def test_axiom_function_replacement(self):
f = Symbol.Function('f', ['x'])
t = Symbol.Function('t', ['y'])
a = Symbol.Predicate('A', [f])
b = Symbol.Predicate('B', [f, t])
axi = Axiom.Axiom(Quantifier.Universal(['x'], a | a & a))
self.assertEqual(repr(axi), '∀(x)[(A(f(x)) | (A(f(x)) & A(f(x))))]')
axi = Axiom.Axiom(Quantifier.Universal(['x', 'y'], b))
self.assertEqual(
repr(axi.substitute_functions()),
'∀(x,y)[∀(t1)[(∀(f1)[(B(f1,t1) & f(x,f1))] & t(y,t1))]]')
def test_axiom_to_pcnf(self):
a = Symbol.Predicate('A', ['x'])
b = Symbol.Predicate('B', ['y'])
c = Symbol.Predicate('C', ['z'])
# Simple test of disjunction over conjunction
axi_one = Axiom.Axiom(Quantifier.Universal(['x', 'y', 'z'], a | b & c))
axi_one = axi_one.to_pcnf()
self.assertEqual('∀(z,y,x)[((A(z) | B(y)) & (A(z) | C(x)))]',
repr(axi_one))
# Simple sanity check, it's already FF-PCNF
axi_two = Axiom.Axiom(
Quantifier.Universal(['x', 'y', 'z'], (a | b) & c))
axi_two = axi_two.to_pcnf()
self.assertEqual('∀(z,y,x)[(C(x) & (A(z) | B(y)))]', repr(axi_two))
# Sanity check we remove functions
c = Symbol.Predicate('C', ['z', Symbol.Function('F', ['z'])])
axi_three = Axiom.Axiom(
Quantifier.Universal(['x', 'y', 'z'], a | b & c))
axi_three = axi_three.to_pcnf()
self.assertEqual(
'∀(z,y,x,w)[((A(z) | C(x,w)) & (A(z) | F(x,w)) & (A(z) | B(y)))]',
repr(axi_three))
def p_function(p):
"""
function : LPAREN NONLOGICAL parameter RPAREN
"""
p[0] = Symbol.Function(p[2], p[3])