Proposal: Applicative => Monad: Call for consensus

[David Menendez]

On Tue, Jan 11, 2011 at 4:53 AM, Maciej Piechotka <uzytkownik2 at gmail.com> wrote:
> On Mon, 2011-01-10 at 19:01 -0500, David Menendez wrote:
>> On Sun, Jan 9, 2011 at 10:41 PM, Maciej Piechotka <uzytkownik2 at gmail.com> wrote:
>> > On Sun, 2011-01-09 at 18:16 -0800, Iavor Diatchki wrote:
>> >> Hello,
>> >> In my experience, defining monads in terms of "fmap" and "join" leads
>> >> to code duplication.  The examples we have seen in this thread---so
>> >> far---are a bit misleading because they compare a partial
>> >> implementation of a monad (join without fmap) with a complete
>> >> implementation (bind).  Here is an example of what I mean:
>> >>
>> >>
>> >> data SP a               = PutChar Char (SP a)
>> >>                         | GetChar (Char -> SP a)
>> >>                         | Return a
>> >>
>> >>
>> >> fmapSP :: (a -> b) -> (SP a -> SP b)
>> >> fmapSP f (PutChar c sp) = PutChar c (fmapSP f sp)
>> >> fmapSP f (GetChar k)    = GetChar (\c -> fmapSP f (k c))
>> >> fmapSP f (Return a)     = Return (f a)
>> >>
>> >>
>> >> joinSP :: SP (SP a) -> SP a
>> >> joinSP (PutChar c sp)   = PutChar c (joinSP sp)
>> >> joinSP (GetChar k)      = GetChar (\c -> joinSP (k c))
>> >> joinSP (Return sp)      = sp
>> >>
>> >>
>> >> bindSP :: (a -> SP b) -> (SP a -> SP b)
>> >> bindSP f (PutChar c sp) = PutChar c (bindSP f sp)
>> >> bindSP f (GetChar k)    = GetChar (\c -> bindSP f (k c))
>> >> bindSP f (Return a)     = f a
>> >>
>> >>
>> >> I chose this example because I think that it illustrates nicely how
>> >> the three operators work, I hope that other readers find it useful.
>> >>
>> >
>> > Yes and no:
>> >
>> > 1. In monad transformers & co. you want weakened conditions on Functor
>> > and Applicative so you cannot reuse (>>=) in them - you end up with a
>> > function anyway.
>>
>> Is this true? Applicative functors compose, so you shouldn't need to
>> use monad transformers. Of the common monad transformers, the only
>> ones where the Applicative instance can be defined in terms of the
>> underlying Applicative instance are Identity, Reader, and Writer, all
>> of which are equivalent to composition (that is, you don't gain
>> anything by using the transformer instead of composition).
>>
>
> 1. Add MaybeT and ListT to 'the only ones'.

If you want the <*> = ap, then you need Monad f => Applicative (MaybeT
f). Otherwise, it's just composition.

The Applicative instance for ListT is just composition with []. Also,
ListT only produces monads when applied to Identity or Reader.

> 2. As of non-trivial Applicative see InterleaveT from last MonadReader
> (issue 17).

InterleaveT is not a monad transformer. It requires a monad, but
produces a non-monad applicative functor.

-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>