LOGO Large Step Interpreter

open System;
  

let sin = Math.Sin
let cos = Math.Cos
let atan = Math.Atan
  

let float_of_int x = (float x)
let int_of_float x = (int x)
  

type logo = | Home
            | Forward of int
            | Turn of int
            | For of int * logo list
  

let pi = 4.0 * atan 1.0
let dsin t = sin(pi * (float_of_int t) / 180.0)
and dcos t = cos(pi * (float_of_int t) / 180.0)
  

let rec interpret f (x,y,d) e =
   let interpret' (x,y,d) e = match e with
                              | Home -> (0,0,0)
                              | Forward(n) -> (x + (int_of_float ((float n) * dsin d)), y + (int_of_float ((float n) * dcos d)), d)
                              | Turn(n) ->  (x, y, d + n)
                              | For(i, xs) -> if i > 0 then
                                                interpret f (interpret_prog f (x,y,d) xs) (For(i - 1, xs))
                                              else
                                                (x,y,d)
   f (x,y,d)
   interpret' (x,y,d) e
and interpret_prog f pos xs =  match xs with
                               | x::xs' ->  interpret_prog f (interpret f pos x) xs'              
                               | [] -> pos
  

let current = (0, 0, 0)
let sample = [Home; For(20, [Turn 18; For(36, [Forward 10; Turn 10])])]
  

let result = interpret_prog (printf "%A") current sample