Message: 2
Date: Tue, 29 Sep 2015 16:40:38 +0100
From: Tom Ellis <tom-lists-haskell-cafe-2013@jaguarpaw.co.uk>
To: haskell-cafe@haskell.org
Subject: Re: [Haskell-cafe] Question, re: Typeclassopedia Ex. 4.2.1
Message-ID: <20150929154037.GS14111@weber>
Content-Type: text/plain; charset=us-ascii

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