関数型言語カリー化まわりメモ

1 min read読了の目安(約1500字

私の理解のためのindex.

https://kazu-yamamoto.hatenablog.jp/entry/20110906/1315279311

toggeterでのまとめ: カリー化と部分適用の違いと誤用

x,y,z -> V をx -> (y->(z->V)) に変換するのがカリー化。x,y,z-> Vのyに値を束縛して結果的にx,z->Vという関数になるのが部分適用。どこが同じなんだろうか。

部分適用は、変数に値を固定して、結果として、「本来必要な変数がすでに入力されている、部分的な関数をつくる(orできる)」というようなことだろうか?

英語の記事たち

n an algebra of functions, dealing with functions that take multiple arguments (or equivalent one argument that's an N-tuple) is somewhat inelegant -- but, as Moses Schönfinkel (and, independently, Haskell Curry) proved, it's not needed: all you need are functions that take one argument.

So how do you deal with something you'd naturally express as, say, f(x,y)? Well, you take that as equivalent to f(x)(y) -- f(x), call it g, is a function, and you apply that function to y. In other words, you only have functions that take one argument -- but some of those functions return other functions (which ALSO take one argument;-).

As usual, wikipedia has a nice summary entry about this, with many useful pointers (probably including ones regarding your favorite languages;-) as well as slightly more rigorous mathematical treatment.