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Marcin will give a short introduction to categories in Haskell, and he will present free construction of categories which embrace monadic actions and their usefulness to build state machines in Haskell.

Among examples are both Kleisli categories and and the pure category -> where monadic actions come from the identity monad. This is important as it gives a way to instantiate an abstract description in a pure setting (e.g. for testing). Such categories admit a free model which allows to build abstract models, and he will present the free construction. Finally, he will present an example application in which a finite state machine will be represented using such a free category. This will give a type safe presentation of a state machine, where each state transition is guarded by the type system.

This talk will be based on his (on going) work on the free-category package published on Hackage. https://hackage.haskell.org/package/free-category

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