Difference between revisions of "Hask"

Revision as of 01:10, 3 October 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.

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.

@@ Line 4: / Line 4: @@
 * [http://www.cs.gunma-u.ac.jp/~hamana/Papers/cpo.pdf Makoto Hamana: ''What is the category for Haskell?'']
+== The seq problem ==
+The right identity law fails in '''Hask''' if we distinguish values which can be distinguished by <hask>seq</hask>, since:
+<hask>id . undefined = \x -> id (undefined x) = \x -> undefined x</hask>
+should be equal to <hask>undefined</hask>, but can be distinguished from it using <hask>seq</hask>:
+    ghci> (undefined :: Int -> Int) `seq` ()
+    * Exception: Prelude.undefined
+    ghci> (id . undefined :: Int -> Int) `seq` ()
+    ()
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