def recur(t, fi):
if isinstance(t, c.That):
if isinstance(t.that, c.FVar):
# special
#rp = [x[1] for x in f if x[0] == t.that][0]
if t.that == f[0]:
newname = star(str(t.const))
newcons = c.Const(newname, c.n0)
allargs = t.terms + fi[0] + vars
out = c.Appl(newcons, allargs[0])
for i in allargs[1:]:
out = c.Appl(out, i)
return out
else:
return t
elif isinstance(t, c.Const) or isinstance(t, c.RVar) or isinstance(
t, c.PVar):
return t
elif isinstance(t, c.Appl):
return c.Appl(recur(t.func, fi), recur(t.arg, fi))
elif isinstance(t, c.Lambda):
return c.Lambda(c.var, recur(t.body, fi))
elif isinstance(t, c.Where):
lst = [c.Assignment(i.left, recur(i.right, fi)) for i in t.set]
return c.Where(recur(t.body, fi), lst)
else:
return t
def fint(t):
allsteps = cf(t)
cfm = allsteps
while isinstance(cfm, Reduce):
cfm = cfm.b[0] #get to Canonical Form
#cfm = cf(t) # no renaming
fi = fint_repl(cfm)
fi0 = fi[0]
if not isinstance(fi0, c.Where):
fi0 = c.Where(fi0, set()) # A = A where {}
vars = [x[1] for x in fi[1]] + [x[1] for x in fi[2]
] # variables to be abstracted over
def lmb(x, st): #construct a lambda term with all variables in st
out = x
for i in st:
if isinstance(i, c.RVar):
v = newvar(i.letter.lower(), i.typ)
else:
v = i
out = c.Lambda(v, out)
return out
lst = [[x[0] for x in fi[2]],
[lmb(fi0.body, vars)]] # all free variables, and the body
for i in fi0.set: #now add all the terms in the where-construct
lst[1].append(lmb(i.right, vars))
return lst + [allsteps] #return the whole list and reduction steps
def reduce_recap(t):
if isinstance(t, c.Appl) and isinstance(t.func, c.Where):
out = c.Where(c.Appl(t.func.body, t.arg), t.func.set)
return out
else:
return t
def func_to_term(f):
global names
global pronouns
if isinstance(f, str): # string
if re.fullmatch('[a-z][0-9]*', f):
n = (None if f[1:] == '' else int(f[1:]))
return c.PVar(f[0], n)
elif re.fullmatch('[A-Z][0-9]*', f):
n = (None if f[1:] == '' else int(f[1:]))
return c.RVar(f[0], n)
elif f in pronouns:
return c.Const(f, c.Type('s', 'e'), True)
else:
try:
out = names[f]
if isinstance(out, c.Term):
return out
else:
raise c.Error('Not a term: ' + f)
except KeyError:
raise c.Error('No such object: ' + f)
m = f.func # function part
a = f.args # argument part
j = [(isinstance(x, c.Func) and x.func == c.Keyword('that')) for x in a]
if any(j[:-1]):
raise c.Error('Non-final that')
else:
if j[-1]: # that-clause
try:
return c.That(names[m], func_to_term(a[-1].args[0]),
*[func_to_term(x) for x in a[:-1]])
except KeyError:
raise c.Error('No such attitudinal constant: ' + str(m))
if isinstance(m, str) or isinstance(m, c.Func):
try:
out = func_to_term(m) # recursive call on function part
for i in a:
out = c.Appl(
out, func_to_term(i)) # recursive call on each argument
result = out
except KeyError:
raise c.Error('No such object: ' + str(m))
elif m == c.Keyword('lambda'):
try:
result = c.Lambda(func_to_term(a[0]), func_to_term(
a[1])) # recursive call for lambda term
except KeyError:
raise c.Error('No such object: ' + str(a[0]))
elif m == c.Keyword('where'):
result = c.Where(func_to_term(a[0]),
{func_to_term(i)
for i in a[1]}) # recursive call for wh construct
elif m == c.Keyword('assign'):
result = c.Assignment(func_to_term(a[0]), func_to_term(
a[1])) # recursive call for assignments
else:
pass
return result
def testRPL():
readfile('SETTINGS')
readfile()
j = c.That(names['knows'], c.FVar('w'), names['John'])
j2 = c.Where(j,
[c.Assignment(c.FVar('w'), c.Fint(fullparse('flat(earth)')))])
d = [[c.FVar('w'), fullparse('flat(earth)')]]
return j2
def reduce_ap(t):
if isinstance(t, c.Appl) and not immediate(t.arg):
nv = newvar('P', c.n0)
out = c.Where(c.Appl(t.func, nv), {c.Assignment(nv, t.arg)})
return out
else:
return t
def reduce_hr(t): # Head Rule
if isinstance(t, c.Where) and isinstance(t.body, c.Where):
k = t.set.union(t.body.set) # take the union of the two sets
r = c.Where(t.body.body, k)
return r
else: # not the right form for this rule
return t
def reduceR(r, ren=True):
if isinstance(r, Reduce):
t = r.b[0]
return reduceR(t)
else:
t = r
if isinstance(t, c.Where) and any([type(x.left) is c.FVar for x in t.set]):
ri = reduce_intens(t)
p = Reduce(t, [ri[0]], '(intensional)')
p.lem = ri[1]
return p
elif isinstance(t, c.Where) and isinstance(t.body, c.Where):
return Reduce(t, [reduce_hr(t)], '(hr)')
elif isinstance(t, c.That):
rd = reduce_that(t)
p = Reduce(t, [rd[0]], '(that)')
p.lem = rd[1]
return p
elif isinstance(t, c.Lambda) and isinstance(t.body, c.Where):
return Reduce(t, [reduce_l(t)], '(lambda)')
elif isinstance(t, c.Where) and any(
[isinstance(i.right, c.Where) for i in t.set]):
return Reduce(t, [reduce_bs(t)], '(BS)')
elif isinstance(t, c.Appl) and isinstance(t.func, c.Where):
return Reduce(t, [reduce_recap(t)], '(recap)')
elif isinstance(t, c.Appl) and not immediate(t.arg):
return Reduce(t, [reduce_ap(t)], '(ap)')
elif isinstance(t, c.Appl):
ff = reduceR(t.func)
aa = reduceR(t.arg)
out = c.Appl(help(ff), help(aa))
s = rmv([ff, aa])
if s:
return Reduce(t, [out] + s, '(rep1)')
else:
return t
elif isinstance(t, c.Lambda):
bdy = reduceR(t.body)
return Reduce(t, [c.Lambda(t.var, help(bdy)), bdy], '(rep2)')
elif isinstance(t, c.Where):
bdy = reduceR(t.body)
lst = [bdy]
nset = set()
for i in t.set:
r = reduceR(i.right)
lst.append(r)
nset.add(c.Assignment(i.left, help(r)))
out = c.Where(help(bdy), nset)
s = rmv(lst)
if s:
return Reduce(t, [out] + s, '(rep3)')
else:
return out
else:
#return Reduce(t,[t],'')
return t
def reduce_bs(t):
if isinstance(t, c.Where):
newset = set()
for i in t.set:
if isinstance(i.right, c.Where):
newset.add(c.Assignment(i.left, i.right.body))
newset.update(i.right.set)
else:
newset.add(i)
#print(newset)
return c.Where(t.body, newset)
else:
return t
def fint_repl(t, stack=None, bound=None):
if stack is None:
stack = []
if bound is None:
bound = []
if isinstance(t, c.Appl):
out = c.Appl(
fint_repl(t.func, stack, bound)[0],
fint_repl(t.arg, stack, bound)[0])
elif isinstance(t, c.Lambda):
bound.append(t.var)
out = c.Lambda(t.var, fint_repl(t.body, stack, bound)[0])
elif isinstance(t, c.Const):
out = t
elif isinstance(t, c.Where):
bound.extend(t.vars())
newbody = fint_repl(t.body, stack, bound)[0]
newset = set()
for i in t.set:
newset.add(
c.Assignment(i.left,
fint_repl(i.right, stack, bound)[0]))
out = c.Where(newbody, newset)
elif isinstance(t, c.RVar):
if c.varin(t, [x[0] for x in stack]):
out = [x[1] for x in stack if c.vareq(x[0], t)][0]
else:
nv = newvar(t.letter.lower(), t.typ) #create new PVar
stack.append([t, nv])
out = nv
elif isinstance(t, c.PVar):
stack.append([t, t])
out = t
elif isinstance(t, c.That):
newlst = []
for i in t.terms:
newlst.append(fint_repl(i, stack, bound)[0])
out = c.That(t.const, fint_repl(t.that, stack, bound)[0], *newlst)
free_vars = [x for x in stack if not c.varin(x[0], bound)]
stack2 = [
x for x in stack if c.varin(x[0], bound) and isinstance(x[0], c.RVar)
]
return [out, stack2, free_vars]
def repl_fvars(f, trm):
fin = fint(f[1])
lm = fin[2]
vars = [newvar('P', c.n0) for x in range(len(fin[1]))]
def recur(t, fi):
if isinstance(t, c.That):
if isinstance(t.that, c.FVar):
# special
#rp = [x[1] for x in f if x[0] == t.that][0]
if t.that == f[0]:
newname = star(str(t.const))
newcons = c.Const(newname, c.n0)
allargs = t.terms + fi[0] + vars
out = c.Appl(newcons, allargs[0])
for i in allargs[1:]:
out = c.Appl(out, i)
return out
else:
return t
elif isinstance(t, c.Const) or isinstance(t, c.RVar) or isinstance(
t, c.PVar):
return t
elif isinstance(t, c.Appl):
return c.Appl(recur(t.func, fi), recur(t.arg, fi))
elif isinstance(t, c.Lambda):
return c.Lambda(c.var, recur(t.body, fi))
elif isinstance(t, c.Where):
lst = [c.Assignment(i.left, recur(i.right, fi)) for i in t.set]
return c.Where(recur(t.body, fi), lst)
else:
return t
final = [c.Assignment(vars[i], fin[1][i]) for i in range(len(vars))]
n = recur(trm, fin)
removal = set([x for x in n.set if x.left == f[0]])
newset = n.set.difference(removal)
if newset == set():
n = n.body
else:
n.set = newset
where = c.Where(n, final)
return [where, lm]
def reduce_l(t):
if isinstance(t, c.Lambda) and isinstance(t.body, c.Where):
replacements = [[x, c.Appl(newvar(x.letter, c.n0), t.var)]
for x in t.body.vars()]
#print(replacements)
newbody = replace_free_RVs(replacements, t.body.body)
newset = set()
for i in t.body.set:
var = [x for x in replacements
if c.vareq(x[0], i.left)][0] # [P1, P2(u)]
new = c.Assignment(
var[1].func,
c.Lambda(t.var, replace_free_RVs(replacements, i.right)))
newset.add(new)
return c.Where(c.Lambda(t.var, newbody), newset)
else:
return t
def replace_free_RVs(reps, form, bound=None):
if bound is None:
bound = []
if isinstance(form, c.Appl):
return c.Appl(replace_free_RVs(reps, form.func),
replace_free_RVs(reps, form.arg, bound))
elif isinstance(form, c.Lambda): # free vars in lambda body
return c.Lambda(form.var, replace_free_RVs(reps, form.body, bound))
elif isinstance(form, c.Where):
vs = form.vars()
bound.extend(vs)
newbody = replace_free_RVs(reps, form.body,
bound) # free vars in the where body
temp = set()
for i in form.set:
temp.add(
c.Assignment(i.left, replace_free_RVs(
reps, i.right, bound))) # free vars in each assignment
bound = [x for x in bound if x not in vs]
return c.Where(newbody, temp)
elif isinstance(form, c.That):
temp = []
for i in form.terms:
temp.append(replace_free_RVs(reps, i, bound))
return c.That(form.const, form.that, *temp)
elif isinstance(form, c.RVar):
if c.varin(form, [x[0] for x in reps]):
if not c.varin(form, bound):
r = [x[1] for x in reps if c.vareq(x[0], form)][0]
return r
else: #bound var
return form
else:
return form
else: # const or pvar
return form
def rename(term, stack=None):
if stack is None:
stack = dict()
if isinstance(term, c.PVar) or isinstance(term, c.RVar):
if str(term) in stack:
s = stack[str(term)]
out = s
else:
s = str(term)
nv = newvar(s[0], term.typ)
stack.update({s: nv})
out = nv
elif isinstance(term, c.Lambda):
s = str(term.var)
old = []
if s in stack:
old = [s, stack.pop(s)] # store old one
nv = newvar(s[0], term.var.typ)
stack.update({s: nv})
out1 = rename(term.body, stack)
stack.pop(s)
if old:
stack.update({old[0]: old[1]}) #restore old one
out = c.Lambda(nv, out1)
elif isinstance(term, c.Appl):
out = c.Appl(rename(term.func, stack), rename(term.arg, stack))
elif isinstance(term, c.Const) or isinstance(term, c.FVar):
out = term
elif isinstance(term, c.Fint):
out = c.Fint(rename(term.term, stack))
elif isinstance(term, c.Where):
old = []
vars = term.vars()
for i in vars: # store old stack
s = str(i)
if s in stack: #already a free var
old.append([s, stack.pop(s)])
for i in vars: # update stack with new bound vars
nv = newvar(i.letter, i.typ)
stack.update({str(i): nv})
out2 = rename(term.body, stack) #recursive call on body
st = set()
for i in {x for x in term.set}: #recursive call on set
st.add(c.Assignment(rename(i.left, stack), rename(i.right, stack)))
for i in vars: #remove bound vars
stack.pop(str(i))
for i in old: #restore old stack
stack.update({i[0]: i[1]})
out = c.Where(out2, st)
elif isinstance(term, c.That):
lst = [rename(x, stack) for x in term.terms]
out = c.That(term.const, rename(term.that, stack), *lst)
return out