Language Processors: FOLLOW(A) = {t | (t is a terminal and S ⇒+ α A t β) or (t is EOF and S ⇒∗ αA)}
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# Narayana Chikkam, Dec, 22, 2015.
import collections
from lib.graph import *
class Grammar:
prodNum = 0
def __init__(self, sg):
self.g = {}
self.np = {}
self.processStringsToGrammar(sg)
self.sigma = self.orderSymbols()
self.v = list(map(str, self.g.keys())) # chg#1
self.t = self.orderTerminals()
self.prepareNullablesMap()
self.numberedProds = None
def processStringsToGrammar(self, sg):
prods = sg.splitlines()
if len(prods) > 0:
self.g = collections.OrderedDict()
self.np = collections.OrderedDict()
S = prods[0].split("->")[0].strip()
self.np[0] = ["%s#"%(S), [S]] # Adding the start production S'
index = 1
for prod in prods:
(lhs, rhs) = prod.split("->")
if index not in self.np:
self.np[index] = [lhs.strip(), list(rhs.strip().split())]
index += 1
for k in self.np:
lhs, rhs = self.np[k][0], self.np[k][1]
if lhs not in self.g:
self.g[lhs] = []
self.g[lhs].append(rhs)
def orderSymbols(self):
symbols = []
for k in self.g: # order really matters
if k not in symbols:
symbols.append(k)
for prods in self.g[k]:
for s in prods:
if s not in symbols:
symbols.append(s)
return symbols
"""
ss = [prods for x in self.g.values() for prods in x]
for prod in ss:
symbols |= set(prod)
return symbols
"""
def orderTerminals(self):
terminals = []
for s in self.sigma:
if s not in self.v:
terminals.append(str(s))
return terminals
# NULLABLES CALCULATION:
# can be optimized, recursion hits for limit 1000 default in Python!!!
######################################################################
def isNullableRecursively(self, v):
if self.visited[v] == False:
self.visited[v] = True
for prod in self.g[v]:
#epsilonProd = ['epsilon']
if 'epsilon' in prod: # Epsilon production
self.nullables_map[v] = True
break
else:
prodNullableCount = 0
for prefix in prod:
if prefix in self.t:
break
if self.isNullableRecursively(prefix):
self.nullables_map[prefix] = True
prodNullableCount += 1
else:
break
if prodNullableCount == len(prod):
self.nullables_map[v] = True
break
if v not in self.nullables_map:
self.nullables_map[v] = False
self.visited[v] = False
return self.nullables_map[v]
def prepareNullablesMap(self):
self.visited = {k: False for k in self.v}
self.nullables_map = {k: False for k in self.v}
for v in self.v:
self.nullables_map[v] = self.isNullableRecursively(v)
def getNullablesMap(self):
return self.nullables_map
# FIRST CALCULATION:
######################################################################
"""
find direct contributions and
contains-the-FIRSTs-of
"""
def findDirectFirstSets(self, v):
first = set()
for prod in self.g[v]:
count = 0 # variable to check if this v could yeild epsilon because other pre-prefixes
for prefix in prod:
if prefix in self.t:
first = first.union([prefix])
break
elif self.nullables_map[prefix] == True: # nullable V, go to next
self.containsFIRSTsOf.append((v, prefix))
count += 1
continue
else:
self.containsFIRSTsOf.append((v, prefix))
break
if count == len(prod):
# all vars could produce nulls so add this v can indirectly produces epsilon
first = first.union(['epsilon'])
return first
def getDirectFirstSets(self):
self.init_first = {}
self.containsFIRSTsOf = []
for v in self.v:
self.init_first[v] = self.findDirectFirstSets(v)
return self.init_first
def FIRST(self):
initFirst = self.getDirectFirstSets()
# create Graph withe the edges from containsOF relation
g = Graph()
for v in self.v:
g.addVertex(v)
for a,b in self.containsFIRSTsOf:
g.addEdge(a, b, 1)
#print "whole Graph: ", ffg
return g.computeFirstUsingSCC(initFirst)
# asking for first(rhs) of a particular production
def FIRSTOFRHS(self, rhs):
first = self.FIRST()
retFirst = set()
count = 0 # variable to check if this v could yeild epsilon because other pre-prefixes
for prefix in rhs:
if prefix in self.t:
retFirst = retFirst.union([prefix])
break
elif self.nullables_map[prefix] == True: # nullable V, go to next
retFirst = retFirst.union(first[prefix] - set(['epsilon']))
count += 1
continue
else:
retFirst = retFirst.union(first[prefix])
break
if count == len(rhs):
# all vars could produce nulls so add this v can indirectly produces epsilon
retFirst = retFirst.union(['epsilon'])
return retFirst
# FOLLOW CALCULATION:
######################################################################
def getDirectFollowSets(self, FIRST):
"""
1. If $ is the input end-marker, and S is the start symbol, $ belongs to FOLLOW(S).
2. If there is a production, A -> Alpha B Beta, then FOLLOW(B) contains (FIRST(Beta) - epsilon)
3. If there is a production, A -> Alpha B, or a production A -> Alpha B Beta, where epsilon is in FIRST(Beta) , then FOLLOW(B) contains FOLLOW(A).
"""
self.init_follow = {v:set() for v in self.v }
self.containsFOLLOWOf = set()
for v in self.v:
if v == self.np[0][0]: # Starting Production
self.init_follow[v] = set(['$']) # $ is in follow of 'S' applying rule 1
for prod in self.g[v]:
for i in range(len(prod)):
if prod[i] in self.v and i+1 < len(prod):
if prod[i+1] in self.t:
self.init_follow[prod[i]] |= set([prod[i+1]])
else:
t = i + 1
while t < len(prod) and prod[t] in self.nullables_map:
if self.nullables_map[prod[t]] == True:
self.init_follow[prod[i]] |= FIRST[prod[t]]-set(['epsilon'])
else:
self.init_follow[prod[i]] |= FIRST[prod[t]]
break
t += 1
if t >= len(prod): # every thing on rhs of prod[i] could produce epsison, rule - 3
self.containsFOLLOWOf |= set([(prod[i], v)])
else: #prod[i+1] is a non nullable prod or prod[t] was a terminal
if prod[t] in self.t:
self.init_follow[prod[i]] |= set([prod[t]])
else:
self.init_follow[prod[i]] |= FIRST[prod[t]]-set(['epsilon'])
elif prod[i] in self.v:
self.containsFOLLOWOf |= set([(prod[i], v)]) # applying rule 2
#self.containsFOLLOWOf = set([(a, b) for (a, b) in self.containsFOLLOWOf if a != b]) # remove the self loops
return self.init_follow
def FOLLOW(self):
first = self.FIRST()
init_follow = self.getDirectFollowSets(first) # populates the containsFOLLOWOf set for SCC
g = Graph()
for v in self.v:
g.addVertex(v)
for a,b in self.containsFOLLOWOf:
g.addEdge(a, b, 1) # dummy edge to keep the edges
return g.computeFollowUsingSCC(first, init_follow)
|
How to compute FOLLOW(A) for each non-terminal A:
• If A is the start non-terminal, put EOF in FOLLOW(A)
Find the productions with A on the right-hand-side:
• For each production X → αAβ, put FIRST(β) − {ǫ} in FOLLOW(A)
• If ǫ is in FIRST(β) then put FOLLOW(X) into FOLLOW(A)
• For each production X → αA, put FOLLOW(X) into FOLLOW(A)
This recipe uses: http://code.activestate.com/recipes/117228-priority-dictionary/
Usage:
stg = """E -> E + T
E -> T
T -> T * F
T -> F
F -> ( E )
F -> id
"""
G = Grammar(stg)
expected = {'E#': set(['$']),
'E': set(['+', ')', '$']),
'T': set(['*', ')', '+', '$']),
'F': set(['*', ')', '+', '$'])
}
actual = G.FOLLOW()
for nt in expected.keys():
e = set()
for t in expected[nt]:
e |= set([t])
a = set()
for t in actual[nt]:
a |= set([t])
self.assertEquals( e, a )
Olá, sou iniciante neste local, gostaria de saber como encontro a lib.graph e como usa-la, se o seu uso pode ser substituído por outra no python... desde já agradeço.