Can the following polymorphic functions
let id x = x;; let compose f g x = f (g x);; let rec fix f = f (fix f);; (*laziness aside*)
be written for types/type constructors or modules/functors? I tried
type 'x id = Id of 'x;; type 'f 'g 'x compose = Compose of ('f ('g 'x));; type 'f fix = Fix of ('f (Fix 'f));;
for types but it doesn't work.
Here's a Haskell version for types:
data Id x = Id x data Compose f g x = Compose (f (g x)) data Fix f = Fix (f (Fix f)) -- examples: l = Compose [Just 'a'] :: Compose  Maybe Char type Natural = Fix Maybe -- natural numbers are fixpoint of Maybe n = Fix (Just (Fix (Just (Fix Nothing)))) :: Natural -- n is 2 -- up to isomorphism composition of identity and f is f: iso :: Compose Id f x -> f x iso (Compose (Id a)) = a
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