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nagat01/join . fmap return = id.hs

Last active December 14, 2015 10:16
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join . fmap return = id.hs
-- monad laws
(>>= f) . return = f
(>>= return) = id
(>>= g) . (>>= f) = (>>= ((>>= g) . f))
-- definitions
fmap f = (>>= (return . f))
join = (>>= id)
-- theorem
join . fmap return
= (>>= id) . (>>= (return . return))
= (>>= ((>>= id) . (return . return)))
= (>>= (((>>= id) . return) . return))
= (>>= (id . return))
= (>>= return)
= id
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