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interpreter.ml
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/
interpreter.ml
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(* Environment *)
type 't env = (string * 't) list
exception WrongBindlist
let emptyenv(x) = [("",x)]
let rec applyenv(x,y) = match x with
| [(_,e)] -> e
| (i1,e1) :: x1 -> if y = i1 then e1
else applyenv (x1, y)
| [] -> failwith ("Wrong environment")
let bind(r, l, e) = (l, e) :: r
(* Abstract syntax *)
type ide = string
type intlist = Nil | Cons of exp * intlist
and exp =
| Eint of int
| Ebool of bool
| Eintlist of intlist
| Den of ide
| OP of string * exp * exp
| And of exp * exp
| Or of exp * exp
| Not of exp
| Eq of exp * exp
| Mineq of exp * exp
| Isempty of exp
| Append of exp * exp
| IfThenElse of exp * exp * exp
| Let of ide * exp * exp
| Fun of ide * exp
| Appl of exp * exp
| Map of exp * exp
| Appllist of exp * int
and eval =
| Int of int
| Bool of bool
| Intlist of intlist
| Unbound
| Funval of efun
and efun = exp * eval env
(* Operations on eval *)
let plus (x,y) =
(match (x,y) with
| (Int(u), Int(w)) -> Int(u+w)
| _ -> failwith ("type error"))
let diff (x,y) =
(match (x,y) with
| (Int(u), Int(w)) -> Int(u-w)
| _ -> failwith ("type error"))
let mult (x,y) =
(match (x,y) with
| (Int(u), Int(w)) -> Int(u*w)
| _ -> failwith ("type error"))
let eq (x,y) =
(match (x,y) with
| (Int(u), Int(w)) -> Bool(u = w)
| _ -> failwith ("type error"))
let mineq (x,y) =
(match (x,y) with
| (Int(u), Int(w)) -> Bool(u <= w)
| _ -> failwith ("type error"))
let et (x,y) =
(match (x,y) with
| (Bool(u), Bool(w)) -> Bool(u && w)
| _ -> failwith ("type error"))
let opp (x,y) =
(match (x,y) with
| (Bool(u), Bool(w)) -> Bool(u || w)
| _ -> failwith ("type error"))
let non x =
(match x with
| Bool(u) -> Bool(not u)
| _ -> failwith ("type error"))
let rec compare x y =
(match x, y with
| Nil, Nil -> true
| Nil, _
| _, Nil -> false
| Cons(Eint(h1), l1), Cons(Eint(h2), l2) -> h1 = h2 && compare l1 l2
| _ -> failwith ("type error"))
let rec sublist x y =
(match x, y with
| Nil, _ -> true
| _, Nil -> false
| Cons(Eint(h1), l1), Cons(Eint(h2), l2) -> h1 = h2 && sublist l1 l2
| _ -> failwith ("type error"))
let isempty x =
(match x with
| Nil -> Bool(true)
| _ -> Bool(false))
let rec append x y =
(match x with
| Nil -> y
| Cons(Eint(hd), l) -> Cons(Eint(hd), append l y)
| _ -> failwith ("type error"))
(* Auxiliary function for map *)
let toeint n =
(match n with
| Int(n) -> Eint(n)
| _ -> failwith ("type error"))
(* Interpreter's semantic *)
let rec sem ((e:exp), (r:eval env)) =
match e with
| Eint(n) -> Int(n)
| Ebool(b) -> Bool(b)
| Eintlist(l) -> Intlist(l)
| Den(i) -> applyenv(r,i)
| OP(op,a,b) ->
(match op with
| "+" -> plus(sem(a, r), sem(b, r))
| "-" -> diff(sem(a, r), sem(b, r))
| "*" -> mult(sem(a, r), sem(b, r))
| "=" -> eq(sem(a, r), sem(b, r))
| "<=" -> mineq(sem(a, r), sem(b, r))
| _ -> failwith ("wrong operator"))
| And(a,b) -> et(sem(a, r), sem(b, r))
| Or(a,b) -> opp(sem(a, r), sem(b, r))
| Not(b) -> non(sem(b, r))
| Eq(a,b) -> (match (sem(a,r), sem(b, r)) with
| (Intlist(u), Intlist(w)) -> Bool(compare u w)
| _ -> failwith ("type error"))
| Mineq(a,b) -> (match (sem(a,r), sem(b, r)) with
| (Intlist(u), Intlist(w)) -> Bool(sublist u w)
| _ -> failwith ("type error"))
| Append(a,b) -> (match (sem(a, r), sem(b, r)) with
| (Intlist(u), Intlist(w)) -> Intlist(append u w)
| _ -> failwith ("type error"))
| Isempty(l) -> (match sem(l, r) with
| Intlist(u) -> isempty u
| _ -> failwith ("type error"))
| IfThenElse(a,b,c) ->
let g = sem(a, r) in
(if g = Bool(true) then sem(b, r)
else (if g = Bool(false) then sem(c, r)
else failwith ("nonboolean guard")))
| Let(i,e1,e2) -> sem(e2, bind(r, i, sem(e1, r)))
| Fun(x,a) -> Funval(e, r)
| Appl(e1,e2) ->
(match sem(e1, r) with
| Funval(Fun(x, a), r1) ->
sem(a, bind(r1, x, sem(e2, r)))
| _ -> failwith ("no funct in apply"))
| Map(e1,e2) ->
(match sem(e1, r) with
| Funval(Fun(x, a), r1) ->
(match sem(e2, r) with
| Intlist(u) ->
Intlist((let rec map f e =
(match e with
| Nil -> Nil
| Cons(Eint(hd),tl) -> Cons(toeint(sem(Appl(f,Eint(hd)), r)), map f tl)
| _ -> failwith ("type error"))
in map e1 u))
| _ -> failwith ("type error"))
| _ -> failwith ("no funct in apply"))
| _ -> failwith ("nonlegal expression for sem")