[Haskell-cafe] Question, re: Typeclassopedia Ex. 4.2.1
David Banas
capn.freako at gmail.com
Tue Sep 29 14:48:05 UTC 2015
Hi all,
In trying to solve exercise 4.2.1 in Typeclassopedia, I’ve come up with the following:
To prove:
pure f <*> x = pure (flip ($)) <*> x <*> pure f
Proof:
pure (flip ($)) <*> x <*> pure f = (interchange)
pure (flip ($)) <*> pure ($ f) <*> x = (homomorphism)
pure (flip ($) ($ f)) <*> x = (definition of flip)
pure ($ ($ f)) <*> x = (interchange)
x <*> pure ($ f) = (interchange) (Is this step valid?)
pure f <*> x
Is the last step in my proof valid?
Thanks,
-db
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