G'day all.
Quoting askyle <[EMAIL PROTECTED]>:
If you use this presentation you also need the following law:
(a . b) >=> c = (a >=> c) . b
that is, compatibility with ordinary function composition. I like to call
this "naturality", since it's instrumental in proving return and bind to be
natural transformations.
Define:
f >=> g = \x -> f x >>= g
fmap f xs = xs >>= return . f
Then:
fmap f . return
= (expand fmap)
\x -> (return x >>= return . f)
= (defn. of >=>)
\x -> (return >=> return . f) x
= (left identity)
\x -> (return . f) x
=
return . f
Therefore return is natural.
Bind (or, equivalently, join) is left as an exercise.
Cheers,
Andrew Bromage
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