The ViterbiNBestDerivation is an example of a more complicated semiring built up from smaller components. It keeps track of the top N scoring paths along with their derivations.

 type ViterbiNBestDerivation n m = ViterbiNBest n (Weighted Prob (Derivation m))

The ViterbiDerivation is a simpler semiring. It just keeps track of the best scoring path and it's derivation.

 type ViterbiDerivation m  = Viterbi (Weighted Prob (Derivation m))