David House wrote:
I've written a chapter for the Wikibook that attempts to teach some basic Category Theory in a Haskell hacker-friendly fashion. http://en.wikibooks.org/wiki/Haskell/Category_theory
Very, very nice! A few comments: A few semicolons were missing in the do blocks of the Points-free style/Do-block style table. I fixed that. I think it would be simpler without the do{} around f x and m - are you sure it's needed? You wrote: "category theory doesn't have a notion of 'polymorphism'". Well, of course it does - after all, this is "abstract nonsense", it has a notion of *everything*. But obviously we don't want to get into that complexity here. Here is a first attempt at a re-write of that paragraph: Note: The function id in Haskell is 'polymorphic' - it can have many different types as its domain and range. But morphisms in category theory are by definition 'monomorphic' - each morphism has one specific object as its domain and one specific object as its range. A polymorphic Haskell function can be made monomorphic by specifying its type, so it would be more precise if we said that the Haskell function corresponding to idA is (id :: A -> A). However, for simplicity, we will ignore this distinction when the meaning is clear. It is nice that you gave proofs of the >>= monad laws in terms of the join monad laws. I think you should state more clearly that the two sets of laws are completely equivalent. (Aren't they?) Maybe give the proofs in the opposite direction as an exercise. Regards, Yitz