Re: [Haskell-cafe] Re: Very crazy

On Tue, 2007-09-25 at 12:24 +0100, Andrew Coppin wrote:

Chaddaï Fouché wrote:

...

2007/9/25, Andrew Coppin :

...

This is why I found it so surprising - and annoying - that you can't use a 2-argument function in a point-free expression.

For example, "zipWith (*)" expects two arguments, and yet

sum . zipWith (*)

fails to type-check. You just instead write

\xs ys -> sum $ zipWith(*) xs ys

(sum . zipWith (*)) xs ys == (sum (zipWith (*) xs)) ys

so you try to apply sum :: [a] -> Int to a function (zipWith (*) xs) :: [a] -> [b], it can't work !

(sum.) . zipWith (*) works, but isn't the most pretty expression I have seen.

I'm still puzzled as to why this breaks with my example, but works perfectly with other people's examples...

So you're saying that

(f3 . f2 . f1) x y z ==> f3 (f2 (f1 x) y) z

? In that case, that would mean that

(map . map) f xss ==> map (map f) xss

which *just happens* to be what we want. But in the general case where you want

f3 (f2 (f1 x y z))

there's nothing you can do except leave point-free.

As people have pointed out, you can do this, and in fact, can -always- do this, i.e. always write things "point-free." lambdabot's @pl command, as mentioned elsewhere, is a constructive proof of this. However, I'm composing this email to point out a historical fact: Essentially, "writing everything point-free" was Haskell Curry's research programme. See the field of combinatory logic of which he is one of the fathers.