def atom_less(t1, t2):
"""Compare two atoms, put constants in front."""
if not t1.has_var() and t2.has_var():
return True
elif not t2.has_var() and t1.has_var():
return False
else:
return term_ord.fast_compare(t1, t2) < 0
def compare_fst(p1, p2):
if isinstance(p1[0], Term):
return term_ord.fast_compare(p1[0], p2[0])
else:
if len(p1[0]) != len(p2[0]):
return term_ord.compare_atom(len(p1[0]), len(p2[0]))
for i in range(len(p1[0])):
if p1[0][i] != p2[0][i]:
return compare_fst(p1[0][i], p2[0][i])
return 0
def compare_atom(t1, t2):
"""Compare two atoms, placing numbers last."""
if t1.is_number() and t2.is_number():
return 0
elif t1.is_number():
return 1
elif t2.is_number():
return -1
else:
return term_ord.fast_compare(t1, t2)
def omega_compare_monomial(t1, t2):
"""Assume t1 and t2 are in the form c1 * body1 and c2 * body2,
compare body1 with body2."""
if t1.is_number() and t2.is_number():
return 0
if t1.is_number() and not t2.is_number():
return 1
if not t1.is_number() and t2.is_number():
return -1
else:
return term_ord.fast_compare(t1.arg, t2.arg)
def get_proof_term(self, t):
pt = refl(t)
if t.arg1 == true:
return pt.on_rhs(rewr_conv('conj_true_left'))
elif t.arg == true:
return pt.on_rhs(rewr_conv('conj_true_right'))
elif t.arg1 == false:
return pt.on_rhs(rewr_conv('conj_false_right'))
elif t.arg == false:
return pt.on_rhs(rewr_conv('conj_false_left'))
elif t.arg.is_conj():
if t.arg1 == Not(t.arg.arg1): # A /\ (A_1 /\ ... /\ A_n)
return pt.on_rhs(rewr_conv('conj_assoc'),
arg1_conv(rewr_conv('conj_neg_pos')),
rewr_conv('conj_false_right'))
elif Not(t.arg1) == t.arg.arg1:
return pt.on_rhs(rewr_conv('conj_assoc'),
arg1_conv(rewr_conv('conj_pos_neg')),
rewr_conv('conj_false_right'))
cp = term_ord.fast_compare(t.arg1, t.arg.arg1)
if cp > 0:
return pt.on_rhs(swap_conj_r(), arg_conv(self), try_conv(self))
elif cp == 0:
return pt.on_rhs(rewr_conv('conj_assoc'),
arg1_conv(rewr_conv('conj_same_atom')))
else:
return pt
else:
if t.arg == Not(t.arg1):
return pt.on_rhs(rewr_conv('conj_pos_neg'))
elif t.arg1 == Not(t.arg):
return pt.on_rhs(rewr_conv('conj_neg_pos'))
cp = term_ord.fast_compare(t.arg1, t.arg)
if cp > 0:
return pt.on_rhs(swap_conj_r())
elif cp == 0:
return pt.on_rhs(rewr_conv('conj_same_atom'))
else:
return pt
def compare_atom(t1, t2):
"""Assume t1 and t2 are in the form a_i^{e_i} and a_j^{e_j},
compare a_i with a_j."""
return term_ord.fast_compare(t1.arg1, t2.arg1)
def compare_monomial(t1, t2):
"""Compare two monomials by their body."""
if has_binary_thms():
return term_ord.fast_compare(dest_monomial(t1), dest_monomial(t2))
else:
return term_ord.fast_compare(t1, t2)