[Haskell-cafe] Haskell-Cafe Digest, Vol 145, Issue 41

[David Banas]

Thanks for your reply, Tom.

That last expression doesn’t seem to have the correct type:

Prelude Control.Applicative> let l1 = \x f -> pure f <*> x
Prelude Control.Applicative> :t l1
l1 :: Applicative f => f a -> (a -> b) -> f b
Prelude Control.Applicative> let l2 = \x f -> fmap f x
Prelude Control.Applicative> :t l2
l2 :: Functor f => f a -> (a -> b) -> f b
Prelude Control.Applicative> let l3 = \x f -> ($ x) <*> pure f
Prelude Control.Applicative> :t l3
l3 :: a1 -> a -> (a1 -> a -> b) -> b

Is there a typo?

Thanks,
-db

On Sep 29, 2015, at 9:08 AM, haskell-cafe-request at haskell.org wrote:

> Message: 2
> Date: Tue, 29 Sep 2015 16:40:38 +0100
> From: Tom Ellis <tom-lists-haskell-cafe-2013 at jaguarpaw.co.uk>
> To: haskell-cafe at haskell.org
> Subject: Re: [Haskell-cafe] Question, re: Typeclassopedia Ex. 4.2.1
> Message-ID: <20150929154037.GS14111 at 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

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