On 16 Dec 2007, at 2:23 AM, Dominic Steinitz wrote:
keep in mind that Haskell "composition" (.)
is not really composition in the category-theoretic
sense, because it adds extra laziness. Use this
Do you have a counter-example of (.) not being function composition in
the categorical sense?
Let bot be the function defined by
bot :: alpha -> beta
bot = bot
By definition,
(.) = \ f -> \ g -> \ x -> f (g x)
Then
bot . id
= ((\ f -> \ g -> \ x -> f (g x)) bot) id
= (\ g -> \ x -> bot (g x)) id
= \ x -> bot (g x)
which /= bot since (seq bot () = bot) but (seq (\ x -> M) () = ())
regardless of what expression we substitute for M.
jcc
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