[Haskell-cafe] binary operator modifiers

[Brent Yorgey]

On 10/29/07, Tim Newsham <newsham at lava.net> wrote:
>
> I would love to have the ability to define binary operator modifiers.
> For example:
>
>    f \overline{op} g       = liftM2 op f g
>    f \overleftarrow{op} n  = liftM2 op f (return n)
>    n \overrightarrow{op} g = liftM2 op (return n) f
>    \widehat{f} x           = liftM f x
>
> so that for example you could define functions like:
>
>     (*3) \overline{+} (/2)
>
> and
>
>     3 \overrightarrow{+} \widehat{read} getContents
>
> Obviously you could write this out the long way:
>
>     liftM2 (3+) $ liftM read getContents
>
> or go through the trouble of defining a bunch of binops
>
>     f <+> g = liftM2 (+) f g
>     n +>  g = return n <+> g
>     f <+  n = f <+> return n
>     read' = liftM read
>
>     (*3) <+> (/2)
>     3 +> read' getContents
>
> but doing this for more than one or two operators gets tedious
> quickly...
>
> Is there any way in Haskell to modify binops in this way and still
> be able to use them infix?  If not, has anyone considered supporting
> strange syntaxes like this?


I've wanted this at times, too, due to using a lot of J a year or so ago.  J
has some weird parsing/semantics rules so that f g h essentially means
liftM2 g f h.  For example, avg =. +/ % #   is the J equivalent of avg =
liftM2 (/) sum length.  Anyway, the closest you can get in Haskell is
something like this, using the infix expressions of Ken Shan and Dylan
Thurston<http://www.haskell.org/pipermail/haskell-cafe/2002-July/003215.html>
:

import Control.Monad
import Control.Monad.Instances

infixr 0 -:, :-

data Infix f y = f :- y
x -: f :- y = x `f` y

ov op = liftM2 op
ovL op f n = liftM2 op f (return n)
ovR op n f = liftM2 op (return n) f
hat f = liftM f

*Main> :t (*3) -:ov (+):- (/2)
(*3) -:ov (+):- (/2) :: forall a1. (Fractional a1) => a1 -> a1
*Main> ((*3) -:ov (+):- (/2)) 7
24.5
*Main> :t 3 -:ovR (+):- ((hat read) getContents)
3 -:ovR (+):- ((hat read) getContents) :: forall a. (Num a, Read a) => IO a

It works (?), but it's pretty ugly and hardly seems worth it, unfortunately.

-Brent
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