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Commit ae97813

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Adding skeletons for LLParsers and top-downBreadthFirstParser. Still a lot of working out to do.
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‎sudkampPython/LLParsers.py‎

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from grammars.grammar import STARTSYMBOL
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from grammars.contextFree import ContextFreeGrammar
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"""
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Algorithm 19.4.1
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input: context-free grammar G = (V, Alphabet, P, S)
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1. for each a that is in Alphabet do F`(a) := {a}
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2. for each A that is in V do F(a) := { {null} if A -> null is rule in P
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{ empty set otherwise
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3. repeat
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3.1 for each A that is in V do F`(A) := F(A)
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3.2 for each rule A -> u<sub>1</sub>u<sub>2</sub>...u<sub>n</sub> with n > 0 do
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F(A) := F(A) UNION
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trunc<sub>k</sub>(F`(u<sub>1</sub>)F`(u<sub>2</sub>)...F`(u<sub>n</sub>)) until F(A) = F`(A) for all A in V
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4. FIRST<sub>k</sub>(A) = F(A)
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"""
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def FIRSTk( k, G ):
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Fprime, F, first_k = {}, {}, {} # initialise dictionaries
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for a in G.terminals:
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Fprime[a] = {a}
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for A in G.vars:
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{None} if Rule(A, None) in G.rules else {}
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while True:
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for A in G.vars:
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Fprime[A] = F[A]
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for rule in [rule for rule in G.rules if len(rule.rhs) > 0]:
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F[A] = F[A] | trunc_k( Fprime[] for all elements of rhs concatenated)
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if all(F[A] == Fprime[A] for A in G.vars):
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break
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for A in G.vars: # Originally just FIRSTk[A] = F[A]
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first_k[A] = F[A]
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return first_k
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"""
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Algorithm 19.5.1
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input: context-free grammar G = (V, Alphabet, P, S)
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FIRSTk(A) for every A in V
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1. FL(S) := {null}
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2. for each A in V - {S} do FL(A) := empty
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3. repeat
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3.1 for each A in V do FL`(A) := FL(A)
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3.2 for each rule A -> w = u<sub>1</sub>u<sub>2</sub>...u<sub>n</sub> with
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w NOT a terminal string do
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3.2.1 L := FL`(A)
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3.2.2 if u<sub>n</sub> in V then FL(u<sub>n</sub>) := FL(u<sub>n</sub>) UNION L
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3.2.3 for i := n - 1 to 1 do
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3.2.3.1 L := trunc<sub>k</sub>(FIRST<sub>k</sub>(u<sub>i+1</sub>)L)
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3.2.3.2 if u<sub>i</sub> in V then FL(u<sub>i</sub>) := FL(u<sub>i</sub>) UNION L
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until FL(A) = FL`(A) for every A in V
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4. FOLLOW<sub>k</sub>(A) := FL(A)
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"""
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def FOLLOWk(k, G, FIRSTk ):
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follow_k, FLprime = {}, {} # initialise
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FL = { STARTSYMBOL : {None} }
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for A in (G.vars - {STARTSYMBOL}): FL[A] = {}
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while True: # repeat
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for A in G.vars: FLprime[A] = FL[A]
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for rule in [r for r in G.rules if any(u.isupper() for u in r.rhs)]:
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A = rule.lhs[0]
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L = FLprime[A]
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n = len(rule.rhs)
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u = rule.rhs
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if u[n-1] in G.vars: FL[u[n-1]] = FL[u[n-1]] | L
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for i in range(len(r.rhs)-2, -1, -1): # equiv to n-1, n-2, n-3, ..., 1
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L = trunc_k( k, FIRSTk( k, u[n+1]).update(L) ) # TODO: this could be wrong!!
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if u[i] in G.vars:
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FL[u[i]] = FL[u[i]] | L
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if all(FL[A] = FLprime[A] for A in G.vars): # until
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break
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for A in G.vars:
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follow_k[A] = FL[A]
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return follow_k
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"""
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Introduced to simplify the definition of the fixed-length lookahead sets,
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trunc_k is a function from powerset(Σ*) to powerset(Σ*) defined by:
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trunc_k(X) = {u | u ε X with len(u) <= k or uv ε X with len(u) = k}
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"""
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def trunc_k( k, X ):
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result = set()
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for uv in X:
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if len(uv) <= k:
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result.add( uv ) # uv is u ε X
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else:
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result.add( uv[:k] )
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return result
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def LA_k( k, A ):
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return trunc_k( k, LA(A))
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"""
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The lookahead set of the variable A, LA(A), is defined by
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LA(A) = {x | S *-> uAv *-> ux ε Σ*}
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For each rule A -> w in P, the lookahead set of the rule A -> w is defined by
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LA(A->w) = {x | wv *-> x where x ε Σ* and S *-> uAv}
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"""
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def LA( X ):
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if type(X) == str: # X is variable, A
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pass # TODO
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#return {x | S *-> uAv *-> ux ε Σ*} # TODO: this is complicated
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else: # X is a rule A -> w
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pass # TODO
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#return {x | wv *-> x where x ε Σ* and S *-> uAv}

‎sudkampPython/breadthFirstParsers.py‎

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from collections import deque
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from grammars.grammar import STARTSYMBOL
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"""
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Algorithm 18.2.1
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Breadth-First Top-Down Parser
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input: context free grammar G = (V, Alphabet, P, S)
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string p, where p is element of Alphabet*
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string p, where p is element of Alphabet*
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data structure: queue Q
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1. initialize T with root S
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INSERT(S, Q)
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2. repeat
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2.1 q := REMOVE(Q) (node to be expanded)
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2.2 i := 0 (number of last rule used)
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2.3 done := false (Boolean indicator of expansion completion)
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Let q = uAv where A is the leftmost variable in q
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2.4 repeat
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2.4.1 if there is no A rule numbered greater than i the done := true
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2.4.2 if not done then
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Let A -> w be the first A rule with number greater than i and
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let j be the number of this rule
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2.4.2.1 if uwv is not element of Alphabet* and the terminal prefix of
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uwv matches a prefix of p then
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2.4.2.1.1 INSERT(uwv, Q)
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2.4.2.1.2 Add node uwv to T. Set a pointer from uwv to q
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end if
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end if
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2.4.3 i := j
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until done or p = uwv
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2.1 q := REMOVE(Q) (node to be expanded)
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2.2 i := 0 (number of last rule used)
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2.3 done := false (Boolean indicator of expansion completion)
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Let q = uAv where A is the leftmost variable in q
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2.4 repeat
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2.4.1 if there is no A rule numbered greater than i the done := true
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2.4.2 if not done then
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Let A -> w be the first A rule with number greater than i and
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let j be the number of this rule
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2.4.2.1 if uwv is not element of Alphabet* and the terminal prefix of
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uwv matches a prefix of p then
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2.4.2.1.1 INSERT(uwv, Q)
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2.4.2.1.2 Add node uwv to T. Set a pointer from uwv to q
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end if
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end if
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2.4.3 i := j
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until done or p = uwv
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until EMPTY(Q) or p = uwv
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3. if p = uwv then accept else reject
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"""
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def breadthFirstTopDownParse( contextFreeGrammar, p):
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def breadthFirstTopDownParse( G, p, Q):
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S = Node( STARTSYMBOL )
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T = SearchTree( S )
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INSERT( S, Q )
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while True: # repeat
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q = REMOVE(Q)
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i = 0
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done = False
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u, A, v = uAv_structure( q.sentForm )
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while True: # repeat
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validRules = [(j, rule) for j, rule in enumerate(G.rules) if (rule.lhs == A) and (j > i)]
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if not validRules:
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done = True
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if not done:
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A, w = validRules[0][1].lhs, validRules[0][1].rhs # rule A -> w
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j = validRules[0][0]
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if (not all(x.islower() for x in u+w+v) and
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***the terminal prefix of uwv matches a prefix of p***):
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uwv = Node(u+w+v)
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INSERT( uwv, Q )
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uwv.parent = q # and add uwv to T
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i = j
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if done or p == uwv: break # until
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if EMPTY(Q) or p == uwv
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return True if p == uwv else False
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def uAv_structure( sentForm ):
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raise NotImplementedError
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def INSERT( x, Q ):
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""" places the string x at the rear of the queue """
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return Q.append(x)
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def REMOVE( Q ):
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""" returns the item at the front of Q and deletes it from Q. """
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return Q.popleft()
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def EMPTY( Q ):
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""" boolean function that returns true if queue is empty, false otherwise. """
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return len(Q) == 0
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class Node( object ):
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""" A node to be a part of the search tree T. Contains a sentential form. """
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def __init__(self, sentForm, parent=None ):
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self.parent = parent
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self.sentForm = sentForm
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class SearchTree( object ):
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"""
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The 'implicit tree' of a grammar is the tree of possible derivation
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paths in that grammar. This 'search tree' is the portion of the implicit
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tree that is examined during the parse.
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"""
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def __init__(self, root=None):
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self.root = root
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# TODO: expand class to fulfil its function within the parsers
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"""
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Algorithm 18.4.1
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Breath-First Bottom-Up Parser
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input: context-free grammar G = (V, Alphabet, P, S)
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string p, where p is element of Alphabet*
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string p, where p is element of Alphabet*
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data structure: queue Q
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1. initialize T with root p
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INSERT(p, Q)
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INSERT(p, Q)
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2. repeat
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q := REMOVE(Q)
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2.1 for each rule A -> w in P do
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2.2.1 for each decomposition uwv of q with v, where v is element of Alphabet* do
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2.1.1.1 INSERT(uAv, Q)
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2.1.1.2 Add node uAv to T. Set a pointer from uAv to q
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end for
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end for
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until q = S or EMPTY(Q)
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q := REMOVE(Q)
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2.1 for each rule A -> w in P do
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2.2.1 for each decomposition uwv of q with v, where v is element of Alphabet* do
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2.1.1.1 INSERT(uAv, Q)
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2.1.1.2 Add node uAv to T. Set a pointer from uAv to q
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end for
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end for
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until q = S or EMPTY(Q)
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3. if q = S then accept else reject
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"""
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def breadthFirstBottomUpParser( contextFreeGrammar, p):

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