  In this work we define formal grammars in terms of free monoidal categories,
along with a functor from the category of formal grammars to the category of
automata. Generalising from the Booleans to arbitrary semirings, we extend our
construction to weighted formal grammars and weighted automata. This allows us
to link the categorical viewpoint on natural language to the standard machine
learning notion of probabilistic language model.
