[Haskell-cafe] Question, re: Typeclassopedia Ex. 4.2.1

[Tom Ellis]

On Tue, Sep 29, 2015 at 07:48:05AM -0700, David Banas wrote:
> pure (flip ($)) <*> x <*> pure f     = (interchange)
> pure (flip ($)) <*> pure ($ f) <*> x = (homomorphism)

For one thing, this step doesn't look right.   <*> does not associate that
way.

It's probably worth at least putting each expression into ghci to check they
have the same time

    Prelude> import Control.Applicative
    Prelude Control.Applicative> let l = \x f -> pure (flip ($)) <*> x <*> pure f
    Prelude Control.Applicative> :t l
    l :: Applicative f => f a -> (a -> b) -> f b
    Prelude Control.Applicative> let l2 = \x f -> pure (flip ($)) <*> pure ($ f) <*> x
    Prelude Control.Applicative> :t l2
    l2 :: Applicative f => f (((a -> b1) -> b1) -> b) -> a -> f b

I imagine you're probably going to want to go via ($ x) rather than ($ f),
and possibly use that 'pure f <*> x = fmap f x = ($ x) <*> pure f'.

Tom