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TRS.py
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TRS.py
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"""
TRS.py - representations for Term Rewriting Systems
Written by: Joshua Rule <[email protected]>
"""
class Atom(object):
def __init__(self, index, alias=None):
self.index = index
self.alias = alias
class Term(object):
def __init__(self, signature):
self.signature = signature
def vars(self):
raise NotImplementedError
def symbols(self):
raise NotImplementedError
class Symbol(Atom):
def __init__(self, index, alias=None, arity=0):
Atom.__init__(self, index=index, alias=alias)
self.arity = arity # can ARS/TRS have Symbols without fixed arity?
def __str__(self):
return self.alias if self.alias else "S{:d}".format(self.index)
def __repr__(self):
return ('Symbol(index={:d}, '
'alias=\'{}\', '
'arity={:d})').format(self.index,
self.alias,
self.arity)
class Variable(Atom, Term):
"""a lone variable"""
def __init__(self, signature, index, alias=None):
Atom.__init__(self, index=index, alias=alias)
Term.__init__(self, signature)
def __str__(self):
return self.alias if self.alias else "V{:d}".format(self.index)
def __repr__(self):
return "Variable(index={:d}, alias=\'{}\')".format(self.index,
self.alias)
def vars(self):
return set([self])
def symbols(self):
return set([])
class Application(Term):
"""a function symbol applied to terms"""
def __init__(self, signature, head, body=[],):
sym_head = isinstance(head, Symbol)
arity_match = len(body) is head.arity
all_terms = all([isinstance(t, Term) for t in body])
sig_match = all([t.signature == signature for t in body])
if sym_head:
if arity_match:
if all_terms:
if sig_match:
Term.__init__(self, signature)
self.head = head
self.body = body
else:
raise SignatureViolationError
else:
raise TRSError('Subterms must be Terms')
else:
raise TRSError(('{} has arity {:d}'
'but given {:d} args').format(
head, head.arity, len(body)))
else:
raise TRSError('The head of an application must be a Term')
def __str__(self):
if len(self.body) is 0:
body = ''
else:
body = '(' + ', '.join([str(t) for t in self.body]) + ')'
return str(self.head) + body
def __repr__(self):
return 'Application(head={}, body={})'.format(self.head, self.body)
def vars(self):
return set([]).union(*[t.vars() for t in self.body])
def symbols(self):
return set([self.head]).union(*[t.symbols() for t in self.body])
class RewriteRule(object):
def __init__(self, signature, lhs, rhs):
sigs_match = lhs.signature == rhs.signature == signature
lhs_is_app = isinstance(lhs, Application)
lhs_ge_rhs = all([v in lhs.vars() for v in rhs.vars()])
if sigs_match:
if lhs_is_app:
if lhs_ge_rhs:
self.signature = signature
self.lhs = lhs
self.rhs = rhs
else:
raise TRSError('RHS {} has variables \
not in LHS {}'.format(rhs, lhs))
else:
raise TRSError('LHS cannot be a variable')
else:
SignatureViolationError
def symbols(self):
return self.lhs.symbols().union(self.rhs.symbols())
def vars(self):
return self.lhs.vars().unoin(self.rhs.vars())
def __str__(self):
return str(self.lhs) + ' -> ' + str(self.rhs)
class TRS(object):
def __init__(self, signature, rules):
all_rules = all([isinstance(r, RewriteRule) for r in rules])
sigs_match = all([r.signature == signature for r in rules])
if all_rules:
if sigs_match:
self.signature = signature
self.rules = rules
else:
raise SignatureViolationError
else:
raise TypeError('TRS needs RewriteRule evaluation rules')
def __str__(self):
return str([str(s) for s in self.signature]) + \
'\n\n' + '\n'.join([str(r) for r in self.rules])
class TRSError(Exception):
pass
class SignatureViolationError(TRSError):
pass
if __name__ == "__main__":
# make SK-logic
s = Symbol(1, 'S', 0)
k = Symbol(2, 'K', 0)
app = Symbol(3, '.', 2)
sig = set([s, k, app])
a = Variable(sig, 1, 'a')
b = Variable(sig, 2, 'b')
c = Variable(sig, 3, 'c')
def make(x, y):
return Application(sig, app, [x, y])
t1 = make(make(make(Application(sig, s, []), a), b), c)
t2 = make(make(a, c), make(b, c))
r1 = RewriteRule(sig, t1, t2)
t3 = make(make(Application(sig, k, []), a), b)
t4 = a
r2 = RewriteRule(sig, t3, t4)
sk = TRS(sig, set([r1, r2]))
print sk