactic = Z3_mk_tactic(self.ctx.ref(), str(tactic))
8335 raise Z3Exception("unknown tactic '%s'" % tactic)
8336 Z3_tactic_inc_ref(self.ctx.ref(), self.tactic)
8338 def __deepcopy__(self, memo={}):
8339 return Tactic(self.tactic, self.ctx)
8342 if self.tactic is not None and self.ctx.ref() is not None and Z3_tactic_dec_ref is not None:
8343 Z3_tactic_dec_ref(self.ctx.ref(), self.tactic)
8345 def solver(self, logFile=None):
8346 """Create a solver using the tactic `self`.
8348 The solver supports the methods `push()` and `pop()`, but it
8349 will always solve each `check()` from scratch.
8351 >>> t = Then('simplify', 'nlsat')
8354 >>> s.add(x**2 == 2, x > 0)
8360 return Solver(Z3_mk_solver_from_tactic(self.ctx.ref(), self.tactic), self.ctx, logFile)
8362 def apply(self, goal, *arguments, **keywords):
8363 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8365 >>> x, y = Ints('x y')
8366 >>> t = Tactic('solve-eqs')
8367 >>> t.apply(And(x == 0, y >= x + 1))
8371 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expressions expected")
8372 goal = _to_goal(goal)
8373 if len(arguments) > 0 or len(keywords) > 0:
8374 p = args2params(arguments, keywords, self.ctx)
8375 return ApplyResult(Z3_tactic_apply_ex(self.ctx.ref(), self.tactic, goal.goal, p.params), self.ctx)
8377 return ApplyResult(Z3_tactic_apply(self.ctx.ref(), self.tactic, goal.goal), self.ctx)
8379 def __call__(self, goal, *arguments, **keywords):
8380 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8382 >>> x, y = Ints('x y')
8383 >>> t = Tactic('solve-eqs')
8384 >>> t(And(x == 0, y >= x + 1))
8387 return self.apply(goal, *arguments, **keywords)
8390 """Display a string containing a description of the available options for the `self` tactic."""
8391 print(Z3_tactic_get_help(self.ctx.ref(), self.tactic))
8393 def param_descrs(self):
8394 """Return the parameter description set."""
8395 return ParamDescrsRef(Z3_tactic_get_param_descrs(self.ctx.ref(), self.tactic), self.ctx)
8399 if isinstance(a, BoolRef):
8400 goal = Goal(ctx=a.ctx)
8407def _to_tactic(t, ctx=None):
8408 if isinstance(t, Tactic):
8411 return Tactic(t, ctx)
8414def _and_then(t1, t2, ctx=None):
8415 t1 = _to_tactic(t1, ctx)
8416 t2 = _to_tactic(t2, ctx)
8418 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8419 return Tactic(Z3_tactic_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8422def _or_else(t1, t2, ctx=None):
8423 t1 = _to_tactic(t1, ctx)
8424 t2 = _to_tactic(t2, ctx)
8426 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8427 return Tactic(Z3_tactic_or_else(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8430def AndThen(*ts, **ks):
8431 """Return a tactic that applies the tactics in `*ts` in sequence.
8433 >>> x, y = Ints('x y')
8434 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8435 >>> t(And(x == 0, y > x + 1))
8437 >>> t(And(x == 0, y > x + 1)).as_expr()
8441 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8442 ctx = ks.get("ctx", None)
8445 for i in range(num - 1):
8446 r = _and_then(r, ts[i + 1], ctx)
8451 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8453 >>> x, y = Ints('x y')
8454 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8455 >>> t(And(x == 0, y > x + 1))
8457 >>> t(And(x == 0, y > x + 1)).as_expr()
8460 return AndThen(*ts, **ks)
8463def OrElse(*ts, **ks):
8464 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8467 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8468 >>> # Tactic split-clause fails if there is no clause in the given goal.
8471 >>> t(Or(x == 0, x == 1))
8472 [[x == 0], [x == 1]]
8475 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8476 ctx = ks.get("ctx", None)
8479 for i in range(num - 1):
8480 r = _or_else(r, ts[i + 1], ctx)
8484def ParOr(*ts, **ks):
8485 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8488 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8493 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8494 ctx = _get_ctx(ks.get("ctx", None))
8495 ts = [_to_tactic(t, ctx) for t in ts]
8497 _args = (TacticObj * sz)()
8499 _args[i] = ts[i].tactic
8500 return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
8503def ParThen(t1, t2, ctx=None):
8504 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8505 The subgoals are processed in parallel.
8507 >>> x, y = Ints('x y')
8508 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8509 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8510 [[x == 1, y == 2], [x == 2, y == 3]]
8512 t1 = _to_tactic(t1, ctx)
8513 t2 = _to_tactic(t2, ctx)
8515 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8516 return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8519def ParAndThen(t1, t2, ctx=None):
8520 """Alias for ParThen(t1, t2, ctx)."""
8521 return ParThen(t1, t2, ctx)
8524def With(t, *args, **keys):
8525 """Return a tactic that applies tactic `t` using the given configuration options.
8527 >>> x, y = Ints('x y')
8528 >>> t = With(Tactic('simplify'), som=True)
8529 >>> t((x + 1)*(y + 2) == 0)
8530 [[2*x + y + x*y == -2]]
8532 ctx = keys.pop("ctx", None)
8533 t = _to_tactic(t, ctx)
8534 p = args2params(args, keys, t.ctx)
8535 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8538def WithParams(t, p):
8539 """Return a tactic that applies tactic `t` using the given configuration options.
8541 >>> x, y = Ints('x y')
8543 >>> p.set("som", True)
8544 >>> t = WithParams(Tactic('simplify'), p)
8545 >>> t((x + 1)*(y + 2) == 0)
8546 [[2*x + y + x*y == -2]]
8548 t = _to_tactic(t, None)
8549 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8552def Repeat(t, max=4294967295, ctx=None):
8553 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8554 or the maximum number of iterations `max` is reached.
8556 >>> x, y = Ints('x y')
8557 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8558 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8560 >>> for subgoal in r: print(subgoal)
8561 [x == 0, y == 0, x > y]
8562 [x == 0, y == 1, x > y]
8563 [x == 1, y == 0, x > y]
8564 [x == 1, y == 1, x > y]
8565 >>> t = Then(t, Tactic('propagate-values'))
8569 t = _to_tactic(t, ctx)
8570 return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
8573def TryFor(t, ms, ctx=None):
8574 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8576 If `t` does not terminate in `ms` milliseconds, then it fails.
8578 t = _to_tactic(t, ctx)
8579 return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
8582def tactics(ctx=None):
8583 """Return a list of all available tactics in Z3.
8586 >>> l.count('simplify') == 1
8590 return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
8593def tactic_description(name, ctx=None):
8594 """Return a short description for the tactic named `name`.
8596 >>> d = tactic_description('simplify')
8599 return Z3_tactic_get_descr(ctx.ref(), name)
8602def describe_tactics():
8603 """Display a (tabular) description of all available tactics in Z3."""
8606 print('<table border="1" cellpadding="2" cellspacing="0">')
8609 print('<tr style="background-color:#CFCFCF">')
8614 print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
8618 print("%s : %s" % (t, tactic_description(t)))
8622 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8623 to decide which solver and/or preprocessing step will be used.
8626 def __init__(self, probe, ctx=None):
8627 self.ctx = _get_ctx(ctx)
8629 if isinstance(probe, ProbeObj):
8631 elif isinstance(probe, float):
8632 self.probe = Z3_probe_const(self.ctx.ref(), probe)
8633 elif _is_int(probe):
8634 self.probe = Z3_probe_const(self.ctx.ref(), float(probe))
8635 elif isinstance(probe, bool):
8637 self.probe = Z3_probe_const(self.ctx.ref(), 1.0)
8639 self.probe = Z3_probe_const(self.ctx.ref(), 0.0)
8642 _z3_assert(isinstance(probe, str), "probe name expected")
8644 self.probe = Z3_mk_probe(self.ctx.ref(), probe)
8646 raise Z3Exception("unknown probe '%s'" % probe)
8647 Z3_probe_inc_ref(self.ctx.ref(), self.probe)
8649 def __deepcopy__(self, memo={}):
8650 return Probe(self.probe, self.ctx)
8653 if self.probe is not None and self.ctx.ref() is not None and Z3_probe_dec_ref is not None:
8654 Z3_probe_dec_ref(self.ctx.ref(), self.probe)
8656 def __lt__(self, other):
8657 """Return a probe that evaluates to "true" when the value returned by `self`
8658 is less than the value returned by `other`.
8660 >>> p = Probe('size') < 10
8668 return Probe(Z3_probe_lt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8670 def __gt__(self, other):
8671 """Return a probe that evaluates to "true" when the value returned by `self`
8672 is greater than the value returned by `other`.
8674 >>> p = Probe('size') > 10
8682 return Probe(Z3_probe_gt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8684 def __le__(self, other):
8685 """Return a probe that evaluates to "true" when the value returned by `self`
8686 is less than or equal to the value returned by `other`.
8688 >>> p = Probe('size') <= 2
8696 return Probe(Z3_probe_le(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8698 def __ge__(self, other):
8699 """Return a probe that evaluates to "true" when the value returned by `self`
8700 is greater than or equal to the value returned by `other`.
8702 >>> p = Probe('size') >= 2
8710 return Probe(Z3_probe_ge(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8712 def __eq__(self, other):
8713 """Return a probe that evaluates to "true" when the value returned by `self`
8714 is equal to the value returned by `other`.
8716 >>> p = Probe('size') == 2
8724 return Probe(Z3_probe_eq(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8726 def __ne__(self, other):
8727 """Return a probe that evaluates to "true" when the value returned by `self`
8728 is not equal to the value returned by `other`.
8730 >>> p = Probe('size') != 2
8738 p = self.__eq__(other)
8739 return Probe(Z3_probe_not(self.ctx.ref(), p.probe), self.ctx)
8741 def __call__(self, goal):
8742 """Evaluate the probe `self` in the given goal.
8744 >>> p = Probe('size')
8754 >>> p = Probe('num-consts')
8757 >>> p = Probe('is-propositional')
8760 >>> p = Probe('is-qflia')
8765 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expression expected")
8766 goal = _to_goal(goal)
8767 return Z3_probe_apply(self.ctx.ref(), self.probe, goal.goal)
8771 """Return `True` if `p` is a Z3 probe.
8773 >>> is_probe(Int('x'))
8775 >>> is_probe(Probe('memory'))
8778 return isinstance(p, Probe)
8781def _to_probe(p, ctx=None):
8785 return Probe(p, ctx)
8788def probes(ctx=None):
8789 """Return a list of all available probes in Z3.
8792 >>> l.count('memory') == 1
8796 return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
8799def probe_description(name, ctx=None):
8800 """Return a short description for the probe named `name`.
8802 >>> d = probe_description('memory')
8805 return Z3_probe_get_descr(ctx.ref(), name)
8808def describe_probes():
8809 """Display a (tabular) description of all available probes in Z3."""
8812 print('<table border="1" cellpadding="2" cellspacing="0">')
8815 print('<tr style="background-color:#CFCFCF">')
8820 print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
8824 print("%s : %s" % (p, probe_description(p)))
8827def _probe_nary(f, args, ctx):
8829 _z3_assert(len(args) > 0, "At least one argument expected")
8831 r = _to_probe(args[0], ctx)
8832 for i in range(num - 1):
8833 r = Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8837def _probe_and(args, ctx):
8838 return _probe_nary(Z3_probe_and, args, ctx)
8841def _probe_or(args, ctx):
8842 return _probe_nary(Z3_probe_or, args, ctx)
8845def FailIf(p, ctx=None):
8846 """Return a tactic that fails if the probe `p` evaluates to true.
8847 Otherwise, it returns the input goal unmodified.
8849 In the following example, the tactic applies 'simplify' if and only if there are
8850 more than 2 constraints in the goal.
8852 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8853 >>> x, y = Ints('x y')
8859 >>> g.add(x == y + 1)
8861 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8863 p = _to_probe(p, ctx)
8864 return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
8867def When(p, t, ctx=None):
8868 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8869 Otherwise, it returns the input goal unmodified.
8871 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8872 >>> x, y = Ints('x y')
8878 >>> g.add(x == y + 1)
8880 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8882 p = _to_probe(p, ctx)
8883 t = _to_tactic(t, ctx)
8884 return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
8887def Cond(p, t1, t2, ctx=None):
8888 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8890 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8892 p = _to_probe(p, ctx)
8893 t1 = _to_tactic(t1, ctx)
8894 t2 = _to_tactic(t2, ctx)
8895 return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
8897#########################################
8901#########################################
8904def simplify(a, *arguments, **keywords):
8905 """Simplify the expression `a` using the given options.
8907 This function has many options. Use `help_simplify` to obtain the complete list.
8911 >>> simplify(x + 1 + y + x + 1)
8913 >>> simplify((x + 1)*(y + 1), som=True)
8915 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
8916 And(Not(x == y), Not(x == 1), Not(y == 1))
8917 >>> simplify(And(x == 0, y == 1), elim_and=True)
8918 Not(Or(Not(x == 0), Not(y == 1)))
8921 _z3_assert(is_expr(a), "Z3 expression expected")
8922 if len(arguments) > 0 or len(keywords) > 0:
8923 p = args2params(arguments, keywords, a.ctx)
8924 return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
8926 return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
8930 """Return a string describing all options available for Z3 `simplify` procedure."""
8931 print(Z3_simplify_get_help(main_ctx().ref()))
8934def simplify_param_descrs():
8935 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
8936 return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
8939def substitute(t, *m):
8940 """Apply substitution m on t, m is a list of pairs of the form (from, to).
8941 Every occurrence in t of from is replaced with to.
8945 >>> substitute(x + 1, (x, y + 1))
8947 >>> f = Function('f', IntSort(), IntSort())
8948 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
8951 if isinstance(m, tuple):
8953 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
8956 _z3_assert(is_expr(t), "Z3 expression expected")
8958 all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
8959 "Z3 invalid substitution, expression pairs expected.")
8961 all([p[0].sort().eq(p[1].sort()) for p in m]),
8962 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
8964 _from = (Ast * num)()
8966 for i in range(num):
8967 _from[i] = m[i][0].as_ast()
8968 _to[i] = m[i][1].as_ast()
8969 return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8972def substitute_vars(t, *m):
8973 """Substitute the free variables in t with the expression in m.
8975 >>> v0 = Var(0, IntSort())
8976 >>> v1 = Var(1, IntSort())
8978 >>> f = Function('f', IntSort(), IntSort(), IntSort())
8979 >>> # replace v0 with x+1 and v1 with x
8980 >>> substitute_vars(f(v0, v1), x + 1, x)
8984 _z3_assert(is_expr(t), "Z3 expression expected")
8985 _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
8988 for i in range(num):
8989 _to[i] = m[i].as_ast()
8990 return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
8992def substitute_funs(t, *m):
8993 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
8994 Every occurrence in to of the function from is replaced with the expression to.
8995 The expression to can have free variables, that refer to the arguments of from.
8998 if isinstance(m, tuple):
9000 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9003 _z3_assert(is_expr(t), "Z3 expression expected")
9004 _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, function pairs expected.")
9006 _from = (FuncDecl * num)()
9008 for i in range(num):
9009 _from[i] = m[i][0].as_func_decl()
9010 _to[i] = m[i][1].as_ast()
9011 return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9015 """Create the sum of the Z3 expressions.
9017 >>> a, b, c = Ints('a b c')
9022 >>> A = IntVector('a', 5)
9024 a__0 + a__1 + a__2 + a__3 + a__4
9026 args = _get_args(args)
9029 ctx = _ctx_from_ast_arg_list(args)
9031 return _reduce(lambda a, b: a + b, args, 0)
9032 args = _coerce_expr_list(args, ctx)
9034 return _reduce(lambda a, b: a + b, args, 0)
9036 _args, sz = _to_ast_array(args)
9037 return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
9041 """Create the product of the Z3 expressions.
9043 >>> a, b, c = Ints('a b c')
9044 >>> Product(a, b, c)
9046 >>> Product([a, b, c])
9048 >>> A = IntVector('a', 5)
9050 a__0*a__1*a__2*a__3*a__4
9052 args = _get_args(args)
9055 ctx = _ctx_from_ast_arg_list(args)
9057 return _reduce(lambda a, b: a * b, args, 1)
9058 args = _coerce_expr_list(args, ctx)
9060 return _reduce(lambda a, b: a * b, args, 1)
9062 _args, sz = _to_ast_array(args)
9063 return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
9066 """Create the absolute value of an arithmetic expression"""
9067 return If(arg > 0, arg, -arg)
9071 """Create an at-most Pseudo-Boolean k constraint.
9073 >>> a, b, c = Bools('a b c')
9074 >>> f = AtMost(a, b, c, 2)
9076 args = _get_args(args)
9078 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9079 ctx = _ctx_from_ast_arg_list(args)
9081 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9082 args1 = _coerce_expr_list(args[:-1], ctx)
9084 _args, sz = _to_ast_array(args1)
9085 return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
9089 """Create an at-least Pseudo-Boolean k constraint.
9091 >>> a, b, c = Bools('a b c')
9092 >>> f = AtLeast(a, b, c, 2)
9094 args = _get_args(args)
9096 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9097 ctx = _ctx_from_ast_arg_list(args)
9099 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9100 args1 = _coerce_expr_list(args[:-1], ctx)
9102 _args, sz = _to_ast_array(args1)
9103 return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
9106def _reorder_pb_arg(arg):
9108 if not _is_int(b) and _is_int(a):
9113def _pb_args_coeffs(args, default_ctx=None):
9114 args = _get_args_ast_list(args)
9116 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9117 args = [_reorder_pb_arg(arg) for arg in args]
9118 args, coeffs = zip(*args)
9120 _z3_assert(len(args) > 0, "Non empty list of arguments expected")
9121 ctx = _ctx_from_ast_arg_list(args)
9123 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9124 args = _coerce_expr_list(args, ctx)
9125 _args, sz = _to_ast_array(args)
9126 _coeffs = (ctypes.c_int * len(coeffs))()
9127 for i in range(len(coeffs)):
9128 _z3_check_cint_overflow(coeffs[i], "coefficient")
9129 _coeffs[i] = coeffs[i]
9130 return ctx, sz, _args, _coeffs, args
9134 """Create a Pseudo-Boolean inequality k constraint.
9136 >>> a, b, c = Bools('a b c')
9137 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9139 _z3_check_cint_overflow(k, "k")
9140 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9141 return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
9145 """Create a Pseudo-Boolean inequality k constraint.
9147 >>> a, b, c = Bools('a b c')
9148 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9150 _z3_check_cint_overflow(k, "k")
9151 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9152 return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
9155def PbEq(args, k, ctx=None):
9156 """Create a Pseudo-Boolean equality k constraint.
9158 >>> a, b, c = Bools('a b c')
9159 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9161 _z3_check_cint_overflow(k, "k")
9162 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9163 return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
9166def solve(*args, **keywords):
9167 """Solve the constraints `*args`.
9169 This is a simple function for creating demonstrations. It creates a solver,
9170 configure it using the options in `keywords`, adds the constraints
9171 in `args`, and invokes check.
9174 >>> solve(a > 0, a < 2)
9177 show = keywords.pop("show", False)
9185 print("no solution")
9187 print("failed to solve")
9196def solve_using(s, *args, **keywords):
9197 """Solve the constraints `*args` using solver `s`.
9199 This is a simple function for creating demonstrations. It is similar to `solve`,
9200 but it uses the given solver `s`.
9201 It configures solver `s` using the options in `keywords`, adds the constraints
9202 in `args`, and invokes check.
9204 show = keywords.pop("show", False)
9206 _z3_assert(isinstance(s, Solver), "Solver object expected")
9214 print("no solution")
9216 print("failed to solve")
9227def prove(claim, show=False, **keywords):
9228 """Try to prove the given claim.
9230 This is a simple function for creating demonstrations. It tries to prove
9231 `claim` by showing the negation is unsatisfiable.
9233 >>> p, q = Bools('p q')
9234 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9238 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9248 print("failed to prove")
9251 print("counterexample")
9255def _solve_html(*args, **keywords):
9256 """Version of function `solve` that renders HTML output."""
9257 show = keywords.pop("show", False)
9262 print("<b>Problem:</b>")
9266 print("<b>no solution</b>")
9268 print("<b>failed to solve</b>")
9275 print("<b>Solution:</b>")
9279def _solve_using_html(s, *args, **keywords):
9280 """Version of function `solve_using` that renders HTML."""
9281 show = keywords.pop("show", False)
9283 _z3_assert(isinstance(s, Solver), "Solver object expected")
9287 print("<b>Problem:</b>")
9291 print("<b>no solution</b>")
9293 print("<b>failed to solve</b>")
9300 print("<b>Solution:</b>")
9304def _prove_html(claim, show=False, **keywords):
9305 """Version of function `prove` that renders HTML."""
9307 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9315 print("<b>proved</b>")
9317 print("<b>failed to prove</b>")
9320 print("<b>counterexample</b>")
9324def _dict2sarray(sorts, ctx):
9326 _names = (Symbol * sz)()
9327 _sorts = (Sort * sz)()
9332 _z3_assert(isinstance(k, str), "String expected")
9333 _z3_assert(is_sort(v), "Z3 sort expected")
9334 _names[i] = to_symbol(k, ctx)
9337 return sz, _names, _sorts
9340def _dict2darray(decls, ctx):
9342 _names = (Symbol * sz)()
9343 _decls = (FuncDecl * sz)()
9348 _z3_assert(isinstance(k, str), "String expected")
9349 _z3_assert(is_func_decl(v) or is_const(v), "Z3 declaration or constant expected")
9350 _names[i] = to_symbol(k, ctx)
9352 _decls[i] = v.decl().ast
9356 return sz, _names, _decls
9359 def __init__(self, ctx= None):
9360 self.ctx = _get_ctx(ctx)
9361 self.pctx = Z3_mk_parser_context(self.ctx.ref())
9362 Z3_parser_context_inc_ref(self.ctx.ref(), self.pctx)
9365 if self.ctx.ref() is not None and self.pctx is not None and Z3_parser_context_dec_ref is not None:
9366 Z3_parser_context_dec_ref(self.ctx.ref(), self.pctx)
9369 def add_sort(self, sort):
9370 Z3_parser_context_add_sort(self.ctx.ref(), self.pctx, sort.as_ast())
9372 def add_decl(self, decl):
9373 Z3_parser_context_add_decl(self.ctx.ref(), self.pctx, decl.as_ast())
9375 def from_string(self, s):
9376 return AstVector(Z3_parser_context_from_string(self.ctx.ref(), self.pctx, s), self.ctx)
9378def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
9379 """Parse a string in SMT 2.0 format using the given sorts and decls.
9381 The arguments sorts and decls are Python dictionaries used to initialize
9382 the symbol table used for the SMT 2.0 parser.
9384 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9386 >>> x, y = Ints('x y')
9387 >>> f = Function('f', IntSort(), IntSort())
9388 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9390 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9394 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9395 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9396 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9399def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9400 """Parse a file in SMT 2.0 format using the given sorts and decls.
9402 This function is similar to parse_smt2_string().
9405 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9406 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9407 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9410#########################################
9412# Floating-Point Arithmetic
9414#########################################
9417# Global default rounding mode
9418_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9419_dflt_fpsort_ebits = 11
9420_dflt_fpsort_sbits = 53
9423def get_default_rounding_mode(ctx=None):
9424 """Retrieves the global default rounding mode."""
9425 global _dflt_rounding_mode
9426 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9428 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9430 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9432 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9434 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9438_ROUNDING_MODES = frozenset({
9439 Z3_OP_FPA_RM_TOWARD_ZERO,
9440 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9441 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9442 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9443 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9447def set_default_rounding_mode(rm, ctx=None):
9448 global _dflt_rounding_mode
9449 if is_fprm_value(rm):
9450 _dflt_rounding_mode = rm.decl().kind()
9452 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9453 _dflt_rounding_mode = rm
9456def get_default_fp_sort(ctx=None):
9457 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9460def set_default_fp_sort(ebits, sbits, ctx=None):
9461 global _dflt_fpsort_ebits
9462 global _dflt_fpsort_sbits
9463 _dflt_fpsort_ebits = ebits
9464 _dflt_fpsort_sbits = sbits
9467def _dflt_rm(ctx=None):
9468 return get_default_rounding_mode(ctx)
9471def _dflt_fps(ctx=None):
9472 return get_default_fp_sort(ctx)
9475def _coerce_fp_expr_list(alist, ctx):
9476 first_fp_sort = None
9479 if first_fp_sort is None:
9480 first_fp_sort = a.sort()
9481 elif first_fp_sort == a.sort():
9482 pass # OK, same as before
9484 # we saw at least 2 different float sorts; something will
9485 # throw a sort mismatch later, for now assume None.
9486 first_fp_sort = None
9490 for i in range(len(alist)):
9492 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9493 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9494 r.append(FPVal(a, None, first_fp_sort, ctx))
9497 return _coerce_expr_list(r, ctx)
9502class FPSortRef(SortRef):
9503 """Floating-point sort."""
9506 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9507 >>> b = FPSort(8, 24)
9511 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9514 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9515 >>> b = FPSort(8, 24)
9519 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9521 def cast(self, val):
9522 """Try to cast `val` as a floating-point expression.
9523 >>> b = FPSort(8, 24)
9526 >>> b.cast(1.0).sexpr()
9527 '(fp #b0 #x7f #b00000000000000000000000)'
9531 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9534 return FPVal(val, None, self, self.ctx)
9537def Float16(ctx=None):
9538 """Floating-point 16-bit (half) sort."""
9540 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9543def FloatHalf(ctx=None):
9544 """Floating-point 16-bit (half) sort."""
9546 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9549def Float32(ctx=None):
9550 """Floating-point 32-bit (single) sort."""
9552 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9555def FloatSingle(ctx=None):
9556 """Floating-point 32-bit (single) sort."""
9558 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9561def Float64(ctx=None):
9562 """Floating-point 64-bit (double) sort."""
9564 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9567def FloatDouble(ctx=None):
9568 """Floating-point 64-bit (double) sort."""
9570 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9573def Float128(ctx=None):
9574 """Floating-point 128-bit (quadruple) sort."""
9576 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9579def FloatQuadruple(ctx=None):
9580 """Floating-point 128-bit (quadruple) sort."""
9582 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9585class FPRMSortRef(SortRef):
9586 """"Floating-point rounding mode sort."""
9590 """Return True if `s` is a Z3 floating-point sort.
9592 >>> is_fp_sort(FPSort(8, 24))
9594 >>> is_fp_sort(IntSort())
9597 return isinstance(s, FPSortRef)
9601 """Return True if `s` is a Z3 floating-point rounding mode sort.
9603 >>> is_fprm_sort(FPSort(8, 24))
9605 >>> is_fprm_sort(RNE().sort())
9608 return isinstance(s, FPRMSortRef)
9613class FPRef(ExprRef):
9614 """Floating-point expressions."""
9617 """Return the sort of the floating-point expression `self`.
9619 >>> x = FP('1.0', FPSort(8, 24))
9622 >>> x.sort() == FPSort(8, 24)
9625 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9628 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9629 >>> b = FPSort(8, 24)
9633 return self.sort().ebits()
9636 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9637 >>> b = FPSort(8, 24)
9641 return self.sort().sbits()
9643 def as_string(self):
9644 """Return a Z3 floating point expression as a Python string."""
9645 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9647 def __le__(self, other):
9648 return fpLEQ(self, other, self.ctx)
9650 def __lt__(self, other):
9651 return fpLT(self, other, self.ctx)
9653 def __ge__(self, other):
9654 return fpGEQ(self, other, self.ctx)
9656 def __gt__(self, other):
9657 return fpGT(self, other, self.ctx)
9659 def __add__(self, other):
9660 """Create the Z3 expression `self + other`.
9662 >>> x = FP('x', FPSort(8, 24))
9663 >>> y = FP('y', FPSort(8, 24))
9669 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9670 return fpAdd(_dflt_rm(), a, b, self.ctx)
9672 def __radd__(self, other):
9673 """Create the Z3 expression `other + self`.
9675 >>> x = FP('x', FPSort(8, 24))
9679 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9680 return fpAdd(_dflt_rm(), a, b, self.ctx)
9682 def __sub__(self, other):
9683 """Create the Z3 expression `self - other`.
9685 >>> x = FP('x', FPSort(8, 24))
9686 >>> y = FP('y', FPSort(8, 24))
9692 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9693 return fpSub(_dflt_rm(), a, b, self.ctx)
9695 def __rsub__(self, other):
9696 """Create the Z3 expression `other - self`.
9698 >>> x = FP('x', FPSort(8, 24))
9702 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9703 return fpSub(_dflt_rm(), a, b, self.ctx)
9705 def __mul__(self, other):
9706 """Create the Z3 expression `self * other`.
9708 >>> x = FP('x', FPSort(8, 24))
9709 >>> y = FP('y', FPSort(8, 24))
9717 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9718 return fpMul(_dflt_rm(), a, b, self.ctx)
9720 def __rmul__(self, other):
9721 """Create the Z3 expression `other * self`.
9723 >>> x = FP('x', FPSort(8, 24))
9724 >>> y = FP('y', FPSort(8, 24))
9730 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9731 return fpMul(_dflt_rm(), a, b, self.ctx)
9734 """Create the Z3 expression `+self`."""
9738 """Create the Z3 expression `-self`.
9740 >>> x = FP('x', Float32())
9746 def __div__(self, other):
9747 """Create the Z3 expression `self / other`.
9749 >>> x = FP('x', FPSort(8, 24))
9750 >>> y = FP('y', FPSort(8, 24))
9758 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9759 return fpDiv(_dflt_rm(), a, b, self.ctx)
9761 def __rdiv__(self, other):
9762 """Create the Z3 expression `other / self`.
9764 >>> x = FP('x', FPSort(8, 24))
9765 >>> y = FP('y', FPSort(8, 24))
9771 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9772 return fpDiv(_dflt_rm(), a, b, self.ctx)
9774 def __truediv__(self, other):
9775 """Create the Z3 expression division `self / other`."""
9776 return self.__div__(other)
9778 def __rtruediv__(self, other):
9779 """Create the Z3 expression division `other / self`."""
9780 return self.__rdiv__(other)
9782 def __mod__(self, other):
9783 """Create the Z3 expression mod `self % other`."""
9784 return fpRem(self, other)
9786 def __rmod__(self, other):
9787 """Create the Z3 expression mod `other % self`."""
9788 return fpRem(other, self)
9791class FPRMRef(ExprRef):
9792 """Floating-point rounding mode expressions"""
9794 def as_string(self):
9795 """Return a Z3 floating point expression as a Python string."""
9796 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9799def RoundNearestTiesToEven(ctx=None):
9801 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9806 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9809def RoundNearestTiesToAway(ctx=None):
9811 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9816 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9819def RoundTowardPositive(ctx=None):
9821 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9826 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9829def RoundTowardNegative(ctx=None):
9831 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9836 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9839def RoundTowardZero(ctx=None):
9841 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9846 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9850 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9859 return isinstance(a, FPRMRef)
9862def is_fprm_value(a):
9863 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9864 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9869class FPNumRef(FPRef):
9870 """The sign of the numeral.
9872 >>> x = FPVal(+1.0, FPSort(8, 24))
9875 >>> x = FPVal(-1.0, FPSort(8, 24))
9881 num = (ctypes.c_int)()
9882 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9884 raise Z3Exception("error retrieving the sign of a numeral.")
9885 return num.value != 0
9887 """The sign of a floating-point numeral as a bit-vector expression.
9889 Remark: NaN's are invalid arguments.
9892 def sign_as_bv(self):
9893 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9895 """The significand of the numeral.
9897 >>> x = FPVal(2.5, FPSort(8, 24))
9902 def significand(self):
9903 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
9905 """The significand of the numeral as a long.
9907 >>> x = FPVal(2.5, FPSort(8, 24))
9908 >>> x.significand_as_long()
9912 def significand_as_long(self):
9913 ptr = (ctypes.c_ulonglong * 1)()
9914 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
9915 raise Z3Exception("error retrieving the significand of a numeral.")
9918 """The significand of the numeral as a bit-vector expression.
9920 Remark: NaN are invalid arguments.
9923 def significand_as_bv(self):
9924 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9926 """The exponent of the numeral.
9928 >>> x = FPVal(2.5, FPSort(8, 24))
9933 def exponent(self, biased=True):
9934 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
9936 """The exponent of the numeral as a long.
9938 >>> x = FPVal(2.5, FPSort(8, 24))
9939 >>> x.exponent_as_long()
9943 def exponent_as_long(self, biased=True):
9944 ptr = (ctypes.c_longlong * 1)()
9945 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
9946 raise Z3Exception("error retrieving the exponent of a numeral.")
9949 """The exponent of the numeral as a bit-vector expression.
9951 Remark: NaNs are invalid arguments.
9954 def exponent_as_bv(self, biased=True):
9955 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
9957 """Indicates whether the numeral is a NaN."""
9960 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
9962 """Indicates whether the numeral is +oo or -oo."""
9965 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
9967 """Indicates whether the numeral is +zero or -zero."""
9970 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
9972 """Indicates whether the numeral is normal."""
9975 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
9977 """Indicates whether the numeral is subnormal."""
9979 def isSubnormal(self):
9980 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
9982 """Indicates whether the numeral is positive."""
9984 def isPositive(self):
9985 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
9987 """Indicates whether the numeral is negative."""
9989 def isNegative(self):
9990 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
9993 The string representation of the numeral.
9995 >>> x = FPVal(20, FPSort(8, 24))
10000 def as_string(self):
10001 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
10002 return ("FPVal(%s, %s)" % (s, self.sort()))
10006 """Return `True` if `a` is a Z3 floating-point expression.
10008 >>> b = FP('b', FPSort(8, 24))
10013 >>> is_fp(Int('x'))
10016 return isinstance(a, FPRef)
10020 """Return `True` if `a` is a Z3 floating-point numeral value.
10022 >>> b = FP('b', FPSort(8, 24))
10025 >>> b = FPVal(1.0, FPSort(8, 24))
10031 return is_fp(a) and _is_numeral(a.ctx, a.ast)
10034def FPSort(ebits, sbits, ctx=None):
10035 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
10037 >>> Single = FPSort(8, 24)
10038 >>> Double = FPSort(11, 53)
10041 >>> x = Const('x', Single)
10042 >>> eq(x, FP('x', FPSort(8, 24)))
10045 ctx = _get_ctx(ctx)
10046 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
10049def _to_float_str(val, exp=0):
10050 if isinstance(val, float):
10051 if math.isnan(val):
10054 sone = math.copysign(1.0, val)
10059 elif val == float("+inf"):
10061 elif val == float("-inf"):
10064 v = val.as_integer_ratio()
10067 rvs = str(num) + "/" + str(den)
10068 res = rvs + "p" + _to_int_str(exp)
10069 elif isinstance(val, bool):
10076 elif isinstance(val, str):
10077 inx = val.find("*(2**")
10080 elif val[-1] == ")":
10082 exp = str(int(val[inx + 5:-1]) + int(exp))
10084 _z3_assert(False, "String does not have floating-point numeral form.")
10086 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10090 return res + "p" + exp
10094 """Create a Z3 floating-point NaN term.
10096 >>> s = FPSort(8, 24)
10097 >>> set_fpa_pretty(True)
10100 >>> pb = get_fpa_pretty()
10101 >>> set_fpa_pretty(False)
10103 fpNaN(FPSort(8, 24))
10104 >>> set_fpa_pretty(pb)
10106 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10107 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10110def fpPlusInfinity(s):
10111 """Create a Z3 floating-point +oo term.
10113 >>> s = FPSort(8, 24)
10114 >>> pb = get_fpa_pretty()
10115 >>> set_fpa_pretty(True)
10116 >>> fpPlusInfinity(s)
10118 >>> set_fpa_pretty(False)
10119 >>> fpPlusInfinity(s)
10120 fpPlusInfinity(FPSort(8, 24))
10121 >>> set_fpa_pretty(pb)
10123 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10124 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10127def fpMinusInfinity(s):
10128 """Create a Z3 floating-point -oo term."""
10129 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10130 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10133def fpInfinity(s, negative):
10134 """Create a Z3 floating-point +oo or -oo term."""
10135 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10136 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10137 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10141 """Create a Z3 floating-point +0.0 term."""
10142 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10143 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10147 """Create a Z3 floating-point -0.0 term."""
10148 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10149 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10152def fpZero(s, negative):
10153 """Create a Z3 floating-point +0.0 or -0.0 term."""
10154 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10155 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10156 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10159def FPVal(sig, exp=None, fps=None, ctx=None):
10160 """Return a floating-point value of value `val` and sort `fps`.
10161 If `ctx=None`, then the global context is used.
10163 >>> v = FPVal(20.0, FPSort(8, 24))
10166 >>> print("0x%.8x" % v.exponent_as_long(False))
10168 >>> v = FPVal(2.25, FPSort(8, 24))
10171 >>> v = FPVal(-2.25, FPSort(8, 24))
10174 >>> FPVal(-0.0, FPSort(8, 24))
10176 >>> FPVal(0.0, FPSort(8, 24))
10178 >>> FPVal(+0.0, FPSort(8, 24))
10181 ctx = _get_ctx(ctx)
10182 if is_fp_sort(exp):
10186 fps = _dflt_fps(ctx)
10187 _z3_assert(is_fp_sort(fps), "sort mismatch")
10190 val = _to_float_str(sig)
10191 if val == "NaN" or val == "nan":
10193 elif val == "-0.0":
10194 return fpMinusZero(fps)
10195 elif val == "0.0" or val == "+0.0":
10196 return fpPlusZero(fps)
10197 elif val == "+oo" or val == "+inf" or val == "+Inf":
10198 return fpPlusInfinity(fps)
10199 elif val == "-oo" or val == "-inf" or val == "-Inf":
10200 return fpMinusInfinity(fps)
10202 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10205def FP(name, fpsort, ctx=None):
10206 """Return a floating-point constant named `name`.
10207 `fpsort` is the floating-point sort.
10208 If `ctx=None`, then the global context is used.
10210 >>> x = FP('x', FPSort(8, 24))
10217 >>> word = FPSort(8, 24)
10218 >>> x2 = FP('x', word)
10222 if isinstance(fpsort, FPSortRef) and ctx is None:
10225 ctx = _get_ctx(ctx)
10226 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10229def FPs(names, fpsort, ctx=None):
10230 """Return an array of floating-point constants.
10232 >>> x, y, z = FPs('x y z', FPSort(8, 24))
10239 >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
10242 ctx = _get_ctx(ctx)
10243 if isinstance(names, str):
10244 names = names.split(" ")
10245 return [FP(name, fpsort, ctx) for name in names]
10248def fpAbs(a, ctx=None):
10249 """Create a Z3 floating-point absolute value expression.
10251 >>> s = FPSort(8, 24)
10253 >>> x = FPVal(1.0, s)
10256 >>> y = FPVal(-20.0, s)
10260 fpAbs(-1.25*(2**4))
10261 >>> fpAbs(-1.25*(2**4))
10262 fpAbs(-1.25*(2**4))
10263 >>> fpAbs(x).sort()
10266 ctx = _get_ctx(ctx)
10267 [a] = _coerce_fp_expr_list([a], ctx)
10268 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10271def fpNeg(a, ctx=None):
10272 """Create a Z3 floating-point addition expression.
10274 >>> s = FPSort(8, 24)
10279 >>> fpNeg(x).sort()
10282 ctx = _get_ctx(ctx)
10283 [a] = _coerce_fp_expr_list([a], ctx)
10284 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10287def _mk_fp_unary(f, rm, a, ctx):
10288 ctx = _get_ctx(ctx)
10289 [a] = _coerce_fp_expr_list([a], ctx)
10291 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10292 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10293 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10296def _mk_fp_unary_pred(f, a, ctx):
10297 ctx = _get_ctx(ctx)
10298 [a] = _coerce_fp_expr_list([a], ctx)
10300 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10301 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10304def _mk_fp_bin(f, rm, a, b, ctx):
10305 ctx = _get_ctx(ctx)
10306 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10308 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10309 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10310 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10313def _mk_fp_bin_norm(f, a, b, ctx):
10314 ctx = _get_ctx(ctx)
10315 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10317 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10318 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10321def _mk_fp_bin_pred(f, a, b, ctx):
10322 ctx = _get_ctx(ctx)
10323 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10325 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10326 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10329def _mk_fp_tern(f, rm, a, b, c, ctx):
10330 ctx = _get_ctx(ctx)
10331 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10333 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10334 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10335 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10336 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10339def fpAdd(rm, a, b, ctx=None):
10340 """Create a Z3 floating-point addition expression.
10342 >>> s = FPSort(8, 24)
10346 >>> fpAdd(rm, x, y)
10348 >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
10350 >>> fpAdd(rm, x, y).sort()
10353 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10356def fpSub(rm, a, b, ctx=None):
10357 """Create a Z3 floating-point subtraction expression.
10359 >>> s = FPSort(8, 24)
10363 >>> fpSub(rm, x, y)
10365 >>> fpSub(rm, x, y).sort()
10368 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10371def fpMul(rm, a, b, ctx=None):
10372 """Create a Z3 floating-point multiplication expression.
10374 >>> s = FPSort(8, 24)
10378 >>> fpMul(rm, x, y)
10380 >>> fpMul(rm, x, y).sort()
10383 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10386def fpDiv(rm, a, b, ctx=None):
10387 """Create a Z3 floating-point division expression.
10389 >>> s = FPSort(8, 24)
10393 >>> fpDiv(rm, x, y)
10395 >>> fpDiv(rm, x, y).sort()
10398 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10401def fpRem(a, b, ctx=None):
10402 """Create a Z3 floating-point remainder expression.
10404 >>> s = FPSort(8, 24)
10409 >>> fpRem(x, y).sort()
10412 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10415def fpMin(a, b, ctx=None):
10416 """Create a Z3 floating-point minimum expression.
10418 >>> s = FPSort(8, 24)
10424 >>> fpMin(x, y).sort()
10427 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10430def fpMax(a, b, ctx=None):
10431 """Create a Z3 floating-point maximum expression.
10433 >>> s = FPSort(8, 24)
10439 >>> fpMax(x, y).sort()
10442 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10445def fpFMA(rm, a, b, c, ctx=None):
10446 """Create a Z3 floating-point fused multiply-add expression.
10448 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10451def fpSqrt(rm, a, ctx=None):
10452 """Create a Z3 floating-point square root expression.
10454 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10457def fpRoundToIntegral(rm, a, ctx=None):
10458 """Create a Z3 floating-point roundToIntegral expression.
10460 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10463def fpIsNaN(a, ctx=None):
10464 """Create a Z3 floating-point isNaN expression.
10466 >>> s = FPSort(8, 24)
10472 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10475def fpIsInf(a, ctx=None):
10476 """Create a Z3 floating-point isInfinite expression.
10478 >>> s = FPSort(8, 24)
10483 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10486def fpIsZero(a, ctx=None):
10487 """Create a Z3 floating-point isZero expression.
10489 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10492def fpIsNormal(a, ctx=None):
10493 """Create a Z3 floating-point isNormal expression.
10495 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10498def fpIsSubnormal(a, ctx=None):
10499 """Create a Z3 floating-point isSubnormal expression.
10501 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10504def fpIsNegative(a, ctx=None):
10505 """Create a Z3 floating-point isNegative expression.
10507 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10510def fpIsPositive(a, ctx=None):
10511 """Create a Z3 floating-point isPositive expression.
10513 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10516def _check_fp_args(a, b):
10518 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10521def fpLT(a, b, ctx=None):
10522 """Create the Z3 floating-point expression `other < self`.
10524 >>> x, y = FPs('x y', FPSort(8, 24))
10527 >>> (x < y).sexpr()
10530 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10533def fpLEQ(a, b, ctx=None):
10534 """Create the Z3 floating-point expression `other <= self`.
10536 >>> x, y = FPs('x y', FPSort(8, 24))
10539 >>> (x <= y).sexpr()
10542 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10545def fpGT(a, b, ctx=None):
10546 """Create the Z3 floating-point expression `other > self`.
10548 >>> x, y = FPs('x y', FPSort(8, 24))
10551 >>> (x > y).sexpr()
10554 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10557def fpGEQ(a, b, ctx=None):
10558 """Create the Z3 floating-point expression `other >= self`.
10560 >>> x, y = FPs('x y', FPSort(8, 24))
10563 >>> (x >= y).sexpr()
10566 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10569def fpEQ(a, b, ctx=None):
10570 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10572 >>> x, y = FPs('x y', FPSort(8, 24))
10575 >>> fpEQ(x, y).sexpr()
10578 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10581def fpNEQ(a, b, ctx=None):
10582 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10584 >>> x, y = FPs('x y', FPSort(8, 24))
10587 >>> (x != y).sexpr()
10590 return Not(fpEQ(a, b, ctx))
10593def fpFP(sgn, exp, sig, ctx=None):
10594 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10596 >>> s = FPSort(8, 24)
10597 >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
10599 fpFP(1, 127, 4194304)
10600 >>> xv = FPVal(-1.5, s)
10603 >>> slvr = Solver()
10604 >>> slvr.add(fpEQ(x, xv))
10607 >>> xv = FPVal(+1.5, s)
10610 >>> slvr = Solver()
10611 >>> slvr.add(fpEQ(x, xv))
10615 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10616 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10617 ctx = _get_ctx(ctx)
10618 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10619 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10622def fpToFP(a1, a2=None, a3=None, ctx=None):
10623 """Create a Z3 floating-point conversion expression from other term sorts
10626 From a bit-vector term in IEEE 754-2008 format:
10627 >>> x = FPVal(1.0, Float32())
10628 >>> x_bv = fpToIEEEBV(x)
10629 >>> simplify(fpToFP(x_bv, Float32()))
10632 From a floating-point term with different precision:
10633 >>> x = FPVal(1.0, Float32())
10634 >>> x_db = fpToFP(RNE(), x, Float64())
10639 >>> x_r = RealVal(1.5)
10640 >>> simplify(fpToFP(RNE(), x_r, Float32()))
10643 From a signed bit-vector term:
10644 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10645 >>> simplify(fpToFP(RNE(), x_signed, Float32()))
10648 ctx = _get_ctx(ctx)
10649 if is_bv(a1) and is_fp_sort(a2):
10650 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10651 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10652 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10653 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10654 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10655 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10656 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10658 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10661def fpBVToFP(v, sort, ctx=None):
10662 """Create a Z3 floating-point conversion expression that represents the
10663 conversion from a bit-vector term to a floating-point term.
10665 >>> x_bv = BitVecVal(0x3F800000, 32)
10666 >>> x_fp = fpBVToFP(x_bv, Float32())
10672 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10673 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10674 ctx = _get_ctx(ctx)
10675 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10678def fpFPToFP(rm, v, sort, ctx=None):
10679 """Create a Z3 floating-point conversion expression that represents the
10680 conversion from a floating-point term to a floating-point term of different precision.
10682 >>> x_sgl = FPVal(1.0, Float32())
10683 >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
10686 >>> simplify(x_dbl)
10691 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10692 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10693 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10694 ctx = _get_ctx(ctx)
10695 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10698def fpRealToFP(rm, v, sort, ctx=None):
10699 """Create a Z3 floating-point conversion expression that represents the
10700 conversion from a real term to a floating-point term.
10702 >>> x_r = RealVal(1.5)
10703 >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
10709 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10710 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10711 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10712 ctx = _get_ctx(ctx)
10713 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10716def fpSignedToFP(rm, v, sort, ctx=None):
10717 """Create a Z3 floating-point conversion expression that represents the
10718 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10720 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10721 >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
10723 fpToFP(RNE(), 4294967291)
10727 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10728 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10729 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10730 ctx = _get_ctx(ctx)
10731 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10734def fpUnsignedToFP(rm, v, sort, ctx=None):
10735 """Create a Z3 floating-point conversion expression that represents the
10736 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10738 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10739 >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
10741 fpToFPUnsigned(RNE(), 4294967291)
10745 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10746 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10747 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10748 ctx = _get_ctx(ctx)
10749 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10752def fpToFPUnsigned(rm, x, s, ctx=None):
10753 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10755 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10756 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10757 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10758 ctx = _get_ctx(ctx)
10759 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10762def fpToSBV(rm, x, s, ctx=None):
10763 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10765 >>> x = FP('x', FPSort(8, 24))
10766 >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
10767 >>> print(is_fp(x))
10769 >>> print(is_bv(y))
10771 >>> print(is_fp(y))
10773 >>> print(is_bv(x))
10777 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10778 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10779 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10780 ctx = _get_ctx(ctx)
10781 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10784def fpToUBV(rm, x, s, ctx=None):
10785 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10787 >>> x = FP('x', FPSort(8, 24))
10788 >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
10789 >>> print(is_fp(x))
10791 >>> print(is_bv(y))
10793 >>> print(is_fp(y))
10795 >>> print(is_bv(x))
10799 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10800 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10801 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10802 ctx = _get_ctx(ctx)
10803 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10806def fpToReal(x, ctx=None):
10807 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10809 >>> x = FP('x', FPSort(8, 24))
10810 >>> y = fpToReal(x)
10811 >>> print(is_fp(x))
10813 >>> print(is_real(y))
10815 >>> print(is_fp(y))
10817 >>> print(is_real(x))
10821 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10822 ctx = _get_ctx(ctx)
10823 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10826def fpToIEEEBV(x, ctx=None):
10827 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10829 The size of the resulting bit-vector is automatically determined.
10831 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10832 knows only one NaN and it will always produce the same bit-vector representation of
10835 >>> x = FP('x', FPSort(8, 24))
10836 >>> y = fpToIEEEBV(x)
10837 >>> print(is_fp(x))
10839 >>> print(is_bv(y))
10841 >>> print(is_fp(y))
10843 >>> print(is_bv(x))
10847 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10848 ctx = _get_ctx(ctx)
10849 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10852#########################################
10854# Strings, Sequences and Regular expressions
10856#########################################
10858class SeqSortRef(SortRef):
10859 """Sequence sort."""
10861 def is_string(self):
10862 """Determine if sort is a string
10863 >>> s = StringSort()
10866 >>> s = SeqSort(IntSort())
10870 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10873 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10875class CharSortRef(SortRef):
10876 """Character sort."""
10879def StringSort(ctx=None):
10880 """Create a string sort
10881 >>> s = StringSort()
10885 ctx = _get_ctx(ctx)
10886 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10888def CharSort(ctx=None):
10889 """Create a character sort
10890 >>> ch = CharSort()
10894 ctx = _get_ctx(ctx)
10895 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
10899 """Create a sequence sort over elements provided in the argument
10900 >>> s = SeqSort(IntSort())
10901 >>> s == Unit(IntVal(1)).sort()
10904 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
10907class SeqRef(ExprRef):
10908 """Sequence expression."""
10911 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
10913 def __add__(self, other):
10914 return Concat(self, other)
10916 def __radd__(self, other):
10917 return Concat(other, self)
10919 def __getitem__(self, i):
10921 i = IntVal(i, self.ctx)
10922 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10926 i = IntVal(i, self.ctx)
10927 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10929 def is_string(self):
10930 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
10932 def is_string_value(self):
10933 return Z3_is_string(self.ctx_ref(), self.as_ast())
10935 def as_string(self):
10936 """Return a string representation of sequence expression."""
10937 if self.is_string_value():
10938 string_length = ctypes.c_uint()
10939 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
10940 return string_at(chars, size=string_length.value).decode("latin-1")
10941 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
10943 def __le__(self, other):
10944 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10946 def __lt__(self, other):
10947 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10949 def __ge__(self, other):
10950 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10952 def __gt__(self, other):
10953 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10956def _coerce_char(ch, ctx=None):
10957 if isinstance(ch, str):
10958 ctx = _get_ctx(ctx)
10959 ch = CharVal(ch, ctx)
10960 if not is_expr(ch):
10961 raise Z3Exception("Character expression expected")
10964class CharRef(ExprRef):
10965 """Character expression."""
10967 def __le__(self, other):
10968 other = _coerce_char(other, self.ctx)
10969 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10972 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
10975 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
10977 def is_digit(self):
10978 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
10981def CharVal(ch, ctx=None):
10982 ctx = _get_ctx(ctx)
10983 if isinstance(ch, str):
10985 if not isinstance(ch, int):
10986 raise Z3Exception("character value should be an ordinal")
10987 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
10990 if not is_expr(bv):
10991 raise Z3Exception("Bit-vector expression needed")
10992 return _to_expr_ref(Z3_mk_char_from_bv(bv.ctx_ref(), bv.as_ast()), bv.ctx)
10994def CharToBv(ch, ctx=None):
10995 ch = _coerce_char(ch, ctx)
10998def CharToInt(ch, ctx=None):
10999 ch = _coerce_char(ch, ctx)
11002def CharIsDigit(ch, ctx=None):
11003 ch = _coerce_char(ch, ctx)
11004 return ch.is_digit()
11006def _coerce_seq(s, ctx=None):
11007 if isinstance(s, str):
11008 ctx = _get_ctx(ctx)
11009 s = StringVal(s, ctx)
11011 raise Z3Exception("Non-expression passed as a sequence")
11013 raise Z3Exception("Non-sequence passed as a sequence")
11017def _get_ctx2(a, b, ctx=None):
11028 """Return `True` if `a` is a Z3 sequence expression.
11029 >>> print (is_seq(Unit(IntVal(0))))
11031 >>> print (is_seq(StringVal("abc")))
11034 return isinstance(a, SeqRef)
11038 """Return `True` if `a` is a Z3 string expression.
11039 >>> print (is_string(StringVal("ab")))
11042 return isinstance(a, SeqRef) and a.is_string()
11045def is_string_value(a):
11046 """return 'True' if 'a' is a Z3 string constant expression.
11047 >>> print (is_string_value(StringVal("a")))
11049 >>> print (is_string_value(StringVal("a") + StringVal("b")))
11052 return isinstance(a, SeqRef) and a.is_string_value()
11054def StringVal(s, ctx=None):
11055 """create a string expression"""
11056 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
11057 ctx = _get_ctx(ctx)
11058 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
11061def String(name, ctx=None):
11062 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
11064 >>> x = String('x')
11066 ctx = _get_ctx(ctx)
11067 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
11070def Strings(names, ctx=None):
11071 """Return a tuple of String constants. """
11072 ctx = _get_ctx(ctx)
11073 if isinstance(names, str):
11074 names = names.split(" ")
11075 return [String(name, ctx) for name in names]
11078def SubString(s, offset, length):
11079 """Extract substring or subsequence starting at offset"""
11080 return Extract(s, offset, length)
11083def SubSeq(s, offset, length):
11084 """Extract substring or subsequence starting at offset"""
11085 return Extract(s, offset, length)
11089 """Create the empty sequence of the given sort
11090 >>> e = Empty(StringSort())
11091 >>> e2 = StringVal("")
11092 >>> print(e.eq(e2))
11094 >>> e3 = Empty(SeqSort(IntSort()))
11097 >>> e4 = Empty(ReSort(SeqSort(IntSort())))
11099 Empty(ReSort(Seq(Int)))
11101 if isinstance(s, SeqSortRef):
11102 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11103 if isinstance(s, ReSortRef):
11104 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11105 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11109 """Create the regular expression that accepts the universal language
11110 >>> e = Full(ReSort(SeqSort(IntSort())))
11112 Full(ReSort(Seq(Int)))
11113 >>> e1 = Full(ReSort(StringSort()))
11115 Full(ReSort(String))
11117 if isinstance(s, ReSortRef):
11118 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11119 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11124 """Create a singleton sequence"""
11125 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11129 """Check if 'a' is a prefix of 'b'
11130 >>> s1 = PrefixOf("ab", "abc")
11133 >>> s2 = PrefixOf("bc", "abc")
11137 ctx = _get_ctx2(a, b)
11138 a = _coerce_seq(a, ctx)
11139 b = _coerce_seq(b, ctx)
11140 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11144 """Check if 'a' is a suffix of 'b'
11145 >>> s1 = SuffixOf("ab", "abc")
11148 >>> s2 = SuffixOf("bc", "abc")
11152 ctx = _get_ctx2(a, b)
11153 a = _coerce_seq(a, ctx)
11154 b = _coerce_seq(b, ctx)
11155 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11159 """Check if 'a' contains 'b'
11160 >>> s1 = Contains("abc", "ab")
11163 >>> s2 = Contains("abc", "bc")
11166 >>> x, y, z = Strings('x y z')
11167 >>> s3 = Contains(Concat(x,y,z), y)
11171 ctx = _get_ctx2(a, b)
11172 a = _coerce_seq(a, ctx)
11173 b = _coerce_seq(b, ctx)
11174 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11177def Replace(s, src, dst):
11178 """Replace the first occurrence of 'src' by 'dst' in 's'
11179 >>> r = Replace("aaa", "a", "b")
11183 ctx = _get_ctx2(dst, s)
11184 if ctx is None and is_expr(src):
11186 src = _coerce_seq(src, ctx)
11187 dst = _coerce_seq(dst, ctx)
11188 s = _coerce_seq(s, ctx)
11189 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11192def IndexOf(s, substr, offset=None):
11193 """Retrieve the index of substring within a string starting at a specified offset.
11194 >>> simplify(IndexOf("abcabc", "bc", 0))
11196 >>> simplify(IndexOf("abcabc", "bc", 2))
11202 if is_expr(offset):
11204 ctx = _get_ctx2(s, substr, ctx)
11205 s = _coerce_seq(s, ctx)
11206 substr = _coerce_seq(substr, ctx)
11207 if _is_int(offset):
11208 offset = IntVal(offset, ctx)
11209 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11212def LastIndexOf(s, substr):
11213 """Retrieve the last index of substring within a string"""
11215 ctx = _get_ctx2(s, substr, ctx)
11216 s = _coerce_seq(s, ctx)
11217 substr = _coerce_seq(substr, ctx)
11218 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11222 """Obtain the length of a sequence 's'
11223 >>> l = Length(StringVal("abc"))
11228 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11231 """Map function 'f' over sequence 's'"""
11232 ctx = _get_ctx2(f, s)
11233 s = _coerce_seq(s, ctx)
11234 return _to_expr_ref(Z3_mk_seq_map(s.ctx_ref(), f.as_ast(), s.as_ast()), ctx)
11236def SeqMapI(f, i, s):
11237 """Map function 'f' over sequence 's' at index 'i'"""
11238 ctx = _get_ctx(f, s)
11239 s = _coerce_seq(s, ctx)
11242 return _to_expr_ref(Z3_mk_seq_mapi(s.ctx_ref(), f.as_ast(), i.as_ast(), s.as_ast()), ctx)
11244def SeqFoldLeft(f, a, s):
11245 ctx = _get_ctx2(f, s)
11246 s = _coerce_seq(s, ctx)
11248 return _to_expr_ref(Z3_mk_seq_foldl(s.ctx_ref(), f.as_ast(), a.as_ast(), s.as_ast()), ctx)
11250def SeqFoldLeftI(f, i, a, s):
11251 ctx = _get_ctx2(f, s)
11252 s = _coerce_seq(s, ctx)
11255 return _to_expr_ref(Z3_mk_seq_foldli(s.ctx_ref(), f.as_ast(), i.as_ast(), a.as_ast(), s.as_ast()), ctx)
11258 """Convert string expression to integer
11259 >>> a = StrToInt("1")
11260 >>> simplify(1 == a)
11262 >>> b = StrToInt("2")
11263 >>> simplify(1 == b)
11265 >>> c = StrToInt(IntToStr(2))
11266 >>> simplify(1 == c)
11270 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11274 """Convert integer expression to string"""
11277 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11281 """Convert a unit length string to integer code"""
11284 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11287 """Convert code to a string"""
11290 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11292def Re(s, ctx=None):
11293 """The regular expression that accepts sequence 's'
11295 >>> s2 = Re(StringVal("ab"))
11296 >>> s3 = Re(Unit(BoolVal(True)))
11298 s = _coerce_seq(s, ctx)
11299 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11302# Regular expressions
11304class ReSortRef(SortRef):
11305 """Regular expression sort."""
11308 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11313 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11314 if s is None or isinstance(s, Context):
11316 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11317 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11320class ReRef(ExprRef):
11321 """Regular expressions."""
11323 def __add__(self, other):
11324 return Union(self, other)
11328 return isinstance(s, ReRef)
11332 """Create regular expression membership test
11333 >>> re = Union(Re("a"),Re("b"))
11334 >>> print (simplify(InRe("a", re)))
11336 >>> print (simplify(InRe("b", re)))
11338 >>> print (simplify(InRe("c", re)))
11341 s = _coerce_seq(s, re.ctx)
11342 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11346 """Create union of regular expressions.
11347 >>> re = Union(Re("a"), Re("b"), Re("c"))
11348 >>> print (simplify(InRe("d", re)))
11351 args = _get_args(args)
11354 _z3_assert(sz > 0, "At least one argument expected.")
11355 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11360 for i in range(sz):
11361 v[i] = args[i].as_ast()
11362 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11365def Intersect(*args):
11366 """Create intersection of regular expressions.
11367 >>> re = Intersect(Re("a"), Re("b"), Re("c"))
11369 args = _get_args(args)
11372 _z3_assert(sz > 0, "At least one argument expected.")
11373 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11378 for i in range(sz):
11379 v[i] = args[i].as_ast()
11380 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11384 """Create the regular expression accepting one or more repetitions of argument.
11385 >>> re = Plus(Re("a"))
11386 >>> print(simplify(InRe("aa", re)))
11388 >>> print(simplify(InRe("ab", re)))
11390 >>> print(simplify(InRe("", re)))
11394 _z3_assert(is_expr(re), "expression expected")
11395 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11399 """Create the regular expression that optionally accepts the argument.
11400 >>> re = Option(Re("a"))
11401 >>> print(simplify(InRe("a", re)))
11403 >>> print(simplify(InRe("", re)))
11405 >>> print(simplify(InRe("aa", re)))
11409 _z3_assert(is_expr(re), "expression expected")
11410 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11414 """Create the complement regular expression."""
11415 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11419 """Create the regular expression accepting zero or more repetitions of argument.
11420 >>> re = Star(Re("a"))
11421 >>> print(simplify(InRe("aa", re)))
11423 >>> print(simplify(InRe("ab", re)))
11425 >>> print(simplify(InRe("", re)))
11429 _z3_assert(is_expr(re), "expression expected")
11430 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11433def Loop(re, lo, hi=0):
11434 """Create the regular expression accepting between a lower and upper bound repetitions
11435 >>> re = Loop(Re("a"), 1, 3)
11436 >>> print(simplify(InRe("aa", re)))
11438 >>> print(simplify(InRe("aaaa", re)))
11440 >>> print(simplify(InRe("", re)))
11444 _z3_assert(is_expr(re), "expression expected")
11445 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11448def Range(lo, hi, ctx=None):
11449 """Create the range regular expression over two sequences of length 1
11450 >>> range = Range("a","z")
11451 >>> print(simplify(InRe("b", range)))
11453 >>> print(simplify(InRe("bb", range)))
11456 lo = _coerce_seq(lo, ctx)
11457 hi = _coerce_seq(hi, ctx)
11459 _z3_assert(is_expr(lo), "expression expected")
11460 _z3_assert(is_expr(hi), "expression expected")
11461 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11463def Diff(a, b, ctx=None):
11464 """Create the difference regular expression
11467 _z3_assert(is_expr(a), "expression expected")
11468 _z3_assert(is_expr(b), "expression expected")
11469 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11471def AllChar(regex_sort, ctx=None):
11472 """Create a regular expression that accepts all single character strings
11474 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11479def PartialOrder(a, index):
11480 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11483def LinearOrder(a, index):
11484 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11487def TreeOrder(a, index):
11488 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11491def PiecewiseLinearOrder(a, index):
11492 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11495def TransitiveClosure(f):
11496 """Given a binary relation R, such that the two arguments have the same sort
11497 create the transitive closure relation R+.
11498 The transitive closure R+ is a new relation.
11500 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11504 super(ctypes.c_void_p, ast).__init__(ptr)
11507def to_ContextObj(ptr,):
11508 ctx = ContextObj(ptr)
11509 super(ctypes.c_void_p, ctx).__init__(ptr)
11512def to_AstVectorObj(ptr,):
11513 v = AstVectorObj(ptr)
11514 super(ctypes.c_void_p, v).__init__(ptr)
11517# NB. my-hacky-class only works for a single instance of OnClause
11518# it should be replaced with a proper correlation between OnClause
11519# and object references that can be passed over the FFI.
11520# for UserPropagator we use a global dictionary, which isn't great code.
11522_my_hacky_class = None
11523def on_clause_eh(ctx, p, n, dep, clause):
11524 onc = _my_hacky_class
11525 p = _to_expr_ref(to_Ast(p), onc.ctx)
11526 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11527 deps = [dep[i] for i in range(n)]
11528 onc.on_clause(p, deps, clause)
11530_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11533 def __init__(self, s, on_clause):
11536 self.on_clause = on_clause
11538 global _my_hacky_class
11539 _my_hacky_class = self
11540 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11544 def __init__(self):
11548 def set_threaded(self):
11549 if self.lock is None:
11551 self.lock = threading.Lock()
11553 def get(self, ctx):
11556 r = self.bases[ctx]
11558 r = self.bases[ctx]
11561 def set(self, ctx, r):
11564 self.bases[ctx] = r
11566 self.bases[ctx] = r
11568 def insert(self, r):
11571 id = len(self.bases) + 3
11574 id = len(self.bases) + 3
11579_prop_closures = None
11582def ensure_prop_closures():
11583 global _prop_closures
11584 if _prop_closures is None:
11585 _prop_closures = PropClosures()
11588def user_prop_push(ctx, cb):
11589 prop = _prop_closures.get(ctx)
11594def user_prop_pop(ctx, cb, num_scopes):
11595 prop = _prop_closures.get(ctx)
11597 prop.pop(num_scopes)
11600def user_prop_fresh(ctx, _new_ctx):
11601 _prop_closures.set_threaded()
11602 prop = _prop_closures.get(ctx)
11604 Z3_del_context(nctx.ctx)
11605 new_ctx = to_ContextObj(_new_ctx)
11607 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11609 new_prop = prop.fresh(nctx)
11610 _prop_closures.set(new_prop.id, new_prop)
11614def user_prop_fixed(ctx, cb, id, value):
11615 prop = _prop_closures.get(ctx)
11618 id = _to_expr_ref(to_Ast(id), prop.ctx())
11619 value = _to_expr_ref(to_Ast(value), prop.ctx())
11620 prop.fixed(id, value)
11623def user_prop_created(ctx, cb, id):
11624 prop = _prop_closures.get(ctx)
11627 id = _to_expr_ref(to_Ast(id), prop.ctx())
11632def user_prop_final(ctx, cb):
11633 prop = _prop_closures.get(ctx)
11639def user_prop_eq(ctx, cb, x, y):
11640 prop = _prop_closures.get(ctx)
11643 x = _to_expr_ref(to_Ast(x), prop.ctx())
11644 y = _to_expr_ref(to_Ast(y), prop.ctx())
11648def user_prop_diseq(ctx, cb, x, y):
11649 prop = _prop_closures.get(ctx)
11652 x = _to_expr_ref(to_Ast(x), prop.ctx())
11653 y = _to_expr_ref(to_Ast(y), prop.ctx())
11657def user_prop_decide(ctx, cb, t, idx, phase):
11658 prop = _prop_closures.get(ctx)
11661 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11662 prop.decide(t, idx, phase)
11666_user_prop_push = Z3_push_eh(user_prop_push)
11667_user_prop_pop = Z3_pop_eh(user_prop_pop)
11668_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11669_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11670_user_prop_created = Z3_created_eh(user_prop_created)
11671_user_prop_final = Z3_final_eh(user_prop_final)
11672_user_prop_eq = Z3_eq_eh(user_prop_eq)
11673_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11674_user_prop_decide = Z3_decide_eh(user_prop_decide)
11677def PropagateFunction(name, *sig):
11678 """Create a function that gets tracked by user propagator.
11679 Every term headed by this function symbol is tracked.
11680 If a term is fixed and the fixed callback is registered a
11681 callback is invoked that the term headed by this function is fixed.
11683 sig = _get_args(sig)
11685 _z3_assert(len(sig) > 0, "At least two arguments expected")
11686 arity = len(sig) - 1
11689 _z3_assert(is_sort(rng), "Z3 sort expected")
11690 dom = (Sort * arity)()
11691 for i in range(arity):
11693 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11694 dom[i] = sig[i].ast
11696 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11700class UserPropagateBase:
11703 # Either solver is set or ctx is set.
11704 # Propagators that are created through callbacks
11705 # to "fresh" inherit the context of that is supplied
11706 # as argument to the callback.
11707 # This context should not be deleted. It is owned by the solver.
11709 def __init__(self, s, ctx=None):
11710 assert s is None or ctx is None
11711 ensure_prop_closures()
11714 self.fresh_ctx = None
11716 self.id = _prop_closures.insert(self)
11721 self.created = None
11723 self.fresh_ctx = ctx
11725 Z3_solver_propagate_init(self.ctx_ref(),
11727 ctypes.c_void_p(self.id),
11734 self._ctx.ctx = None
11738 return self.fresh_ctx
11740 return self.solver.ctx
11743 return self.ctx().ref()
11745 def add_fixed(self, fixed):
11746 assert not self.fixed
11747 assert not self._ctx
11749 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11752 def add_created(self, created):
11753 assert not self.created
11754 assert not self._ctx
11756 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11757 self.created = created
11759 def add_final(self, final):
11760 assert not self.final
11761 assert not self._ctx
11763 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11766 def add_eq(self, eq):
11768 assert not self._ctx
11770 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11773 def add_diseq(self, diseq):
11774 assert not self.diseq
11775 assert not self._ctx
11777 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11780 def add_decide(self, decide):
11781 assert not self.decide
11782 assert not self._ctx
11784 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11785 self.decide = decide
11788 raise Z3Exception("push needs to be overwritten")
11790 def pop(self, num_scopes):
11791 raise Z3Exception("pop needs to be overwritten")
11793 def fresh(self, new_ctx):
11794 raise Z3Exception("fresh needs to be overwritten")
11797 assert not self._ctx
11799 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11801 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11804 # Tell the solver to perform the next split on a given term
11805 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11806 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11808 def next_split(self, t, idx, phase):
11809 return Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11812 # Propagation can only be invoked as during a fixed or final callback.
11814 def propagate(self, e, ids, eqs=[]):
11815 _ids, num_fixed = _to_ast_array(ids)
11817 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11818 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11819 return Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11820 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11822 def conflict(self, deps = [], eqs = []):
11823 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
approx(self, precision=10)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, m=None, ctx=None)
__deepcopy__(self, memo={})
__init__(self, ast, ctx=None)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__init__(self, v=None, ctx=None)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, *args, **kws)
__deepcopy__(self, memo={})
__init__(self, name, ctx=None)
declare(self, name, *args)
declare_core(self, name, rec_name, *args)
__deepcopy__(self, memo={})
__init__(self, entry, ctx)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__deepcopy__(self, memo={})
assert_exprs(self, *args)
dimacs(self, include_names=True)
simplify(self, *arguments, **keywords)
convert_model(self, model)
__init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
__deepcopy__(self, memo={})
eval(self, t, model_completion=False)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
check(self, *assumptions)
__exit__(self, *exc_info)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_sort Z3_API Z3_mk_int_sort(Z3_context c)
Create the integer type.
Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const *domain, Z3_sort range)
Create an array type with N arguments.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_denominator(Z3_context c, Z3_ast a)
Return the denominator (as a numeral AST) of a numeral AST of sort Real.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
void Z3_API Z3_solver_assert_and_track(Z3_context c, Z3_solver s, Z3_ast a, Z3_ast p)
Assert a constraint a into the solver, and track it (in the unsat) core using the Boolean constant p.
Z3_ast Z3_API Z3_func_interp_get_else(Z3_context c, Z3_func_interp f)
Return the 'else' value of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsge(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than or equal to.
void Z3_API Z3_ast_map_inc_ref(Z3_context c, Z3_ast_map m)
Increment the reference counter of the given AST map.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
Z3_ast Z3_API Z3_mk_bvsle(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than or equal to.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_ast Z3_API Z3_ast_map_find(Z3_context c, Z3_ast_map m, Z3_ast k)
Return the value associated with the key k.
Z3_string Z3_API Z3_ast_map_to_string(Z3_context c, Z3_ast_map m)
Convert the given map into a string.
Z3_string Z3_API Z3_param_descrs_to_string(Z3_context c, Z3_param_descrs p)
Convert a parameter description set into a string. This function is mainly used for printing the cont...
Z3_ast Z3_API Z3_mk_zero_ext(Z3_context c, unsigned i, Z3_ast t1)
Extend the given bit-vector with zeros to the (unsigned) equivalent bit-vector of size m+i,...
void Z3_API Z3_solver_set_params(Z3_context c, Z3_solver s, Z3_params p)
Set the given solver using the given parameters.
Z3_ast Z3_API Z3_mk_set_intersect(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the intersection of a list of sets.
Z3_params Z3_API Z3_mk_params(Z3_context c)
Create a Z3 (empty) parameter set. Starting at Z3 4.0, parameter sets are used to configure many comp...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
Z3_ast Z3_API Z3_mk_set_subset(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Check for subsetness of sets.
Z3_ast Z3_API Z3_mk_bvule(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than or equal to.
Z3_ast Z3_API Z3_mk_full_set(Z3_context c, Z3_sort domain)
Create the full set.
Z3_param_kind Z3_API Z3_param_descrs_get_kind(Z3_context c, Z3_param_descrs p, Z3_symbol n)
Return the kind associated with the given parameter name n.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_mk_set_union(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the union of a list of sets.
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
Z3_ast Z3_API Z3_mk_bvsdiv_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
void Z3_API Z3_ast_vector_set(Z3_context c, Z3_ast_vector v, unsigned i, Z3_ast a)
Update position i of the AST vector v with the AST a.
Z3_ast Z3_API Z3_mk_bvxor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise exclusive-or.
Z3_string Z3_API Z3_stats_to_string(Z3_context c, Z3_stats s)
Convert a statistics into a string.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, unsigned num_bound, Z3_app const bound[], Z3_ast body)
Create a lambda expression using a list of constants that form the set of bound variables.
void Z3_API Z3_solver_dec_ref(Z3_context c, Z3_solver s)
Decrement the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_bvslt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than.
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
bool Z3_API Z3_ast_map_contains(Z3_context c, Z3_ast_map m, Z3_ast k)
Return true if the map m contains the AST key k.
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_symbol Z3_API Z3_get_quantifier_skolem_id(Z3_context c, Z3_ast a)
Obtain skolem id of quantifier.
Z3_ast Z3_API Z3_get_numerator(Z3_context c, Z3_ast a)
Return the numerator (as a numeral AST) of a numeral AST of sort Real.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_ast Z3_API Z3_mk_and(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] and ... and args[num_args-1].
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
Z3_symbol Z3_API Z3_param_descrs_get_name(Z3_context c, Z3_param_descrs p, unsigned i)
Return the name of the parameter at given index i.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
Z3_ast Z3_API Z3_mk_false(Z3_context c)
Create an AST node representing false.
Z3_ast_vector Z3_API Z3_ast_map_keys(Z3_context c, Z3_ast_map m)
Return the keys stored in the given map.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null,...
void Z3_API Z3_del_constructor(Z3_context c, Z3_constructor constr)
Reclaim memory allocated to constructor.
Z3_ast Z3_API Z3_mk_bvsgt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than.
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context....
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_mk_set_complement(Z3_context c, Z3_ast arg)
Take the complement of a set.
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.
bool Z3_API Z3_stats_is_uint(Z3_context c, Z3_stats s, unsigned idx)
Return true if the given statistical data is a unsigned integer.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_ast Z3_API Z3_mk_extract(Z3_context c, unsigned high, unsigned low, Z3_ast t1)
Extract the bits high down to low from a bit-vector of size m to yield a new bit-vector of size n,...
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
Z3_ast Z3_API Z3_mk_set_add(Z3_context c, Z3_ast set, Z3_ast elem)
Add an element to a set.
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.
Z3_ast Z3_API Z3_mk_bvadd_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
Z3_ast Z3_API Z3_mk_bvadd_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
Z3_ast Z3_API Z3_mk_array_default(Z3_context c, Z3_ast array)
Access the array default value. Produces the default range value, for arrays that can be represented ...
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.
Z3_constructor Z3_API Z3_mk_constructor(Z3_context c, Z3_symbol name, Z3_symbol recognizer, unsigned num_fields, Z3_symbol const field_names[], Z3_sort_opt const sorts[], unsigned sort_refs[])
Create a constructor.
Z3_ast_vector Z3_API Z3_ast_vector_translate(Z3_context s, Z3_ast_vector v, Z3_context t)
Translate the AST vector v from context s into an AST vector in context t.
void Z3_API Z3_func_entry_inc_ref(Z3_context c, Z3_func_entry e)
Increment the reference counter of the given Z3_func_entry object.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.
Z3_ast Z3_API Z3_mk_bvsub_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
void Z3_API Z3_solver_push(Z3_context c, Z3_solver s)
Create a backtracking point.
Z3_ast Z3_API Z3_mk_bvsub_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
Z3_ast Z3_API Z3_mk_bvudiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned division.
Z3_string Z3_API Z3_ast_vector_to_string(Z3_context c, Z3_ast_vector v)
Convert AST vector into a string.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
bool Z3_API Z3_is_numeral_ast(Z3_context c, Z3_ast a)
Z3_ast Z3_API Z3_mk_bvsrem(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows dividend).
bool Z3_API Z3_is_as_array(Z3_context c, Z3_ast a)
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3....
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
Z3_ast Z3_API Z3_mk_is_int(Z3_context c, Z3_ast t1)
Check if a real number is an integer.
void Z3_API Z3_params_set_bool(Z3_context c, Z3_params p, Z3_symbol k, bool v)
Add a Boolean parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.
Z3_ast Z3_API Z3_mk_sign_ext(Z3_context c, unsigned i, Z3_ast t1)
Sign-extend of the given bit-vector to the (signed) equivalent bit-vector of size m+i,...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
void Z3_API Z3_stats_inc_ref(Z3_context c, Z3_stats s)
Increment the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs)
n-ary Array read. The argument a is the array and idxs are the indices of the array that gets read.
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
void Z3_API Z3_func_interp_inc_ref(Z3_context c, Z3_func_interp f)
Increment the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_set_double(Z3_context c, Z3_params p, Z3_symbol k, double v)
Add a double parameter k with value v to the parameter set p.
Z3_string Z3_API Z3_param_descrs_get_documentation(Z3_context c, Z3_param_descrs p, Z3_symbol s)
Retrieve documentation string corresponding to parameter name s.
Z3_sort Z3_API Z3_mk_datatype_sort(Z3_context c, Z3_symbol name)
create a forward reference to a recursive datatype being declared. The forward reference can be used ...
Z3_solver Z3_API Z3_mk_solver(Z3_context c)
Create a new solver. This solver is a "combined solver" (see combined_solver module) that internally ...
Z3_model Z3_API Z3_solver_get_model(Z3_context c, Z3_solver s)
Retrieve the model for the last Z3_solver_check or Z3_solver_check_assumptions.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
Z3_func_decl Z3_API Z3_get_as_array_func_decl(Z3_context c, Z3_ast a)
Return the function declaration f associated with a (_ as_array f) node.
Z3_ast Z3_API Z3_mk_ext_rotate_left(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the left t2 times.
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
void Z3_API Z3_params_set_uint(Z3_context c, Z3_params p, Z3_symbol k, unsigned v)
Add a unsigned parameter k with value v to the parameter set p.
Z3_lbool Z3_API Z3_solver_check_assumptions(Z3_context c, Z3_solver s, unsigned num_assumptions, Z3_ast const assumptions[])
Check whether the assertions in the given solver and optional assumptions are consistent or not.
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.
Z3_ast Z3_API Z3_mk_bvashr(Z3_context c, Z3_ast t1, Z3_ast t2)
Arithmetic shift right.
Z3_ast Z3_API Z3_mk_bv2int(Z3_context c, Z3_ast t1, bool is_signed)
Create an integer from the bit-vector argument t1. If is_signed is false, then the bit-vector t1 is t...
Z3_sort Z3_API Z3_get_array_sort_domain_n(Z3_context c, Z3_sort t, unsigned idx)
Return the i'th domain sort of an n-dimensional array.
Z3_ast Z3_API Z3_mk_set_del(Z3_context c, Z3_ast set, Z3_ast elem)
Remove an element to a set.
Z3_ast Z3_API Z3_mk_bvmul_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
Z3_ast Z3_API Z3_mk_bvor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise or.
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th constructor.
void Z3_API Z3_ast_vector_resize(Z3_context c, Z3_ast_vector v, unsigned n)
Resize the AST vector v.
Z3_ast Z3_API Z3_mk_quantifier_const_ex(Z3_context c, bool is_forall, unsigned weight, Z3_symbol quantifier_id, Z3_symbol skolem_id, unsigned num_bound, Z3_app const bound[], unsigned num_patterns, Z3_pattern const patterns[], unsigned num_no_patterns, Z3_ast const no_patterns[], Z3_ast body)
Create a universal or existential quantifier using a list of constants that will form the set of boun...
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[])
Create a pattern for quantifier instantiation.
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
unsigned Z3_API Z3_stats_get_uint_value(Z3_context c, Z3_stats s, unsigned idx)
Return the unsigned value of the given statistical data.
Z3_sort Z3_API Z3_get_array_sort_domain(Z3_context c, Z3_sort t)
Return the domain of the given array sort. In the case of a multi-dimensional array,...
Z3_ast Z3_API Z3_mk_bvmul_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflo...
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
Z3_ast Z3_API Z3_mk_bvadd(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement addition.
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.
void Z3_API Z3_params_dec_ref(Z3_context c, Z3_params p)
Decrement the reference counter of the given parameter set.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
unsigned Z3_API Z3_ast_map_size(Z3_context c, Z3_ast_map m)
Return the size of the given map.
unsigned Z3_API Z3_param_descrs_size(Z3_context c, Z3_param_descrs p)
Return the number of parameters in the given parameter description set.
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
double Z3_API Z3_stats_get_double_value(Z3_context c, Z3_stats s, unsigned idx)
Return the double value of the given statistical data.
Z3_ast Z3_API Z3_mk_bvugt(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than.
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_ast Z3_API Z3_pattern_to_ast(Z3_context c, Z3_pattern p)
Convert a Z3_pattern into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_bvnot(Z3_context c, Z3_ast t1)
Bitwise negation.
Z3_ast Z3_API Z3_mk_bvurem(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned remainder.
void Z3_API Z3_mk_datatypes(Z3_context c, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort sorts[], Z3_constructor_list constructor_lists[])
Create mutually recursive datatypes.
unsigned Z3_API Z3_func_interp_get_arity(Z3_context c, Z3_func_interp f)
Return the arity (number of arguments) of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.
Z3_ast Z3_API Z3_mk_seq_concat(Z3_context c, unsigned n, Z3_ast const args[])
Concatenate sequences.
Z3_sort Z3_API Z3_mk_enumeration_sort(Z3_context c, Z3_symbol name, unsigned n, Z3_symbol const enum_names[], Z3_func_decl enum_consts[], Z3_func_decl enum_testers[])
Create a enumeration sort.
unsigned Z3_API Z3_get_bv_sort_size(Z3_context c, Z3_sort t)
Return the size of the given bit-vector sort.
Z3_ast Z3_API Z3_mk_set_member(Z3_context c, Z3_ast elem, Z3_ast set)
Check for set membership.
void Z3_API Z3_ast_vector_dec_ref(Z3_context c, Z3_ast_vector v)
Decrement the reference counter of the given AST vector.
void Z3_API Z3_func_interp_dec_ref(Z3_context c, Z3_func_interp f)
Decrement the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_inc_ref(Z3_context c, Z3_params p)
Increment the reference counter of the given parameter set.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
Z3_sort Z3_API Z3_mk_bv_sort(Z3_context c, unsigned sz)
Create a bit-vector type of the given size.
Z3_ast Z3_API Z3_mk_bvult(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than.
void Z3_API Z3_ast_map_dec_ref(Z3_context c, Z3_ast_map m)
Decrement the reference counter of the given AST map.
Z3_string Z3_API Z3_params_to_string(Z3_context c, Z3_params p)
Convert a parameter set into a string. This function is mainly used for printing the contents of a pa...
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.
void Z3_API Z3_func_entry_dec_ref(Z3_context c, Z3_func_entry e)
Decrement the reference counter of the given Z3_func_entry object.
unsigned Z3_API Z3_stats_size(Z3_context c, Z3_stats s)
Return the number of statistical data in s.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.
void Z3_API Z3_param_descrs_dec_ref(Z3_context c, Z3_param_descrs p)
Decrement the reference counter of the given parameter description set.
Z3_model Z3_API Z3_mk_model(Z3_context c)
Create a fresh model object. It has reference count 0.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
Z3_ast Z3_API Z3_mk_bvneg_no_overflow(Z3_context c, Z3_ast t1)
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
Z3_string Z3_API Z3_stats_get_key(Z3_context c, Z3_stats s, unsigned idx)
Return the key (a string) for a particular statistical data.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast Z3_API Z3_mk_bvsmod(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows divisor).
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_ast Z3_API Z3_mk_int2bv(Z3_context c, unsigned n, Z3_ast t1)
Create an n bit bit-vector from the integer argument t1.
void Z3_API Z3_solver_assert(Z3_context c, Z3_solver s, Z3_ast a)
Assert a constraint into the solver.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.
unsigned Z3_API Z3_solver_get_num_scopes(Z3_context c, Z3_solver s)
Return the number of backtracking points.
Z3_sort Z3_API Z3_get_array_sort_range(Z3_context c, Z3_sort t)
Return the range of the given array sort.
void Z3_API Z3_del_constructor_list(Z3_context c, Z3_constructor_list clist)
Reclaim memory allocated for constructor list.
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_ast Z3_API Z3_func_entry_get_arg(Z3_context c, Z3_func_entry e, unsigned i)
Return an argument of a Z3_func_entry object.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
void Z3_API Z3_ast_vector_inc_ref(Z3_context c, Z3_ast_vector v)
Increment the reference counter of the given AST vector.
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_ast Z3_API Z3_mk_set_has_size(Z3_context c, Z3_ast set, Z3_ast k)
Create predicate that holds if Boolean array set has k elements set to true.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
void Z3_API Z3_solver_pop(Z3_context c, Z3_solver s, unsigned n)
Backtrack n backtracking points.
void Z3_API Z3_ast_map_erase(Z3_context c, Z3_ast_map m, Z3_ast k)
Erase a key from the map.
Z3_ast Z3_API Z3_mk_int2real(Z3_context c, Z3_ast t1)
Coerce an integer to a real.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
void Z3_API Z3_params_validate(Z3_context c, Z3_params p, Z3_param_descrs d)
Validate the parameter set p against the parameter description set d.
Z3_func_decl Z3_API Z3_get_datatype_sort_recognizer(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th recognizer.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_ast_vector_push(Z3_context c, Z3_ast_vector v, Z3_ast a)
Add the AST a in the end of the AST vector v. The size of v is increased by one.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
Z3_ast Z3_API Z3_mk_map(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast const *args)
Map f on the argument arrays.
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
void Z3_API Z3_param_descrs_inc_ref(Z3_context c, Z3_param_descrs p)
Increment the reference counter of the given parameter description set.
void Z3_API Z3_stats_dec_ref(Z3_context c, Z3_stats s)
Decrement the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_array_ext(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create array extensionality index given two arrays with the same sort. The meaning is given by the ax...
Z3_ast Z3_API Z3_mk_re_concat(Z3_context c, unsigned n, Z3_ast const args[])
Create the concatenation of the regular languages.
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
Z3_func_entry Z3_API Z3_func_interp_get_entry(Z3_context c, Z3_func_interp f, unsigned i)
Return a "point" of the given function interpretation. It represents the value of f in a particular p...
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....
Z3_ast Z3_API Z3_mk_concat(Z3_context c, Z3_ast t1, Z3_ast t2)
Concatenate the given bit-vectors.
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
Z3_constructor_list Z3_API Z3_mk_constructor_list(Z3_context c, unsigned num_constructors, Z3_constructor const constructors[])
Create list of constructors.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
Z3_ast Z3_API Z3_mk_bvneg(Z3_context c, Z3_ast t1)
Standard two's complement unary minus.
Z3_ast Z3_API Z3_mk_store_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs, Z3_ast v)
n-ary Array update.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
Z3_sort Z3_API Z3_mk_bool_sort(Z3_context c)
Create the Boolean type.
void Z3_API Z3_params_set_symbol(Z3_context c, Z3_params p, Z3_symbol k, Z3_symbol v)
Add a symbol parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_ast_vector_get(Z3_context c, Z3_ast_vector v, unsigned i)
Return the AST at position i in the AST vector v.
Z3_func_decl Z3_API Z3_to_func_decl(Z3_context c, Z3_ast a)
Convert an AST into a FUNC_DECL_AST. This is just type casting.
Z3_ast Z3_API Z3_mk_set_difference(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Take the set difference between two sets.
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_ast Z3_API Z3_mk_bvlshr(Z3_context c, Z3_ast t1, Z3_ast t2)
Logical shift right.
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_not(Z3_context c, Z3_ast a)
Create an AST node representing not(a).
Z3_ast Z3_API Z3_mk_or(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] or ... or args[num_args-1].
Z3_sort Z3_API Z3_mk_array_sort(Z3_context c, Z3_sort domain, Z3_sort range)
Create an array type.
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
Z3_ast Z3_API Z3_mk_seq_extract(Z3_context c, Z3_ast s, Z3_ast offset, Z3_ast length)
Extract subsequence starting at offset of length.
Z3_sort Z3_API Z3_mk_type_variable(Z3_context c, Z3_symbol s)
Create a type variable.
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.
Z3_ast Z3_API Z3_mk_bvuge(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than or equal to.
Z3_string Z3_API Z3_get_numeral_binary_string(Z3_context c, Z3_ast a)
Return numeral value, as a binary string of a numeric constant term.
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
unsigned Z3_API Z3_func_interp_get_num_entries(Z3_context c, Z3_func_interp f)
Return the number of entries in the given function interpretation.
void Z3_API Z3_ast_map_insert(Z3_context c, Z3_ast_map m, Z3_ast k, Z3_ast v)
Store/Replace a new key, value pair in the given map.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_real2int(Z3_context c, Z3_ast t1)
Coerce a real to an integer.
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.
Z3_ast Z3_API Z3_mk_ext_rotate_right(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the right t2 times.
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor_accessor(Z3_context c, Z3_sort t, unsigned idx_c, unsigned idx_a)
Return idx_a'th accessor for the idx_c'th constructor.
Z3_ast Z3_API Z3_mk_bvredor(Z3_context c, Z3_ast t1)
Take disjunction of bits in vector, return vector of length 1.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
void Z3_API Z3_solver_reset(Z3_context c, Z3_solver s)
Remove all assertions from the solver.
bool Z3_API Z3_is_algebraic_number(Z3_context c, Z3_ast a)
Return true if the given AST is a real algebraic number.
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
_ctx_from_ast_args(*args)
_to_func_decl_ref(a, ctx)
_valid_accessor(acc)
Datatypes.
BitVec(name, bv, ctx=None)
DeclareSort(name, ctx=None)
RecAddDefinition(f, args, body)
DeclareTypeVar(name, ctx=None)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
_coerce_expr_list(alist, ctx=None)
RealVector(prefix, sz, ctx=None)
BitVecs(names, bv, ctx=None)
BoolVector(prefix, sz, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
FreshReal(prefix="b", ctx=None)
_reduce(func, sequence, initial)
BVAddNoOverflow(a, b, signed)
FreshBool(prefix="b", ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
IntVector(prefix, sz, ctx=None)
RealVarVector(n, ctx=None)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])