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test_serializer_ulkb_and.py
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# Copyright (C) 2023 IBM Corp.
# SPDX-License-Identifier: Apache-2.0
from ulkb import *
from .test_serializer_ulkb import TestSerializerULKB
from .tests import main
class TestSerializerULKB_And(TestSerializerULKB):
def test_defaults(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(x, y),
'x ∧ y : 𝔹'),
(And(x, y, z),
'x ∧ y ∧ z : 𝔹'),
(And(x, y, z, w),
'x ∧ y ∧ z ∧ w : 𝔹'),
(And(And(x, y, z), w),
'(x ∧ y ∧ z) ∧ w : 𝔹'),
(And(And(And(x, y), z), w),
'((x ∧ y) ∧ z) ∧ w : 𝔹'),
omit_types=True)
self.assert_to_ulkb(
(And(x, y),
'(x : 𝔹) ∧ (y : 𝔹) : 𝔹'),
(And(x, y, z),
'(x : 𝔹) ∧ (y : 𝔹) ∧ (z : 𝔹) : 𝔹'),
(And(x, y, z, w),
'(x : 𝔹) ∧ (y : 𝔹) ∧ (z : 𝔹) ∧ (w : 𝔹) : 𝔹'),
(And(And(x, y, z), w),
'((x : 𝔹) ∧ (y : 𝔹) ∧ (z : 𝔹)) ∧ (w : 𝔹) : 𝔹'),
(And(And(And(x, y), z), w),
'(((x : 𝔹) ∧ (y : 𝔹)) ∧ (z : 𝔹)) ∧ (w : 𝔹) : 𝔹'),
show_types=True)
def test_ensure_ascii(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(x, y),
'x and y : bool'),
(And(x, y, z),
'x and y and z : bool'),
(And(x, y, z, w),
'x and y and z and w : bool'),
(And(x, And(y, z), w),
'x and (y and z) and w : bool'),
ensure_ascii=True, omit_types=True)
def test_show_annotations(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(x@{'i': 1}, y@{'j': 2}, k=3),
'(x {i=1}) ∧ (y {j=2}) {k=3} : 𝔹'),
(And(x@{'i': 1}, y@{'j': 2}, z, k=3),
'(x {i=1}) ∧ (y {j=2}) ∧ z {k=3} : 𝔹'),
(And(x@{'i': 1}, And(y@{'j': 2}, z, k=3)),
'(x {i=1}) ∧ ((y {j=2}) ∧ z {k=3}) : 𝔹'),
show_annotations=True, omit_types=True)
self.assert_to_ulkb(
(And(x@{'i': 1}, y@{'j': 2}, z, k=3),
'(x {i=1}) ∧ ((y {j=2}) ∧ z) {k=3} : 𝔹'),
(And(x@{'i': 1}, y@{'j': 2}, z, k=3),
'(x {i=1}) ∧ ((y {j=2}) ∧ z) {k=3} : 𝔹'),
show_annotations=True, show_parentheses=True, omit_types=True)
def test_show_parentheses(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(x, y),
'x ∧ y : 𝔹'),
(And(x, y, z),
'x ∧ (y ∧ z) : 𝔹'),
(And(x, y, z, w),
'x ∧ (y ∧ (z ∧ w)) : 𝔹'),
(And(x, And(y, z), w),
'x ∧ ((y ∧ z) ∧ w) : 𝔹'),
show_parentheses=True, show_types=False)
def test_show_types(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(x@bool, y, z@bool),
'(x : 𝔹) ∧ (y : 𝔹) ∧ (z : 𝔹) : 𝔹'))
def test_application(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(f(And(x, y)),
'f (x ∧ y) : 𝔹'),
(And(f(x), y),
'f x ∧ y : 𝔹'),
(And(x, f(y)),
'x ∧ f y : 𝔹'),
show_types=False)
def test_abstraction(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
v = Variable('v', type=a)
self.assert_to_ulkb(
(Abstraction(v, And(x, y)),
'(𝜆 v ⇒ x ∧ y) : a → 𝔹'),
(And(Abstraction(v, And(x, y))(x), y),
'(𝜆 v ⇒ x ∧ y) x ∧ y : 𝔹'),
(And(x, Abstraction(v, And(x, y))(f(x))),
'x ∧ (𝜆 v ⇒ x ∧ y) (f x) : 𝔹'),
show_types=False)
def test_not(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(And(Not(x), Falsity()),
'¬x ∧ ⊥ : 𝔹'),
(Not(And(x, Falsity())),
'¬(x ∧ ⊥) : 𝔹'),
(And(Not(And(x, y, z)), w),
'¬(x ∧ y ∧ z) ∧ w : 𝔹'),
omit_types=True)
def test_or(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(Or(And(x, y), z),
'x ∧ y ∨ z : 𝔹'),
(And(Or(x, y), z),
'(x ∨ y) ∧ z : 𝔹'),
(And(x, Or(y, z)),
'x ∧ (y ∨ z) : 𝔹'),
omit_types=True)
def test_implies(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(Implies(And(x, y), z),
'x ∧ y → z : 𝔹'),
(And(Implies(x, y), z),
'(x → y) ∧ z : 𝔹'),
(And(x, Implies(y, z)),
'x ∧ (y → z) : 𝔹'),
omit_types=True)
def test_iff(self):
a = TypeVariable('a')
x, y, z, w = Constants('x', 'y', 'z', 'w', bool)
f = Constant('f', FunctionType(a, a))
g = Constant('g', FunctionType(a, a, a))
self.assert_to_ulkb(
(Iff(And(x, y), z),
'x ∧ y ↔ z : 𝔹'),
(And(Iff(x, y), z),
'(x ↔ y) ∧ z : 𝔹'),
(And(x, Iff(y, z)),
'x ∧ (y ↔ z) : 𝔹'),
omit_types=True)
def test_forall(self):
x, y = Variables('x', 'y', bool)
self.assert_to_ulkb(
(Forall(x, And(x, y)),
'(∀ x, x ∧ y) : 𝔹'),
(And(Forall(x, And(x, y)), y),
'(∀ x, x ∧ y) ∧ y : 𝔹'),
(And(x, Forall(x, And(x, y))),
'x ∧ (∀ x, x ∧ y) : 𝔹'),
omit_types=True)
def test_exists(self):
x, y = Variables('x', 'y', bool)
self.assert_to_ulkb(
(Exists(x, And(x, y)),
'(∃ x, x ∧ y) : 𝔹'),
(And(Exists(x, And(x, y)), y),
'(∃ x, x ∧ y) ∧ y : 𝔹'),
(And(x, Exists(x, And(x, y))),
'x ∧ (∃ x, x ∧ y) : 𝔹'),
omit_types=True)
def test_misc(self):
a = TypeVariable('a')
b = TypeVariable('b')
a = TypeVariable('a')
f = Constant('f', a >> a)
g = Constant('g', (a, a) >> a)
A, B = Variables('A', 'B', bool)
P, Q, R, = Constants('P', 'Q', 'R', bool)
x, y, z = Variables('x', 'y', 'z', bool)
t = And(And(A, B), Not(A), Not(B), k1=1)
self.assert_to_ulkb(
(t,
'(A ∧ B) ∧ ¬A ∧ ¬B : 𝔹'),
(And(A, true),
'A ∧ ⊤ : 𝔹'),
(And(false, B),
'⊥ ∧ B : 𝔹'),
omit_types=True)
self.assert_to_ulkb(
(And(P, Q, R),
'P ∧ Q ∧ R : 𝔹'),
(And(P, Or(Q, Q), R),
'P ∧ (Q ∨ Q) ∧ R : 𝔹'),
(And(And(P, Q), R),
'(P ∧ Q) ∧ R : 𝔹'),
show_types=False)
self.assert_to_ulkb(
(And(P, Q, R, P),
'P ∧ (Q ∧ (R ∧ P)) : 𝔹'),
omit_parentheses=False, show_types=False)
self.assert_to_ulkb(
(And(P, Q, g(g(x, y), z)),
'P and Q and g (g x y) z : bool'),
ensure_ascii=True, show_types=False)
if __name__ == '__main__':
main()