(* lecture 8: curried functions; the "real" versions of map/filter/reduce *)

use "utility.sml";

(* so that I can use foldl, foldr, filter *)
open List;

(* len function computes the length of the given list.
   This version uses curried functions. *)
fun len(lst) = foldl op+ 0 (map (fn(x)=>1) lst);

val lentest = [10, 20, 30, 40];


(* curried version of pow function.
   its type is (int -> int -> int) *)
fun pow x 0 = 1
|   pow x y = x * pow x (y-1);


(* A currying example.
   sum3 takes 3 parameters and adds them. *)
fun sum3 a b c = a+b+c;

(* f is a partial instantiation of sum3.
   f is a new function that binds sum3's "a" parameter to be 42, and accepts
   the other two parameters b and c. *)
fun f = sum3 42;

(* g binds sum3's a and b to be 42 and 9, and accepts the third parameter c. *)
fun g = f 9;

val result = g 24;  (* result = 42+9+24 = 75 *)



(* Examples of function composition, and the 'real' curried version of map. *)
val x = map (round o Math.sqrt o real) (1--100);

fun squareWhole lst = map (real o (fn x => x*x) o trunc) lst;
val sqtest = [3.4, 1.7, 5.8, 10.6];