1 (* evaluation2.ml: evaluation-based interpreter *)
3 type literal = Num of int | Bool of bool (* intersection of values and Constant terms *)
4 type primFunction = Succ | Pred | IsZero | Leq (* | Leq_partially_applied of int *)
6 (* these have to be declared later, inside the Env modules ...
7 type value = LiteralV of literal | Closure of lambdaTerm * env
8 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 *)
11 type constant = LiteralC of literal | FunctC of primFunction
12 type identifier = string
14 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
18 type value = LiteralV of literal | Closure of lambdaTerm * env
19 type bound_value = value
21 val push: identifier -> bound_value -> env -> env
22 val lookup: identifier -> env -> bound_value option
25 module Env1: Env = struct
26 type env = (identifier * bound_value) list
27 and value = LiteralV of literal | Closure of lambdaTerm * env
28 and bound_value = value
30 let push ident value env = (ident,value)::env
31 let rec lookup ident' env = match env with
33 | (ident,value)::_ when ident = ident' -> Some value
34 | _::env' -> lookup ident' env'
37 module Env2: Env = struct
38 type env = identifier -> bound_value option
39 and value = LiteralV of literal | Closure of lambdaTerm * env
40 and bound_value = value
41 let empty = fun _ -> None
42 let push ident value env = fun ident' -> if ident = ident' then Some value else env ident'
43 let lookup ident' env = env ident'
48 exception Stuck of lambdaTerm
50 let rec eval (term:lambdaTerm) (r:env) : value =
52 | IfThenElse(test, yes, no) -> (match eval test r with
53 | LiteralV(Bool true) -> eval yes r
54 | LiteralV(Bool false) -> eval no r
55 | LiteralV lit -> raise (Stuck (IfThenElse(Constant(LiteralC lit),yes,no)))
56 | Closure(term, _) -> raise (Stuck (IfThenElse(term,yes,no))))
57 | Let(bound_ident, arg, body) -> (match eval arg r with
58 | value -> eval body (push bound_ident value r))
59 | App(head, arg) -> (match eval head r with
60 | LiteralV lit -> raise (Stuck (App(Constant(LiteralC lit), arg)))
61 | Closure (Abstract(bound_ident, body), saved_r) -> eval body (push bound_ident arg saved_r) (* FIX ME *)
62 | Closure (Constant (FunctC Leq), saved_r) -> failwith "not yet implemented"
63 | Closure (Constant (FunctC (_ as prim)), saved_r) ->
64 (match (prim, eval arg r) with
65 | (Succ, LiteralV(Num n)) -> LiteralV(Num (n+1))
66 | (Pred, LiteralV(Num n)) -> LiteralV(Num (if n = 0 then 0 else n-1))
67 | (IsZero, LiteralV(Num n)) -> LiteralV(Bool (n=0))
68 | (_, LiteralV lit) -> raise (Stuck (App(Constant(FunctC prim), Constant(LiteralC lit))))
69 | (_, Closure(term, _)) -> raise (Stuck (App(Constant(FunctC prim), term))))
70 | Closure (term, _) -> raise (Stuck (App(term, arg))))
71 | Var ident -> (match lookup ident r with
73 | None -> raise (Stuck term)) (* free variables are stuck *)
74 | Constant (LiteralC lit) -> LiteralV lit
75 | Constant (FunctC _) -> Closure(term, empty) (* primFunctions evaluate as Closures with empty environments *)
76 | 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 *)
78 let rec check_numbers (term:lambdaTerm) : unit =
80 | Constant(LiteralC(Num n)) when n < 0 -> failwith ("Bad Number: " ^ string_of_int n)
83 | Abstract(_, body) -> check_numbers body
84 | App(head, arg) -> let () = check_numbers head
86 | Let(_, arg, body) -> let () = check_numbers arg
88 | IfThenElse(test, yes, no) -> let () = check_numbers test
89 in let () = check_numbers yes
92 let evaluate (term:lambdaTerm) : value =
93 (* scan to verify that term doesn't have any Const(Num (negative)) *)
94 let () = check_numbers term
95 (* evaluate starting with empty env *)