(* Programming Languages (F28PL) lecture transcript - 4th October at 11:15 *)

Char.succ; (* has type char -> char *)
val incrementstring = implode o (map Char.succ) o explode;
incrementstring "HAL"; (* returns "IBM" *)
implode; (* has type char list -> string *)
map Char.succ; (* has type char list -> char list *)
explode; (* has type string -> char list *)

op =; (* takes in two equality types (alpha primed) *)

(fn x => x*x) 5;

(* Our sumlist function *)
fun sumlisth s [] = s 
  | sumlisth s (h::t) = sumlisth (s+h) t;

fun sumlist l = sumlisth 0 l;

(* A function which creates a big list *)
fun gigantalist 0 = [1]
  | gigantalist n = (gigantalist (n-1))@[n*n*n*n]@(gigantalist (n-1));

gigantalist 16;
length (gigantalist 16);
val mylist = gigatalist 20;
sumlist mylist;

(* A *hopefully* faster sumlist function *)
fun sumlistr [] = 0 
  | sumlistr (h::t) = h + (sumlistr t);

(* Functions from http://www.macs.hw.ac.uk/~gabbay/F28PL/notes/tail-recursion.ml *)
fun factr 0 = 1
  | factr n = n*(factr (n-1));

fun facth c 0 = c
  | facth c n = facth (n*c) (n-1);

fun fact n = facth 1 n;

factr 10;
factr 30; (* overflow raised exception *)
factr 20;

fun sumto f 0 = 0.0 
  | sumto f n = (f n) + (sumto f (n-1));

sumto (fn x => real x) 10;