just for fun - grammar for trigram models in GF

1 files changed, 34 insertions, 0 deletions

diff --git a/examples/trigram/Trigram.gf b/examples/trigram/Trigram.gf
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+++ b/examples/trigram/Trigram.gf
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+abstract Trigram = {
+
+cat 
+    -- A lexicon is a set of 'Word's
+    Word ;
+
+    -- All N-gram instances seen in the corpus are abstract syntax constants
+    Unigram (a     : Word) ;
+    Bigram  (a,b   : Word) ;
+    Trigram (a,b,c : Word) ;
+
+    -- A text is a sequence words where the sequence is indexed by the last two tokens
+    Seq (a,b : Word) ;
+
+    -- The estimated probability of the trigram 'a b c' is the total probability of all 
+    -- trees of type Prob a b c.
+    Prob (a,b,c : Word) ;
+
+data
+    -- Here we construct sequence by using nil and cons. The Prob argument ensures
+    -- that the sequence contains only valid N-grams and contributes with the right
+    -- probability mass
+    nil  : (a,b,c : Word) -> Prob a b c -> Seq b c ;
+    cons : ({a,b} : Word) -> Seq a b -> (c : Word) -> Prob a b c -> Seq b c ;
+
+    -- Here we construct probabilities. There are two ways: by trigrams, by bigrams and
+    -- by unigrams. Since the trigramP, bigramP, unigramP functions have some associated
+    -- probabilities as well this results in linear smoothing between the unigram, bigram 
+    -- and trigram models
+    trigramP : ({a,b,c} : Word) -> Trigram a b c -> Prob a b c ;
+    bigramP  : ({a,b,c} : Word) -> Bigram a b -> Bigram b c -> Prob a b c ;
+    unigramP : ({a,b,c} : Word) -> Unigram a -> Unigram b -> Unigram c -> Prob a b c ;
+
+}
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