(* evaluation2.ml: evaluation-based interpreter *)

type literal = Num of int | Bool of bool (* intersection of values and Constant terms *)
type primFunction = Succ | Pred | IsZero | Leq (* | Leq_partially_applied of int *)

(* these have to be declared later, inside the Env modules ...
type value = LiteralV of literal | Closure of lambdaTerm * env
type bound_value = value (* for now, "x" is bound to the same type of thing that Var "x" expresses, but in later stages that won't always be true *)
*)

type constant = LiteralC of literal | FunctC of primFunction
type identifier = string

type lambdaTerm = Constant of constant | Var of identifier | Abstract of identifier * lambdaTerm | App of lambdaTerm * lambdaTerm | IfThenElse of lambdaTerm * lambdaTerm * lambdaTerm | Let of identifier * lambdaTerm * lambdaTerm

module type Env = sig
  type env
  type value = LiteralV of literal | Closure of lambdaTerm * env
  type bound_value = value
  val empty: env
  val push: identifier -> bound_value -> env -> env
  val lookup: identifier -> env -> bound_value option
end

module Env1: Env = struct
  type env = (identifier * bound_value) list
  and value = LiteralV of literal | Closure of lambdaTerm * env
  and bound_value = value
  let empty = []
  let push ident value env = (ident,value)::env
  let rec lookup ident' env = match env with
    | [] -> None
    | (ident,value)::_ when ident = ident' -> Some value
    | _::env' -> lookup ident' env'
end

module Env2: Env = struct
  type env = identifier -> bound_value option
  and value = LiteralV of literal | Closure of lambdaTerm * env
  and bound_value = value
  let empty = fun _ -> None
  let push ident value env = fun ident' -> if ident = ident' then Some value else env ident'
  let lookup ident' env = env ident'
end

open Env1

exception Stuck of lambdaTerm

let rec eval (term:lambdaTerm) (r:env) : value =
  match term with
    | IfThenElse(test, yes, no) -> (match eval test r with
                                      | LiteralV(Bool true) -> eval yes r
                                      | LiteralV(Bool false) -> eval no r
                                      | LiteralV lit -> raise (Stuck (IfThenElse(Constant(LiteralC lit),yes,no)))
                                      | Closure(term, _) -> raise (Stuck (IfThenElse(term,yes,no))))
    | Let(bound_ident, arg, body) -> (match eval arg r with
                                      | value -> eval body (push bound_ident value r))
    | App(head, arg) -> (match eval head r with
                           | LiteralV lit -> raise (Stuck (App(Constant(LiteralC lit), arg)))
                           | Closure (Abstract(bound_ident, body), saved_r) -> eval body (push bound_ident arg saved_r) (* FIX ME *)
                           | Closure (Constant (FunctC Leq), saved_r) -> failwith "not yet implemented"
                           | Closure (Constant (FunctC (_ as prim)), saved_r) ->
                                     (match (prim, eval arg r) with
                                        | (Succ, LiteralV(Num n)) -> LiteralV(Num (n+1))
                                        | (Pred, LiteralV(Num n)) -> LiteralV(Num (if n = 0 then 0 else n-1))
                                        | (IsZero, LiteralV(Num n)) -> LiteralV(Bool (n=0))
                                        | (_, LiteralV lit) -> raise (Stuck (App(Constant(FunctC prim), Constant(LiteralC lit))))
                                        | (_, Closure(term, _)) -> raise (Stuck (App(Constant(FunctC prim), term))))
                           | Closure (term, _) -> raise (Stuck (App(term, arg))))
    | Var ident -> (match lookup ident r with
                              | Some v -> v
                              | None -> raise (Stuck term)) (* free variables are stuck *)
    | Constant (LiteralC lit) -> LiteralV lit
    | Constant (FunctC _) -> Closure(term, empty) (* primFunctions evaluate as Closures with empty environments *)
    | Abstract (_,_) -> Closure(term, r) (* Abstracts evaluate as Closures with the current environment; a more efficient implementation would save only that part of the environment that binds variables that are free in the Abstract *)

let rec check_numbers (term:lambdaTerm) : unit =
  match term with
    | Constant(LiteralC(Num n)) when n < 0 -> failwith ("Bad Number: " ^ string_of_int n)
    | Constant _ -> ()
    | Var _ -> ()
    | Abstract(_, body) -> check_numbers body
    | App(head, arg) -> let () = check_numbers head
                        in check_numbers arg
    | Let(_, arg, body) -> let () = check_numbers arg
                           in check_numbers body
    | IfThenElse(test, yes, no) -> let () = check_numbers test
                           in let () = check_numbers yes
                           in check_numbers no

let evaluate (term:lambdaTerm) : value =
  (* scan to verify that term doesn't have any Const(Num (negative)) *)
  let () = check_numbers term
  (* evaluate starting with empty env *)
  in eval term empty