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prop.py
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prop.py
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#!/usr/bin/python
import re
from pyparsing import Literal,Word,ZeroOrMore,Forward,nums,oneOf,Group,srange
class Prop():
def __init__(self):
pass
global flagset
flagset = set()
#The following two methods define wffs and check them in the proof.
def syntax(self):
op = oneOf( '\\/ -> * ::')
lpar = Literal('(')
rpar = Literal( ')' )
statement = Word(srange('[A-Z]'),srange('[a-z]'))
expr = Forward()
atom = statement | lpar + expr + rpar
expr << atom + ZeroOrMore( op + expr )
expr.setResultsName("expr")
return expr
def confirm_wff(self, form1):
expr = self.syntax()
form1 = self.strip_form(form1)
try:
result = ''.join(list(expr.parseString(form1)))
except:
result = None
return result == form1
#Rules of inference.
def mp(self, form1, form2, form3):
return (self.__mp_one_way(form1, form2, form3) or
self.__mp_one_way(form2, form1, form3))
def __mp_one_way(self, form1, form2, form3): #Modus Ponens
a = self.split_form(form1)
try:
return (a[2] == 'imp' and
self.strip_form(form2) == a[0] and
self.strip_form(form3) == a[1])
except:
return False
def mt(self, form1, form2, form3):
return (self.__mt_one_way(form1, form2, form3) or
self.__mt_one_way(form2, form1, form3))
def __mt_one_way(self, form1, form2, form3): # Modus Tollens
a = self.split_form(form1)
strip2 = self.strip_form(form2)
strip3 = self.strip_form(form3)
try:
return (a[2] == 'imp' and
strip2[0] == '~' and
strip3[0] == '~' and
a[0] == self.strip_form(strip3[1:]) and
a[1] == self.strip_form(strip2[1:])
)
except:
return False
def hs(self, form1, form2, form3):
return (self.__hs_one_way(form1, form2, form3) or
self.__hs_one_way(form2, form1, form3))
def __hs_one_way(self, form1, form2, form3): #Hypothetical Syllogism
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(form3)
try:
return (a[2] == 'imp' and
b[2] == 'imp' and
c[2] == 'imp' and
a[0] == c[0] and
a[1] == b[0] and
b[1] == c[1])
except:
return False
def simp(self, form1, form2): #Simplification
a = self.split_form(form1)
strip2 = self.strip_form(form2)
try:
return (a[2] == 'and' and
(a[0] == strip2 or
a[1] == strip2)
)
except:
return False
def conj(self, form1, form2, form3): #Conjunction
return self.simp(form3,form1) and self.simp(form3,form2)
def dil(self, form1, form2, form3, form4):
return (self.__dil_one_way(form1, form2, form3, form4) or
self.__dil_one_way(form1, form3, form2, form4) or
self.__dil_one_way(form2, form1, form3, form4) or
self.__dil_one_way(form2, form3, form1, form4) or
self.__dil_one_way(form3, form1, form2, form4) or
self.__dil_one_way(form3, form2, form1, form4))
def __dil_one_way(self, form1, form2, form3, form4): #Dilemma
tup1 = self.split_form(form1)
tup2 = self.split_form(form2)
tup3 = self.split_form(form3)
tup4 = self.split_form(form4)
return ((tup1[2], tup2[2], tup3[2], tup4[2]) == ('imp','imp','or','or')
and {tup3[0],tup3[1]} == {tup1[0],tup2[0]}
and {tup4[0],tup4[1]} == {tup1[1],tup2[1]})
def ds(self, form1, form2, form3):
return (self.__ds_one_way(form1, form2, form3) or
self.__ds_one_way(form2, form1, form3))
def __ds_one_way(self, form1, form2, form3): #Disjunctive Syllogism
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.strip_form(form3)
return ((a[2] == 'or' and
b[1] == 'neg') and
((a[0] == b[0] and
a[1] == c)
or
(a[1] == b[0] and
a[0] == c)
))
except:
return False
def add(self, form1, form2): #Addition
a = self.split_form(form2)
strip1 = self.strip_form(form1)
try:
return (a[2] == 'or' and
(a[0] == strip1 or a[1] == strip1))
except:
return False
#Replacement Rules
def dn(self, form1, form2): #Double Negation
return ((form1[:2] == '~~' and
self.strip_form(form1[2:]) == self.strip_form(form2))
or
(form2[:2] == '~~' and
self.strip_form(form2[2:]) == self.strip_form(form1))
)
def dup(self, form1, form2):
return (self.__dup1(form1, form2) or
self.__dup1(form2, form1))
def __dup1(self, form1, form2): #Duplication
a = self.split_form(form2)
return (self.conj(form1, form1, form2) or(
self.add(form1, form2) and
a[0] == a[1]))
def comm(self, form1, form2): #Commutation
a = (self.find_main_op(form1)[0], self.find_main_op(form1)[1],
self.find_main_op(form2)[1])
return ((a[1],a[2]) in [('or','or'),('and','and')] and
form1[a[0]+1:] + form1[a[0]] + form1[:a[0]] == form2)
def assoc(self,form1, form2): #Association
"""
First we will decide which way the association rule is applied.
Then we will apply it and finally we will decide if
it is valid.
"""
a = self.split_form(form1)
try:
if a[2] == 'or':
return self.assocor(form1,form2)
else:
return self.assocand(form1,form2)
except:
return False
def assocor(self, form1, form2):
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[0])
d = self.split_form(b[1])
if (a[1] == d[1] and
b[0] == c[0] and
c[1] == d[0] and
(a[2],b[2],c[2],d[2]) ==
('or','or','or','or')):
return True
except:
pass
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[1])
d = self.split_form(b[0])
if (a[0] == d[0] and
b[1] == c[1] and
c[0] == d[1] and
(a[2],b[2],c[2],d[2]) ==
('or','or','or','or')):
return True
except:
pass
return False
def assocand(self, form1, form2):
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[0])
d = self.split_form(b[1])
if (a[1] == d[1] and
b[0] == c[0] and
c[1] == d[0] and
(a[2],b[2],c[2],d[2]) ==
('and','and','and','and')):
return True
except:
pass
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[1])
d = self.split_form(b[0])
if (a[0] == d[0] and
b[1] == c[1] and
c[0] == d[1] and
(a[2],b[2],c[2],d[2]) ==
('and','and','and','and')):
return True
except:
pass
return False
def contra(self, form1, form2):
return (self.__contra1(form1, form2) or
self.__contra1(form2, form1))
def __contra1(self, form1, form2): #Contraposition
a = self.split_form(form1)
b = self.split_form(form2)
try:
return (self.strip_form(b[0][1:]) == a[1] and
self.strip_form(b[1][1:]) == a[0] and
a[2] == 'imp' and
b[2] == 'imp')
except:
return False
def dem(self, form1, form2):
return (self.__dem1(form1, form2) or
self.__dem1(form2, form1))
def __dem1(self, form1, form2): #DeMorgan's
try:
split_form1 = self.split_form(form1)
split_form2 = self.split_form(form2)
if split_form1[1] != 'neg':
return False
split_form1 = self.split_form(split_form1[0])
if split_form1[2] == 'and':
return self.__demand(split_form1, split_form2)
else:
return self.__demor(split_form1, split_form2)
except:
return False
def __demor(self, split_form1, split_form2):
a = split_form1
b = split_form2
try:
return ('~' + a[0] == b[0] and
'~' + a[1] == b[1] and b[2] == 'and')
except:
return False
def __demand(self, split_form1, split_form2):
a = split_form1
b = split_form2
try:
return ('~' + a[0] == b[0] and
'~' + a[1] == b[1] and b[2] == 'or')
except:
return False
def be(self, form1, form2):
try:
return (self.__be1(form1, form2) or
self.__be1(form2, form1))
except:
return False
def __be1(self, form1, form2):
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(b[0])
d = self.split_form(b[1])
return (a[2] == 'equiv' and
b[2] == 'and' and
c[2] == 'imp' and
d[2] == 'imp' and
a[0] == c[0] and
a[0] == d[1] and
a[1] == c[1] and
a[1] == d[0]
)
def ce(self, form1, form2):
try:
return (self.__ce1(form1, form2) or
self.__ce1(form2, form1))
except:
return False
def __ce1(self, form1, form2):
a = self.split_form(form1)
b = self.split_form(form2)
return (a[2] == 'imp' and
b[2] == 'or' and
'~' + a[0] == b[0] and
a[1] == b[1])
def dist(self, form1, form2):
try:
return (self.__dist1(form1, form2) or
self.__dist1(form2, form1))
except:
return False
def __dist1(self, form1, form2):
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[1])
d = self.split_form(b[0])
e = self.split_form(b[1])
if a[2] == 'and':
return self.__distand(a,b,c,d,e)
else:
return self.__distor(a, b, c, d, e)
except:
return False
def __distand(self,a,b,c,d,e):
try:
return (a[2] == 'and' and
b[2] == 'or' and
c[2] == 'or' and
d[2] == 'and' and
e[2] == 'and' and
a[0] == d[0] and
c[0] == d[1] and
c[1] == e[1] and
d[0] == e[0]
)
except:
return False
def __distor(self,a,b,c,d,e):
try:
return (a[2] == 'or' and
b[2] == 'and' and
c[2] == 'and' and
d[2] == 'or' and
e[2] == 'or' and
a[0] == d[0] and
c[0] == d[1] and
c[1] == e[1] and
d[0] == e[0]
)
except:
return False
def exp(self, form1, form2): #Exportation
try:
return (self.__exp1(form1, form2) or
self.__exp1(form2, form1))
except:
return False
def __exp1(self, form1, form2):
try:
a = self.split_form(form1)
b = self.split_form(form2)
c = self.split_form(a[0])
d = self.split_form(b[1])
return (a[2] == 'imp' and
b[2] == 'imp' and
c[2] == 'and' and
d[2] == 'imp' and
a[1] == d[1] and
b[0] == c[0] and
c[1] == d[0])
except:
return False
#Conditional proof methods and structural checks.
def cp(self, form1, form2, form3):
a = self.split_form(form3)
form1 = self.strip_form(form1)
form2 = self.strip_form(form2)
return (form1 == a[0] and
form2 == a[1] and
a[2] == 'imp')
def ip(self, form1, form2, form3):
form1 = self.strip_form(form1)
form3 = self.strip_form(form3)
return (self.__is_contradiction(form2) and
(form1 == '~' + form3 or
form3 == '~' + form1 or
form1 == '~(' + form3 + ')' or
form3 == '~(' + form1 + ')'))
def __is_contradiction(self,form1):
a = self.split_form(form1)
try:
return (a[2] == 'and' and
(a[0] == '~' + a[1] or
a[1] == '~' + a[0] or
a[0] == '~(' + a[1] + ')' or
a[1] == '~(' + a[0] + ')'))
except:
return False
def confirm_structure(self, ip, refs):
for tuple1 in refs:
if not len(tuple1) == 1:
lst1 = []
for tuple2 in ip:
# if the line number is outside the scope of
# an assumption we must be cautious
if tuple1[0] > tuple2[1]:
lst1.append(tuple2)
for ref in tuple1[1:]:
if self.__is_between(ref,lst1):
return False
return True
def __is_between(self,ref,lst1):
if lst1:
for range1 in lst1:
if (ref <= range1[1] and
ref >= range1[0]):
return True
return False
def ip_do_not_cross(self,lst1):
lst2 = []
for element in lst1:
if (element[1] == 'assp' or
element[1] == 'fs'):
lst2.append(element[0])
if element[1] in ('ip','cp', 'ug'):
x = lst2.pop()
if not element[2] == x:
return False
return not bool(lst2)
#Predicate Logic Methods
def ui(self, form1, form2):
try:
dict1 = {}
form1 = self.strip_form(form1)
form2 = self.strip_form(form2)
var = form1[1]
form1 = form1[4:-1]
for i in range(len(form1)):
if form1[i] == var:
if not dict1.has_key(var):
dict1[var] = form2[i]
else:
return re.sub(var,dict1[var],form1) == form2
except:
return False
def eg(self, form1, form2):
try:
dict1 = {}
form1 = self.strip_form(form1)
form2 = self.strip_form(form2)
var = form2[8]
form2 = form2[11:-1]
for i in range(len(form2)):
if form2[i] == var:
if not dict1.has_key(var):
dict1[var] = form1[i]
else:
return re.sub(var,dict1[var],form2) == form1
except:
return False
def ei(self, form1, form2):
try:
global flagset
dict1 = {}
form1 = self.strip_form(form1)
form2 = self.strip_form(form2)
var = form1[8]
form1 = form1[11:-1]
for i in range(len(form1)):
if form1[i] == var:
if not dict1.has_key(var):
dict1[var] = form2[i]
break
if dict1[var] not in flagset and re.sub(var,dict1[var],form1) == form2:
flagset.add(dict1[var])
return True
except:
return False
def ug(self, flag, form1, form2):
global flagset
try:
form1 = self.strip_form(form1)
form2 = self.strip_form(form2)
var = form2[1]
form2 = form2[4:-1]
bool1 = bool(re.sub(var,flag,form2) == form1)
if bool:
flagset.discard(flag)
return True
else:
return False
except:
return False
def fs(self, flag):
try:
global flagset
bool1 = bool(flag not in flagset)
if bool1:
flagset.add(flag)
return True
else:
return False
except:
return False
#Utilities used by above methods.
def strip_form(self, form):
form = re.sub(' ','',form)
depth = 0
for i,char in enumerate(form):
if char == '(':
depth += 1
if char == ')':
depth -= 1
if depth == 0 and i == len(form) -1 and len(form) > 1:
return self.strip_form(form[1:-1])
elif depth == 0:
break
return form
def find_main_op(self, form):
"""
Takes a stripped formula as an argument. Not used
directly. Used as a helper function to split_form.
"""
subdepth = 0
try:
for i, char in enumerate(form):
if char == '(':
subdepth += 1
if char == ')':
subdepth -= 1
if char == '*' and subdepth == 0:
return (i, 'and')
if char == '\\' and subdepth == 0:
if form[i+1] == '/':
return (i, 'or')
if char == ':' and subdepth == 0:
if form[i+1] == ':':
return (i, 'equiv')
if char == '-' and subdepth == 0:
if form[i+1] == '>':
return (i, 'imp')
if form[0] == '~':
return (0, 'neg')
except:
pass
def split_form(self, form):
"""
Splits a formula up into a tuple where the first element is the
first part of the formula before the main operator, the second
element is the second part of the formula after the main operator,
and the third is the name of the main operator.
"""
form = self.strip_form(form)
a = self.find_main_op(form)
#checks for None
if not a:
return None
if a[1] == 'neg':
return (self.strip_form(form[1:]), 'neg')
if a[1] in ['or','imp','equiv']:
tuple1 = (self.strip_form(form[:a[0]]), self.strip_form(form[a[0]+2:]),
a[1])
else:
tuple1 = (self.strip_form(form[:a[0]]), self.strip_form(form[a[0]+1:]),
a[1])
return tuple1
#The following methods control the entire checking process.
def confirm_validity(self, file1):
global flagset
lst1,ip,refs = self.proof_to_list(file1)
lst2 = []
for element in lst1:
lst2.append(self.test(element))
flagset = set()
return (all(lst2) and
self.confirm_structure(ip, refs)
and
self.ip_do_not_cross(lst1))
def confirm_validity_string(self, file1):
str1 = ("There is a problem with the " +
"following lines: ")
lst1,ip,refs = self.proof_to_list(file1)
lst2 = []
for element in lst1:
lst2.append(self.test(element))
if all(lst2):
return "Proof is valid."
else:
for i,elem in enumerate(lst2):
if elem == False:
str1 += str(i+1) + ", "
return str1[:-2]
def test(self, lst1):
lst1[1]
lst2 = []
if lst1[0] == 'return False':
return False
if not (lst1[1] == 'pr' or lst1[1] == 'assp'
or lst1[1] == 'fs'):
str1 = "self." + lst1[1] + "(*lst2)"
for x in lst1[2:]:
lst2.append(x)
lst2.append(lst1[0])
try:
return eval(str1)
except:
return False
return True
def proof_to_list(self, file1):
lst1 = []
lst3 = []
for line in file1:
line = line.rstrip()
line = re.sub(r"\t+","\t",line)
line = re.sub(r"\.\t+","\t",line)
lst2 = line.split("\t")
if len(lst2) == 3:
lst2 = lst2[1:]
lst2 = self.convert1(lst2)
lst1.append(lst2)
elif re.sub(r"\s+","",lst2[0]):
lst1.append(['return False','return False'])
ip = self.__ip(lst1)
refs = self.__refs(lst1)
for element in lst1:
lst2 = self.convert2(element, lst1)
lst2[1] = lst2[1].lower()
lst3.append(lst2)
return (lst3,ip,refs)
def __refs(self,lst1):
lst2 = []
for i,element in enumerate(lst1):
if (not isinstance(element[-1],int)
or
element[-3].lower() in ('cp','ip','ug')):
lst2.append((i+1,))
elif not isinstance(element[-2],int):
lst2.append((i+1,element[-1]))
else:
lst2.append((i+1,element[-2],element[-1]))
return lst2
def __ip(self,lst1):
lst2 = []
for element in lst1:
try:
if element[1].lower() in ('cp','ip','ug'):
lst2.append((element[-2],element[-1]))
except:
pass
return lst2
def flatten(self, x):
result = []
for el in x:
if hasattr(el, "__iter__") and not isinstance(el, basestring):
result.extend(self.flatten(el))
else:
result.append(el)
return result
def convert1(self, lst1):
lst1[1] = lst1[1].split(' ')
try:
lst1[1][1] = lst1[1][1].split(',')
except:
pass
lst1 = self.flatten(lst1)
if len(lst1) > 2:
for i, x in enumerate(lst1[2:]):
lst1[i + 2] = int(x)
return lst1
def convert2(self, lst1, lst2):
if not len(lst1) == 2: #Not a premise or assumption.
for i, x in enumerate(lst1[2:]):
lst1[i+2] = lst2[x - 1][0]
return lst1
def prompt_for_file(self):
filename = raw_input("Please enter the name of the file to be checked: ")
return open(filename, 'r')
if __name__ == '__main__':
a = Prop()
# print a.confirm_validity_string(file1)
# a.mt("Za->(Ha*Wa)","~(Ha*Wa)","~Za")
#
# file1 = a.prompt_for_file()
# print a.confirm_validity(file1)
# print a.split_form("(F::G) -> (A -> F )")
file1 = open("proofs/proof13.txt",'r')
print a.confirm_validity(file1)