Proposal: Applicative => Monad: Call for consensus

[Maciej Piechotka]

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

Regards
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