Thursday, 10 September 2009

Catamorphism (generalised fold on type)

// Catamorphism
// Generalised Fold on a datatype

type exp = | Var of string
| Lambda of string * exp
| Apply of exp * exp

// This fold was made Tail Recursive using continuations.
let foldExpr varF lamF appF exp =
let rec Loop e cont =
match e with
| Var x -> cont (varF x)
| Lambda (x, body) -> Loop body (fun bodyAcc -> cont (lamF x bodyAcc))
| Apply (l, r) -> Loop l (fun lAcc ->
Loop r (fun rAcc ->
cont (appF lAcc rAcc)))
Loop exp (fun x -> x)

let toString =
(fun x -> sprintf "%s" x)
(fun x y -> sprintf "(λ%s.%s)" x y)
(fun x y -> sprintf "(%s %s)" x y)

printf "%s" (toString (Apply(Lambda("x", Var "x"), Lambda("y", Var "y"))))

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