Ejemplo n.º 1
0
 def test_bv_ule_constants(self):
     f = BVULE(BVZero(32), BVOne(32))
     self.check_equal_and_valid(f, Bool(True))
Ejemplo n.º 2
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 def test_bv_lshr_constants(self):
     f = BVLShr(BV(0xff, 32), BVOne(32))
     self.check_equal_and_valid(f, BV(0x7f, 32))
Ejemplo n.º 3
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 def test_bv_urem_1(self):
     x = Symbol("x", BVType(32))
     f = BVURem(x, BVOne(32))
     self.check_equal_and_valid(f, BVZero(32))
Ejemplo n.º 4
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 def test_bv_udiv_1(self):
     x = Symbol("x", BVType(32))
     f = BVUDiv(x, BVOne(32))
     self.check_equal_and_valid(f, x)
Ejemplo n.º 5
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 def test_bv_mul_1(self):
     x = Symbol("x", BVType(32))
     f = BVMul(x, BVOne(32))
     self.check_equal_and_valid(f, x)
Ejemplo n.º 6
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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
Ejemplo n.º 7
0
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