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
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