Hask

(Difference between revisions)

Revision as of 04:29, 13 November 2009

Hask is the name usually given to the category having Haskell types as objects and Haskell functions between them as morphisms.

A type-constructor that is an instance of the Functor class is an endofunctor on Hask.

A solution approach to the issue of partiality making many of the identities required by categorical constructions not literally true in Haskell:

The right identity law fails in Hask if we distinguish values which can be distinguished by

seq

, since:

id . undefined = \x -> id (undefined x) = \x -> undefined x

should be equal to

undefined

, but can be distinguished from it using

seq

: ghci>

(undefined :: Int -> Int) `seq` ()

   * Exception: Prelude.undefined

ghci>

(id . undefined :: Int -> Int) `seq` ()

()

This article is a stub. You can help by expanding it.

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 * [http://www.cs.gunma-u.ac.jp/~hamana/Papers/cpo.pdf Makoto Hamana: ''What is the category for Haskell?'']
+A solution approach to the issue of partiality making many of the identities required by categorical constructions not literally true in Haskell:
+* [http://www.cs.nott.ac.uk/~nad/publications/danielsson-popl2006-tr.pdf Nils A. Danielsson, John Hughes, Patrik Jansson, and Jeremy Gibbons. ''Fast and loose reasoning is morally correct.'']
 == The seq problem ==
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     ghci> <hask>(id . undefined :: Int -> Int) `seq` ()</hask>
     ()
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 [[Category:Mathematics]]