def test_lira(self):
varA = Symbol("A", REAL)
varB = Symbol("B", INT)
with self.assertRaises(PysmtTypeError):
f = And(LT(varA, Plus(varA, Real(1))), GT(varA,
Minus(varB, Int(1))))
f = And(LT(varA, Plus(varA, Real(1))),
GT(varA, ToReal(Minus(varB, Int(1)))))
g = Equals(varA, ToReal(varB))
self.assertUnsat(And(f, g, Equals(varA, Real(1.2))),
"Formula was expected to be unsat",
logic=QF_UFLIRA)
def test_toreal(self):
p = Symbol("p", INT)
rp = ToReal(p)
self.assertEqual(rp.to_smtlib(daggify=False), "(to_real p)")
self.assertEqual(rp.to_smtlib(daggify=True),
"(let ((.def_0 (to_real p))) .def_0)")
def test_dependencies_not_includes_toreal(self):
p = Symbol("p", INT)
r = ToReal(p)
deps = r.get_free_variables()
self.assertIn(p, deps)
self.assertNotIn(r, deps)
def test_qe_z3(self):
qe = QuantifierEliminator(name='z3')
self._bool_example(qe)
self._real_example(qe)
self._int_example(qe)
self._alternation_bool_example(qe)
self._alternation_real_example(qe)
self._alternation_int_example(qe)
self._std_examples(qe, LRA)
self._std_examples(qe, LIA)
# Additional test for raising error on back conversion of
# quantified formulae
p, q = Symbol("p", INT), Symbol("q", INT)
f = ForAll([p], Exists([q], Equals(ToReal(p),
Plus(ToReal(q), ToReal(Int(1))))))
with self.assertRaises(NotImplementedError):
qe.eliminate_quantifiers(f).simplify()
def get_full_example_formulae(environment=None):
"""Return a list of Examples using the given environment."""
if environment is None:
environment = get_env()
with environment:
x = Symbol("x", BOOL)
y = Symbol("y", BOOL)
p = Symbol("p", INT)
q = Symbol("q", INT)
r = Symbol("r", REAL)
s = Symbol("s", REAL)
aii = Symbol("aii", ARRAY_INT_INT)
ari = Symbol("ari", ArrayType(REAL, INT))
arb = Symbol("arb", ArrayType(REAL, BV8))
abb = Symbol("abb", ArrayType(BV8, BV8))
nested_a = Symbol("a_arb_aii",
ArrayType(ArrayType(REAL, BV8), ARRAY_INT_INT))
rf = Symbol("rf", FunctionType(REAL, [REAL, REAL]))
rg = Symbol("rg", FunctionType(REAL, [REAL]))
ih = Symbol("ih", FunctionType(INT, [REAL, INT]))
ig = Symbol("ig", FunctionType(INT, [INT]))
bf = Symbol("bf", FunctionType(BOOL, [BOOL]))
bg = Symbol("bg", FunctionType(BOOL, [BOOL]))
bv8 = Symbol("bv1", BV8)
bv16 = Symbol("bv2", BV16)
result = [
# Formula, is_valid, is_sat, is_qf
Example(hr="(x & y)",
expr=And(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x <-> y)",
expr=Iff(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="((x | y) & (! (x | y)))",
expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x & (! y))",
expr=And(x, Not(y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(False -> True)",
expr=Implies(FALSE(), TRUE()),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# LIA
#
Example(hr="((q < p) & (x -> y))",
expr=And(GT(p, q), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(((p + q) = 5) & (q < p))",
expr=And(Equals(Plus(p, q), Int(5)), GT(p, q)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="((q <= p) | (p <= q))",
expr=Or(GE(p, q), LE(p, q)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(! (p < (q * 2)))",
expr=Not(LT(p, Times(q, Int(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (p - (5 - 2)))",
expr=GT(Minus(p, Minus(Int(5), Int(2))), p),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_IDL),
Example(hr="((x ? 7 : ((p + -1) * 3)) = q)",
expr=Equals(
Ite(x, Int(7), Times(Plus(p, Int(-1)), Int(3))), q),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (q + 1))",
expr=LT(p, Plus(q, Int(1))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
#
# LRA
#
Example(hr="((s < r) & (x -> y))",
expr=And(GT(r, s), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(((r + s) = 28/5) & (s < r))",
expr=And(Equals(Plus(r, s), Real(Fraction("5.6"))),
GT(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((s <= r) | (r <= s))",
expr=Or(GE(r, s), LE(r, s)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(! ((r * 2.0) < (s * 2.0)))",
expr=Not(LT(Div(r, Real((1, 2))), Times(s, Real(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(! (r < (r - (5.0 - 2.0))))",
expr=Not(GT(Minus(r, Minus(Real(5), Real(2))), r)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="((x ? 7.0 : ((s + -1.0) * 3.0)) = r)",
expr=Equals(
Ite(x, Real(7), Times(Plus(s, Real(-1)), Real(3))), r),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
#
# EUF
#
Example(hr="(bf(x) <-> bg(x))",
expr=Iff(Function(bf, (x, )), Function(bg, (x, ))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UF),
Example(hr="(rf(5.0, rg(r)) = 0.0)",
expr=Equals(Function(rf, (Real(5), Function(rg, (r, )))),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(hr="((rg(r) = (5.0 + 2.0)) <-> (rg(r) = 7.0))",
expr=Iff(Equals(Function(rg, [r]), Plus(Real(5), Real(2))),
Equals(Function(rg, [r]), Real(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(
hr="((r = (s + 1.0)) & (rg(s) = 5.0) & (rg((r - 1.0)) = 7.0))",
expr=And([
Equals(r, Plus(s, Real(1))),
Equals(Function(rg, [s]), Real(5)),
Equals(Function(rg, [Minus(r, Real(1))]), Real(7))
]),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLRA),
#
# BV
#
Example(hr="((1_32 & 0_32) = 0_32)",
expr=Equals(BVAnd(BVOne(32), BVZero(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((! 2_3) = 5_3)",
expr=Equals(BVNot(BV("010")), BV("101")),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((7_3 xor 0_3) = 0_3)",
expr=Equals(BVXor(BV("111"), BV("000")), BV("000")),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv1::bv1) u< 0_16)",
expr=BVULT(BVConcat(bv8, bv8), BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(1_32[0:7] = 1_8)",
expr=Equals(BVExtract(BVOne(32), end=7), BVOne(8)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_8 u< (((bv1 + 1_8) * 5_8) u/ 5_8))",
expr=BVUGT(
BVUDiv(BVMul(BVAdd(bv8, BVOne(8)), BV(5, width=8)),
BV(5, width=8)), BVZero(8)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 u<= bv2)",
expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 s<= bv2)",
expr=BVSGE(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(
hr="((0_32 u< (5_32 u% 2_32)) & ((5_32 u% 2_32) u<= 1_32))",
expr=And(
BVUGT(BVURem(BV(5, width=32), BV(2, width=32)),
BVZero(32)),
BVULE(BVURem(BV(5, width=32), BV(2, width=32)),
BVOne(32))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((((1_32 + (- 1_32)) << 1_32) >> 1_32) = 1_32)",
expr=Equals(
BVLShr(BVLShl(BVAdd(BVOne(32), BVNeg(BVOne(32))), 1),
1), BVOne(32)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((1_32 - 1_32) = 0_32)",
expr=Equals(BVSub(BVOne(32), BVOne(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Rotations
Example(hr="(((1_32 ROL 1) ROR 1) = 1_32)",
expr=Equals(BVRor(BVRol(BVOne(32), 1), 1), BVOne(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Extensions
Example(hr="((0_5 ZEXT 11) = (0_1 SEXT 15))",
expr=Equals(BVZExt(BVZero(5), 11), BVSExt(BVZero(1), 15)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 - bv2) = 0_16)",
expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 - bv2)[0:7] = bv1)",
expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2[0:7] bvcomp bv1) = 1_1)",
expr=Equals(BVComp(BVExtract(bv16, 0, 7), bv8), BVOne(1)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 bvcomp bv2) = 0_1)",
expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 s< bv2)",
expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 s< 0_16)",
expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s< 0_16) | (0_16 s<= bv2))",
expr=Or(BVSGT(BVZero(16), bv16), BVSGE(bv16, BVZero(16))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 u< bv2)",
expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 u< 0_16)",
expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 | 0_16) = bv2)",
expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 & 0_16) = 0_16)",
expr=Equals(BVAnd(bv16, BVZero(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv2) & ((bv2 s/ 65535_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSDiv(bv16, SBV(-1, 16)), BVZero(16))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv2) & ((bv2 s% 1_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSRem(bv16, BVOne(16)), BVZero(16))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 u% 1_16) = 0_16)",
expr=Equals(BVURem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s% 1_16) = 0_16)",
expr=Equals(BVSRem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s% (- 1_16)) = 0_16)",
expr=Equals(BVSRem(bv16, BVNeg(BVOne(16))), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 a>> 0_16) = bv2)",
expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s<= bv2) & ((bv2 a>> 1_16) = (bv2 >> 1_16)))",
expr=And(
BVSLE(BVZero(16), bv16),
Equals(BVAShr(bv16, BVOne(16)),
BVLShr(bv16, BVOne(16)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
#
# Quantification
#
Example(hr="(forall y . (x -> y))",
expr=ForAll([y], Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(forall p, q . ((p + q) = 0))",
expr=ForAll([p, q], Equals(Plus(p, q), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LIA),
Example(
hr="(forall r, s . (((0.0 < r) & (0.0 < s)) -> ((r - s) < r)))",
expr=ForAll([r, s],
Implies(And(GT(r, Real(0)), GT(s, Real(0))),
(LT(Minus(r, s), r)))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(exists x, y . (x -> y))",
expr=Exists([x, y], Implies(x, y)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(exists p, q . ((p + q) = 0))",
expr=Exists([p, q], Equals(Plus(p, q), Int(0))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LIA),
Example(hr="(exists r . (forall s . (r < (r - s))))",
expr=Exists([r], ForAll([s], GT(Minus(r, s), r))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(forall r . (exists s . (r < (r - s))))",
expr=ForAll([r], Exists([s], GT(Minus(r, s), r))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(x & (forall r . ((r + s) = 5.0)))",
expr=And(x, ForAll([r], Equals(Plus(r, s), Real(5)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(exists x . ((x <-> (5.0 < s)) & (s < 3.0)))",
expr=Exists([x],
(And(Iff(x, GT(s, Real(5))), LT(s, Real(3))))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.LRA),
#
# UFLIRA
#
Example(hr="((p < ih(r, q)) & (x -> y))",
expr=And(GT(Function(ih, (r, q)), p), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((p - 3) = q) -> ((p < ih(r, (q + 3))) | (ih(r, p) <= p)))",
expr=Implies(
Equals(Minus(p, Int(3)), q),
Or(GT(Function(ih, (r, Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((ToReal((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (ih(r, p) <= p)))",
expr=Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(
ih,
(ToReal(Minus(p, Int(3))), Plus(q, Int(3)))),
p), LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(! (((ToReal((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (ih(r, p) <= p))))",
expr=Not(
Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(ih, (ToReal(Minus(
p, Int(3))), Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"""("Did you know that any string works? #yolo" & "10" & "|#somesolverskeepthe||" & " ")""",
expr=And(Symbol("Did you know that any string works? #yolo"),
Symbol("10"), Symbol("|#somesolverskeepthe||"),
Symbol(" ")),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# Arrays
#
Example(hr="((q = 0) -> (aii[0 := 0] = aii[0 := q]))",
expr=Implies(
Equals(q, Int(0)),
Equals(Store(aii, Int(0), Int(0)),
Store(aii, Int(0), q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="(aii[0 := 0][0] = 0)",
expr=Equals(Select(Store(aii, Int(0), Int(0)), Int(0)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="((Array{Int, Int}(0)[1 := 1] = aii) & (aii[1] = 0))",
expr=And(Equals(Array(INT, Int(0), {Int(1): Int(1)}), aii),
Equals(Select(aii, Int(1)), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")),
Example(hr="((Array{Int, Int}(0)[1 := 3] = aii) & (aii[1] = 3))",
expr=And(Equals(Array(INT, Int(0), {Int(1): Int(3)}), aii),
Equals(Select(aii, Int(1)), Int(3))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")),
Example(hr="((Array{Real, Int}(10) = ari) & (ari[6/5] = 0))",
expr=And(Equals(Array(REAL, Int(10)), ari),
Equals(Select(ari, Real((6, 5))), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40))))",
expr=And(
Equals(
Array(
REAL, Int(0), {
Real(1): Int(10),
Real(2): Int(20),
Real(3): Int(30),
Real(4): Int(40)
}), ari),
Not(
And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40][5.0 := 50] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40) & (ari[5.0] = 50))))",
expr=And(
Equals(
Array(
REAL, Int(0), {
Real(1): Int(10),
Real(2): Int(20),
Real(3): Int(30),
Real(4): Int(40),
Real(5): Int(50)
}), ari),
Not(
And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40)),
Equals(Select(ari, Real(5)), Int(50))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((a_arb_aii = Array{Array{Real, BV{8}}, Array{Int, Int}}(Array{Int, Int}(7))) -> (a_arb_aii[arb][42] = 7))",
expr=Implies(
Equals(nested_a,
Array(ArrayType(REAL, BV8), Array(INT, Int(7)))),
Equals(Select(Select(nested_a, arb), Int(42)), Int(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(hr="(abb[bv1 := y_][bv1 := z_] = abb[bv1 := z_])",
expr=Equals(
Store(Store(abb, bv8, Symbol("y_", BV8)), bv8,
Symbol("z_", BV8)),
Store(abb, bv8, Symbol("z_", BV8))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ABV),
Example(hr="((r / s) = (r * s))",
expr=Equals(Div(r, s), Times(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="(2.0 = (r * r))",
expr=Equals(Real(2), Times(r, r)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((p ^ 2) = 0)",
expr=Equals(Pow(p, Int(2)), Int(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NIA),
Example(hr="((r ^ 2.0) = 0.0)",
expr=Equals(Pow(r, Real(2)), Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((r * r * r) = 25.0)",
expr=Equals(Times(r, r, r), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((5.0 * r * 5.0) = 25.0)",
expr=Equals(Times(Real(5), r, Real(5)), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((p * p * p) = 25)",
expr=Equals(Times(p, p, p), Int(25)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_NIA),
Example(hr="((5 * p * 5) = 25)",
expr=Equals(Times(Int(5), p, Int(5)), Int(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(((1 - 1) * p * 1) = 0)",
expr=Equals(Times(Minus(Int(1), Int(1)), p, Int(1)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_LIA),
# Huge Fractions:
Example(
hr=
"((r * 1606938044258990275541962092341162602522202993782792835301376/7) = -20480000000000000000000000.0)",
expr=Equals(Times(r, Real(Fraction(2**200, 7))),
Real(-200**11)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(((r + 5.0 + s) * (s + 2.0 + r)) = 0.0)",
expr=Equals(
Times(Plus(r, Real(5), s), Plus(s, Real(2), r)),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(
hr=
"(((p + 5 + q) * (p - (q - 5))) = ((p * p) + (10 * p) + 25 + (-1 * q * q)))",
expr=Equals(
Times(Plus(p, Int(5), q), Minus(p, Minus(q, Int(5)))),
Plus(Times(p, p), Times(Int(10), p), Int(25),
Times(Int(-1), q, q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_NIA),
]
return result
def expr_to_pysmt(context: TranslationContext,
expr: Expr,
*,
is_expectation: bool = False,
allow_infinity: bool = False) -> FNode:
"""
Translate a pGCL expression to a pySMT formula.
Note that substitution expressions are not allowed here (they are not
supported in pySMT).
You can pass in the optional `is_expectation` parameter to have all integer
values converted to real values.
If `allow_infinity` is `True`, then infinity expressions will be mapped
directly to the `infinity` variable of the given
:py:class:`TranslationContext`. Take care to appropriately constrain the
`infinity` variable! Note that arithmetic expressions may not contain
infinity, to prevent expressions like `infinity - infinity`.
.. doctest::
>>> from probably.pgcl.parser import parse_expr
>>> from pysmt.shortcuts import Symbol
>>> from pysmt.typing import INT
>>> expr = parse_expr("x + 4 * 13")
>>> context = TranslationContext({"x": Symbol("x", INT)})
>>> expr_to_pysmt(context, expr)
(x + (4 * 13))
"""
if isinstance(expr, BoolLitExpr):
return TRUE() if expr.value else FALSE()
elif isinstance(expr, NatLitExpr):
if is_expectation:
return ToReal(Int(expr.value))
else:
return Int(expr.value)
elif isinstance(expr, FloatLitExpr):
if expr.is_infinite():
if not allow_infinity:
raise Exception(
f"Infinity is not allowed in this expression: {expr}")
return context.infinity
else:
return Real(Fraction(expr.value))
elif isinstance(expr, VarExpr):
var = context.variables[expr.var]
if is_expectation and get_type(var) == INT:
var = ToReal(var)
return var
elif isinstance(expr, UnopExpr):
operand = expr_to_pysmt(context,
expr.expr,
is_expectation=False,
allow_infinity=allow_infinity)
if expr.operator == Unop.NEG:
return Not(operand)
elif expr.operator == Unop.IVERSON:
return Ite(operand, Real(1), Real(0))
elif isinstance(expr, BinopExpr):
# `is_expectation` is disabled if we enter a non-arithmetic expression
# (we do not convert integers to reals within a boolean expression such
# as `x == y`, for example).
#
# Similarly, `allow_infinity` is disabled if we enter an arithmetic
# expression because calculations with infinity are hard to make sense of.
is_arith_op = expr.operator in [Binop.PLUS, Binop.MINUS, Binop.TIMES]
is_expectation = is_expectation # TODO: and is_arith_op
allow_infinity = allow_infinity # TODO: and not is_arith_op?!??!
lhs = expr_to_pysmt(context,
expr.lhs,
is_expectation=is_expectation,
allow_infinity=allow_infinity)
rhs = expr_to_pysmt(context,
expr.rhs,
is_expectation=is_expectation,
allow_infinity=allow_infinity)
if expr.operator == Binop.OR:
return Or(lhs, rhs)
elif expr.operator == Binop.AND:
return And(lhs, rhs)
elif expr.operator == Binop.LEQ:
return LE(lhs, rhs)
elif expr.operator == Binop.LE:
return LT(lhs, rhs)
elif expr.operator == Binop.EQ:
return EqualsOrIff(lhs, rhs)
elif expr.operator == Binop.PLUS:
return Plus(lhs, rhs)
elif expr.operator == Binop.MINUS:
return Ite(LE(lhs, rhs),
(Int(0) if get_type(lhs) == INT else Real(0)),
Minus(lhs, rhs))
elif expr.operator == Binop.TIMES:
return Times(lhs, rhs)
elif isinstance(expr, SubstExpr):
raise Exception("Substitution expression is not allowed here.")
raise Exception("unreachable")
def test_toreal(self):
p = Symbol("p", INT)
rp = ToReal(p)
rp_string = self.print_to_string(rp)
self.assertEqual(rp_string, "(to_real p)")
# We create a map from BitVectors to Reals, so that each bitvector
# value (interpreted as unary number) is equal to the Real
# value.
#
# The map is represented by an Array of type BV8 -> Real
map_type = ArrayType(BV8, REAL)
my_map = Symbol("my_map", map_type)
# Fill-up the map, by defining all 256 values:
for i in range(0, 255):
my_map = my_map.Store(BV(i, 8), Real(i))
# We want to find find a value for which our relation does not work.
# In other words, we ask if there is a value for the bitvector
# s.t. the corresponding value in the array is different from the
# unary interpretation of the bitvector.
bv_var = Symbol("bv", BV8)
int_var = Symbol("int", INT)
real_var = Symbol("real", REAL)
f = And(
# Convert the BV into INT
int_var.Equals(BVToNatural(bv_var)),
# Convert the INT into REAL
real_var.Equals(ToReal(int_var)),
# Compare the value stored in the map with the REAL value
my_map.Select(bv_var).NotEquals(real_var)
)
print(get_model(f)) # Indeed our range only gets up to 254!!!
def test_substitute_to_real(self):
p = Symbol("p", INT)
f = LT(ToReal(p), Real(0))
new_f = f.substitute({p: Real(1)}).simplify()
self.assertEqual(new_f, Bool(False))
def get_example_formulae(environment=None):
if environment is None:
environment = get_env()
with environment:
x = Symbol("x", BOOL)
y = Symbol("y", BOOL)
p = Symbol("p", INT)
q = Symbol("q", INT)
r = Symbol("r", REAL)
s = Symbol("s", REAL)
rf = Symbol("rf", FunctionType(REAL, [REAL, REAL]))
rg = Symbol("rg", FunctionType(REAL, [REAL]))
ih = Symbol("ih", FunctionType(INT, [REAL, INT]))
ig = Symbol("ig", FunctionType(INT, [INT]))
bv8 = Symbol("bv1", BV8)
bv16 = Symbol("bv2", BV16)
result = [
# Formula, is_valid, is_sat, is_qf
# x /\ y
Example(expr=And(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
# x <-> y
Example(expr=Iff(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
# (x \/ y ) /\ ! ( x \/ y )
Example(expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL),
# (x /\ !y)
Example(expr=And(x, Not(y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
# False -> True
Example(expr=Implies(FALSE(), TRUE()),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# LIA
#
# (p > q) /\ x -> y
Example(expr=And(GT(p, q), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_IDL),
# (p + q) = 5 /\ (p > q)
Example(expr=And(Equals(Plus(p, q), Int(5)), GT(p, q)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
# (p >= q) \/ ( p <= q)
Example(expr=Or(GE(p, q), LE(p, q)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_IDL),
# !( p < q * 2 )
Example(expr=Not(LT(p, Times(q, Int(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
# p - (5 - 2) > p
Example(expr=GT(Minus(p, Minus(Int(5), Int(2))), p),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_IDL),
# x ? 7: (p + -1) * 3 = q
Example(expr=Equals(
Ite(x, Int(7), Times(Plus(p, Int(-1)), Int(3))), q),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(expr=LT(p, Plus(q, Int(1))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
#
# LRA
#
# (r > s) /\ x -> y
Example(expr=And(GT(r, s), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_RDL),
# (r + s) = 5.6 /\ (r > s)
Example(expr=And(Equals(Plus(r, s), Real(Fraction("5.6"))),
GT(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
# (r >= s) \/ ( r <= s)
Example(expr=Or(GE(r, s), LE(r, s)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
# !( (r / (1/2)) < s * 2 )
Example(expr=Not(LT(Div(r, Real((1, 2))), Times(s, Real(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
# ! ( r - (5 - 2) > r )
Example(expr=Not(GT(Minus(r, Minus(Real(5), Real(2))), r)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
# x ? 7: (s + -1) * 3 = r
Example(expr=Equals(
Ite(x, Real(7), Times(Plus(s, Real(-1)), Real(3))), r),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
#
# EUF
#
# rf(5, rg(2)) = 0
Example(expr=Equals(Function(rf, (Real(5), Function(rg, (r, )))),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
# (rg(r) = 5 + 2) <-> (rg(r) = 7)
Example(expr=Iff(Equals(Function(rg, [r]), Plus(Real(5), Real(2))),
Equals(Function(rg, [r]), Real(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
# (r = s + 1) & (rg(s) = 5) & (rg(r - 1) = 7)
Example(expr=And([
Equals(r, Plus(s, Real(1))),
Equals(Function(rg, [s]), Real(5)),
Equals(Function(rg, [Minus(r, Real(1))]), Real(7))
]),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLRA),
#
# BV
#
# bv_one & bv_zero == bv_zero
Example(expr=Equals(BVAnd(BVOne(32), BVZero(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# ~(010) == 101
Example(expr=Equals(BVNot(BV("010")), BV("101")),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# "111" xor "000" == "000"
Example(expr=Equals(BVXor(BV("111"), BV("000")), BV("000")),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv8 :: bv8 < bv_zero
Example(expr=BVULT(BVConcat(bv8, bv8), BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv_one[:7] == bv_one
Example(expr=Equals(BVExtract(BVOne(32), end=7), BVOne(8)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (((bv8 + bv_one) * bv(5)) / bv(5)) > bv(0)
Example(expr=BVUGT(
BVUDiv(BVMul(BVAdd(bv8, BVOne(8)), BV(5, width=8)),
BV(5, width=8)), BVZero(8)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 >=u bv(0)
Example(expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 >=s bv(0)
Example(expr=BVSGE(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (BV(5) rem BV(2) > bv_zero) /\ (BV(5) rem BV(2) < bv_one)
Example(expr=And(
BVUGT(BVURem(BV(5, width=32), BV(2, width=32)), BVZero(32)),
BVULE(BVURem(BV(5, width=32), BV(2, width=32)), BVOne(32))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# ((bv_one + (- bv_one)) << 1) >> 1 == bv_one
Example(expr=Equals(
BVLShr(BVLShl(BVAdd(BVOne(32), BVNeg(BVOne(32))), 1), 1),
BVOne(32)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv_one - bv_one == bv_zero
Example(expr=Equals(BVSub(BVOne(32), BVOne(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Rotations
Example(expr=Equals(BVRor(BVRol(BVOne(32), 1), 1), BVOne(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Extensions
Example(expr=Equals(BVZExt(BVZero(5), 11), BVSExt(BVZero(1), 15)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 - bv16 = 0_16
Example(expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 - bv16)[0:7] = bv8
Example(expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16[0,7] comp bv8) = bv1
Example(expr=Equals(BVComp(BVExtract(bv16, 0, 7), bv8), BVOne(1)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 comp bv16) = bv0
Example(expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< bv16)
Example(expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< 0_16)
Example(expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 u< bv16)
Example(expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< 0_16)
Example(expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 | 0_16) = bv16
Example(expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 & 0_16) = 0_16
Example(expr=Equals(BVAnd(bv16, BVZero(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# 0_16 s< bv16 & ((bv16 s/ -1) s< 0)
Example(expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSDiv(bv16, SBV(-1, 16)), BVZero(16))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# 0_16 s< bv16 & ((bv16 s% -1) s< 0)
Example(expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSRem(bv16, BVOne(16)), BVZero(16))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv16 u% 1 = 0_16
Example(expr=Equals(BVURem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 s% 1 = 0_16
Example(expr=Equals(BVSRem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 s% -1 = 0_16
Example(expr=Equals(BVSRem(bv16, BVNeg(BVOne(16))), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 a>> 0 = bv16
Example(expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# 0 s<= bv16 & bv16 a>> 1 = bv16 >> 1
Example(expr=And(
BVSLE(BVZero(16), bv16),
Equals(BVAShr(bv16, BVOne(16)), BVLShr(bv16, BVOne(16)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
#
# Quantification
#
# forall y . x -> y
Example(expr=ForAll([y], Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.BOOL),
# forall p,q . p + q = 0
Example(expr=ForAll([p, q], Equals(Plus(p, q), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LIA),
# forall r,s . ((r > 0) & (s > 0)) -> (r - s < r)
Example(expr=ForAll([r, s],
Implies(And(GT(r, Real(0)), GT(s, Real(0))),
(LT(Minus(r, s), r)))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
# exists x,y . x -> y
Example(expr=Exists([x, y], Implies(x, y)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.BOOL),
# exists p,q . p + q = 0
Example(expr=Exists([p, q], Equals(Plus(p, q), Int(0))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LIA),
# exists r . forall s . (r - s > r)
Example(expr=Exists([r], ForAll([s], GT(Minus(r, s), r))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
# forall r . exists s . (r - s > r)
Example(expr=ForAll([r], Exists([s], GT(Minus(r, s), r))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
# x /\ forall r. (r + s = 5)
Example(expr=And(x, ForAll([r], Equals(Plus(r, s), Real(5)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
#
# UFLIRA
#
# ih(r,q) > p /\ (x -> y)
Example(expr=And(GT(Function(ih, (r, q)), p), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
# ( (p - 3) = q ) -> ( ih(r, q + 3) > p \/ ih(r, p) <= p )
Example(expr=Implies(
Equals(Minus(p, Int(3)), q),
Or(GT(Function(ih, (r, Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
# ( (ToReal(p - 3) = r) /\ (ToReal(q) = r) ) ->
# ( ( ih(ToReal(p - 3), q + 3) > p ) \/ (ih(r, p) <= p) )
Example(expr=Implies(
And(Equals(ToReal(Minus(p, Int(3))), r), Equals(ToReal(q), r)),
Or(
GT(
Function(ih,
(ToReal(Minus(p, Int(3))), Plus(q, Int(3)))),
p), LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
# ! ( (ToReal(p - 3) = r /\ ToReal(q) = r) ->
# ( ih(ToReal(p - 3), q + 3) > p \/
# ih(r,p) <= p ) )
Example(expr=Not(
Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(
ih,
(ToReal(Minus(p, Int(3))), Plus(q, Int(3)))),
p), LE(Function(ih, (r, p)), p)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLIRA),
# Test complex names
Example(expr=And(
Symbol("Did you know that any string works? #yolo"),
Symbol("10"), Symbol("|#somesolverskeepthe||"), Symbol(" ")),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
]
return result
def probably_expr_to_pysmt(expr,
pysmt_infinity_variable=None,
treat_minus_as_monus=False,
monus_euf=None,
toReal=False):
"""
Convert a Probably expression to a pysmt expression.
Infinity must not occur in a composed arithmetic expression.
:param expr: The Propbably expression that is to be converted.
:param pysmt_infinity_variable: The pysmt variable used to represent infinity.
:param toReal: Whether variables and NatLitExpr shall be cast to Real or not.
:param treat_minus_as_monus: Whether to repalace every expression of the form a - b by monus_euf(a,b)
:param monus_euf: The uninterpreted function that is to be used for monus.
:return: The resulting PySMT expression.
"""
env = get_env()
if isinstance(expr, BoolLitExpr):
if expr.value == True:
return TRUE()
elif expr.value == False:
return FALSE()
else:
raise Exception("Unkown expression value.")
elif isinstance(expr, NatLitExpr):
return Int(expr.value) if not toReal else Real(expr.value)
elif isinstance(expr, FloatLitExpr):
# This value might be infinity
if expr.is_infinite():
if pysmt_infinity_variable == None:
raise Exception(
"If infinity occurs in an arithmetic expression, then pysmt_infinity_variable must not be none."
)
return pysmt_infinity_variable
else:
return Real(expr.to_fraction())
elif isinstance(expr, VarExpr):
return env.formula_manager.get_symbol(
expr.var) if not toReal else ToReal(
env.formula_manager.get_symbol(expr.var))
elif isinstance(expr, TickExpr):
if not isinstance(expr.expr, NatLitExpr):
raise Exception(
"Currently we allow for constants in tick(..) expressions only."
)
else:
return probably_expr_to_pysmt(expr.expr, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
elif isinstance(expr, BinopExpr):
if expr.operator == Binop.OR:
return Or(
probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal),
probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal))
if expr.operator == Binop.AND:
return And(
probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal),
probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal))
if expr.operator == Binop.LEQ:
return LE(
probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal),
probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal))
if expr.operator == Binop.LE:
return LT(
probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal),
probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal))
if expr.operator == Binop.EQ:
lhs = probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
rhs = probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
return EqualsOrIff(lhs, rhs)
if expr.operator == Binop.PLUS:
summand_1 = probably_expr_to_pysmt(expr.lhs,
pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
summand_2 = probably_expr_to_pysmt(expr.rhs,
pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
if summand_1 == pysmt_infinity_variable or summand_2 == pysmt_infinity_variable:
raise Exception(
"Infinity must not occur in a composed arithmetic expression."
)
return Plus(summand_1, summand_2)
if expr.operator == Binop.MINUS:
min_1 = probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
min_2 = probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
if min_1 == pysmt_infinity_variable or min_2 == pysmt_infinity_variable:
raise Exception(
"Infinity must not occur in a composed arithmetic expression."
)
# Do we have to treat minus as monus?
if treat_minus_as_monus:
if monus_euf == None:
raise Exception(
"If minus is to be treated as monus, then a monus_euf has to be provided."
)
monus_expr = Function(monus_euf, (min_1, min_2))
if toReal:
encountered_real_monus_pairs.add((min_1, min_2))
else:
encountered_monus_pairs.add((min_1, min_2))
return monus_expr
else:
return Minus(min_1, min_2)
if expr.operator == Binop.TIMES:
fac_1 = probably_expr_to_pysmt(expr.lhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
fac_2 = probably_expr_to_pysmt(expr.rhs, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
if fac_1 == pysmt_infinity_variable or fac_2 == pysmt_infinity_variable:
raise Exception(
"Infinity must not occur in a composed arithmetic expression."
)
return Times(fac_1, fac_2)
elif isinstance(expr, UnopExpr):
if expr.operator == Unop.NEG:
return Not(
probably_expr_to_pysmt(expr.expr, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal))
elif expr.operator == Unop.IVERSON:
return probably_expr_to_pysmt(expr.expr, pysmt_infinity_variable,
treat_minus_as_monus, monus_euf,
toReal)
else:
raise Exception("Unsupported Unop Operator")
else:
raise Exception("Invalid expression {expr}")