[Haskell-cafe] Re: ((a -> b) -> c) -> (a -> m b) -> m c

[apfelmus]

Henning Thielemann wrote:
> On Sun, 9 Sep 2007, Stuart Cook wrote:
>> When combining monadic and non-monadic code, I've often wished for a
>> magical combinator of type
>>
>>  (Monad m) => ((a -> b) -> c) -> (a -> m b) -> m c
>>
>> which would let me inject a monadic function into a pure one, then
>> wrap the ultimate result to ensure that no nastiness escapes.
> 
> If the signature would be
>   (Monad m) => ((a -> b) -> c) -> m (a -> b) -> m c
>    it would be possible, and the implementation would be 'liftM'/'fmap'.
> 
> In the Reader monad you can even convert
>   (a -> m b)   to   m (a -> b)

The existence of a conversion

   convert :: (a -> m b) -> m (a -> b)

between those two types for a given monad m is equivalent to the 
existence of

   magic :: ((a -> b) -> c) -> (a -> m b) -> m c

since we have

   convert   = magic id
   magic f g = return f `ap` convert g

Regards,
apfelmus