PCFG example

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+-- example of probabilistic grammar from Jurafsky & Martin p. 449
+
+PredVP.  S   ::= NP VP ; --# prob 0.80 
+PredAux. S   ::= Aux NP VP ; --# prob 0.15
+JustVP.  S   ::= VP ; --# prob  0.05
+
+DetNO.   NP  ::= Det Nom ; --# prob 0.20
+PNounNP. NP  ::= PNoun ; --# prob 0.35
+NomNP.   NP  ::= Nom ; --# prob 0.05
+ProNP.   NP  ::= Pro ; --# prob 0.40
+
+NounNom.  Nom ::= Noun ; --# prob 0.75
+CompNom.  Nom ::= Noun Nom ; --# prob 0.20
+PNounNom. Nom ::= PNoun Nom ; --# prob 0.05
+
+IntrVP. VP  ::= Verb ; --# prob 0.55
+TrVP.   VP  ::= Verb NP ; --# prob 0.40
+DitrVP: VP  ::= Verb NP NP ; --# prob 0.05
+
+that. Det ::= "that" ; --# prob 0.05
+the.  Det ::= "the" ; --# prob 0.80
+a.    Det ::= "a" ; --# prob 0.15
+
+bookN.   Noun  ::= "book" ; --# prob 0.10
+flights. Noun  ::= "flights" ; --# prob 0.50
+meal.    Noun  ::= "meal" ; --# prob 0.40
+
+bookV.    Verb  ::= "book" ; --# prob 0.30
+includeV. Verb  ::= "include" ; --# prob 0.30
+want.     Verb  ::= "want" ; --# prob 0.40
+
+can.  Aux ::= "can" ; --# prob 0.40
+does. Aux ::= "does" ; --# prob 0.30
+do.   Aux ::= "do" ; --# prob 0.30
+
+TWA.    PNoun ::= "TWA" ; --# prob 0.40
+Denver. PNoun ::= "Denver" ; --# prob 0.60
+
+you. Pro ::= "you" ; --# prob 0.40
+I.   Pro ::= "I" ; --# prob 0.60
+
+-- > p -prob "can you book TWA flights"
+--
+-- 4.3200000000000016e-7
+-- 3.7800000000000013e-7
+-- PredAux can (ProNP you) (TrVP bookV (NomNP (PNounNom TWA (NounNom flights))))
+-- PredAux can (ProNP you) (DitrVP bookV (PNounNP TWA) (NomNP (NounNom flights)))
+-- [0.15,  0.40,0.40, 0.40, 0.05,  0.30,  0.35,   0.40, 0.05,  0.75,   0.50]
+--
+-- J&M have different figures, but they seem to be wrong. For
+-- instance, the products have 12 terms although the trees have only
+-- 11 constructors.