open LambdaCal
(* 1. Can we implement recursion in terms of shift and reduce? Re recursion is an effect *)

(* The term i want to define is:
fix (\sum. (\x. if x = 0 then 0 else sum (x - 1)))

Let us create the nameless representation
fix (\. (\. if $0 = 0 then 0 else $0 + $1 ($0 - 1)))
*)

val args = CommandLine.arguments()
val input_string = hd args
val input_number = valOf (Int64.fromString input_string)
val func_name = hd (tl args)
val method_name = hd (tl (tl args))

local
  val cond = BuiltinApp (Equal, Var 0, Int 0)
  fun decrement x = BuiltinApp (Sub, x, Int 1)
  fun add x y = BuiltinApp (Sum, x, y)
  val branch = Branch (cond, Int 0, add (Int 1) (App (Var 1, decrement (Var 0))))
in
  fun sum input_number = App (Fix (Lambda branch), Int input_number)
end


(* The term i want to define is:
fix (\sum. (\acc. \n. if n = 0 then acc else sum (acc + 1) (n - 1)))

Let us create the nameless representation
fix (\. (\. \. if $0 = 0 then $1 else $2 ($1 + $0) ($0 - 1)))
*)

local
  val cond = BuiltinApp (Equal, Var 0, Int 0)
  fun decrement x = BuiltinApp (Sub, x, Int 1)
  fun sum x y = BuiltinApp (Sum, x, y)
  val branch = Branch (cond, Var 1, App (App (Var 2, sum (Var 1) (Var 0)), decrement (Var 0)))
in
  fun iter_sum input_number = App (App (Fix (Lambda (Lambda branch)), Int 0), Int input_number)
end

(* The term i want to define is:
fix (\fib. (\x. if x < 2 then x else fib (x - 1) + fib (x - 2)))

Let us create the nameless representation
fix (\. (\. if $0 < 2 then $0 else $1 ($0 - 1) + $1 ($0 - 2))) *)

local
  val cond = BuiltinApp (LessThan, Var 0, Int 2)
  fun sub x y = BuiltinApp (Sub, x, y)
  val fib_minus_1 = App (Var 1, sub (Var 0) (Int 1))
  val fib_minus_2 = App (Var 1, sub (Var 0) (Int 2))
  val recursive_case = BuiltinApp (Sum, fib_minus_1, fib_minus_2)
  val branch = Branch (cond, Var 0, recursive_case)
in
  fun fib input_number = App (Fix (Lambda branch), Int input_number)
end

exception InvalidAlgo

val algo = case func_name of
    "sum" => sum
  | "fib" => fib
  | "iter_sum" => iter_sum
  | _ => raise InvalidAlgo

val term = algo input_number
val timer = Timer.startCPUTimer()
val _ = LambdaCal.pretty_print_value (LambdaCal.evaluate term)
val _ = print ((Int64.toString input_number) ^ " ")
val {usr, sys} = Timer.checkCPUTimer timer
val tot = Time.+ (usr, sys)

fun showMs t = Time.toString t

val _ = print (showMs tot)
val _ = print "\n"