def proveUniversal(C6, bfactlist, bgoal) :
""" Tries to prove a bgoal of form, ["forall", lo, i, hi, bprop_i_]
from bfactlist. First, attempts to show hi <= lo, meaning
quantification ranges over empty set. If this fails, tries
to establish numerical lower and upper bounds for the quantification
and enumerate proofs for all elements within these bounds.
If this fails, then searches
for a bfact in bfactlist that is a forall of the same form,
but where its upper bound is hi-1. If success, then tries
to prove bprop_hi-1_.
If I have the energy, I'll try to make this smarter later....
"""
#print "proveUNIVERSAL: bfactlist=", bfactlist
#print "goal=", bgoal
lo = bgoal[1]
hi = bgoal[3]
i = bgoal[2]
bprop = bgoal[4]
# first, see if bgoal in premises:
success = bgoal in bfactlist
if not success :
# next, try to prove that domain is empty, ie, hi <= lo :
success = verifyRelation(C6, bfactlist, ["<=", hi, lo])
if not success:
# next, try to establish numerical lower and upper bounds and
# prove bprop for all elements in the numerical range:
lonum = PE.evallToInt(C6, lo)
hinum = PE.evallToInt(C6, hi)
if isinstance(lonum, int) and isinstance(hinum, int):
success = True # so far, so good...
for j in range(lonum, hinum):
stree = Parse.substituteTree(["int", str(j)], i, bprop)
success = success and proveSequent(C6, bfactlist, stree)
if not success:
# then search bfactlist for a forall goal whose body
# matches bprop and whose bounds cover bgoal's all but one:
possibles = [ f for f in bfactlist
if f[0] == "forall" \
and Parse.substituteTree(i, f[2], f[4]) == bprop \
#and verifyRelation(C6, bfactlist, ["==", f[1], lo]) \
and verifyRelation(C6, bfactlist, ["<=", f[1], lo]) \
and verifyRelation(C6, bfactlist, \
["==", ["+", f[3], ["int", "1"]], hi]) \
]
if len(possibles) > 0 :
success = proveSequent(C6, bfactlist,
Parse.substituteTree \
(["-", hi, ["int", "1"]], i, bprop) )
if not success:
#search bfactlist for a forall goal whose body
# matches bprop and whose bounds cover bgoal's:
possibles = [ f for f in bfactlist
if f[0] == "forall" \
and Parse.substituteTree(i, f[2], f[4]) == bprop \
and verifyRelation(C6, bfactlist, ["<=", f[1], lo]) \
and verifyRelation(C6, bfactlist, [">=", f[3], hi]) \
]
success = (len(possibles) > 0)
return success
