#contents * equi-recursive type in ocaml [#a4970a31] 参考: [[Developing Applications With Objective Caml:http://caml.inria.fr/pub/docs/oreilly-book/]] より、 - [[Cyclic types:http://caml.inria.fr/pub/docs/oreilly-book/html/book-ora208.html]] - [[Option -rectypes:http://caml.inria.fr/pub/docs/oreilly-book/html/book-ora209.html]] たとえば、タプル型でリストを作ったりできる。以下の例では、-rectypesを使って、1の無限リストを直積型で実現する。 Haskellではこれはできない。Nominalな型システムだから?(耳学問、ソース求む) $ ocaml Objective Caml version 3.09.3 # let rec ones = (1, ones);; This expression has type int * (int * 'a) but is here used with type int * 'a # ^D $ ocaml -rectypes Objective Caml version 3.09.3 # let rec ones = (1,ones);; val ones : int * 'a as 'a = (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (1, (...))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) # val x : int * 'a as 'a という型表現に注目して頂きたい。不動点演算子μで書くとμ'a.int*'a という感じ。 ** Haskellでムリヤリ同じことをやる [#g9493987] Haskellでムリヤリ実現するには。 data Rec t = R (t (Rec t)) という「型レベルの不動点演算子」みたいなものを作る。Haskellでは、不動点演算子Yは y = f (y f)となるのを思い出してほしい。 ones = R (1, ones) などとして使う。このonesの型は *Main> :t ones ones :: Rec ((,) Integer) データ構築子Rを介して再帰を展開する必要がある: printRec (R (a,r)) = "(" ++ show a ++ "," ++ printRec r *Main> printRec ones (1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,(1,.... (けいご)