(* Programming Languages (F28PL) lecture transcript - 13th September at 15:15 *)

(* Checking the type of the + operator *)
op +;

(* Defining a function which inputs x and returns x ; has type 'a -> 'a *)
fun identity x = x;

(* This would return 5 *)
identity 5;

(* Since it has polymorphic type, we can pass anything to it *)
identity "Hello world";

(* Power function in the built-in library *)
Math.pow(2.0, 8.0);

(* Let's make our own "tail recursive" power function *)
fun pow x 0 = 1
  | pow x y = x*(pow x (y-1));

(* This will return 1 as it matches the first case (if x=0, return 1) *)
pow 2 0;

(* This should return 256 *)
pow 2 8;

(* Let's make another function, which is not tail recursive *)
fun crazy x 0 = x
  | crazy x y = (crazy x (y-1))*(crazy x (y-1));

(* We can see that a simple task would take longer with the crazy function *)
crazy 2 10;

(* We can pass the first integer to the pow function *)
pow 2;

(* Now we can pass another integer to 'it' *)
pow 8;

(* In this example, f has type int -> 'a *)
fun atzero f = f 0;

(* Here we specify that f must have type int -> int *)
fun atzero f = (f 0):int;

(* Now we can use atzero to pass a second integer (0) to pow *)
atzero (pow 2);

(* We can now make another function, but instead of passing 0, it would pass 8 *)
fun ateight f = (f 8):int;

(* And we can see the result of 3^8 *)
ateight (pow 3);

(* Let's make our own plus function *)
fun plus x y = x+y;

(* Simple, no big deal *)
plus 0 4;

(* Now let's make another one *)
fun otherplus (x,y) = x+y;

otherplus (2,3);
(* Should return 5, just as *)
plus 2 3;

(* If we only provide one number with plus we get something sensible *)
plus 2;

(* otherplus 2; (* however will give us an error *) *)

(* A stupid recursive add function *)
fun stupidadd x 0 = x
  | stupidadd x n = 1+(stupidadd x (n-1));

(* We can show the type of two integers *)
(5,4);

(* We can see for length, it take in a list of alphas and returns an integer *)
length;

(* 0.0 has type real *)
0.0;

(* we cannot add an int and a real; raises a type error *) 
0.0+5; 

(* real can input an integer and output a real *)
real;
real 5;

(* To convert a real to an integer we have to use the floor function *)
floor;

(* We can chain functions with the o operator, similar to pipelining in bash *)
real o floor; (* real -> real *)