無限数列

整数の無限数列のジェネレータみたいなもの。

# type intseq= Cons of int * (int -> intseq);;
type intseq = Cons of int * (int -> intseq)

フィボナッチ数列のジェネレータ

# let fib = 
    let rec f x y = Cons (x, f (x+y)) in
    Cons (1, f 1);;

実際に計算する関数

# let rec nthseq n (Cons (x, f)) = 
    if n = 1 then x
    else nthseq (n-1) (f x);;
val nthseq : int -> intseq -> int = <fun>

結果

# nthseq 1 fib;;
- : int = 1
# nthseq 2 fib;;
- : int = 1
# nthseq 3 fib;;
- : int = 2
# nthseq 4 fib;;
- : int = 3
# nthseq 5 fib;;
- : int = 5
# nthseq 6 fib;;
- : int = 8
# nthseq 7 fib;;
- : int = 13
# nthseq 8 fib;;
- : int = 21
# nthseq 9 fib;;
- : int = 34
# nthseq 10 fib;;
- : int = 55

リスト形式で結果を得るようにしてみた。

# let rec repeat n f x = 
    if n = 0 then []
    else f x :: repeat (n-1) f (f x);;
val repeat : int -> ('a -> 'a) -> 'a -> 'a list = <fun>
# let rec map f = function
    [] -> []
  | x :: rest -> f x :: map f rest;;
# map (fun (Cons (x, f)) -> x) (repeat 10 (fun (Cons (x, f)) -> f x) fib);;
- : int list = [1; 1; 2; 3; 5; 8; 13; 21; 34; 55]