type exp = CstInt of int
| CstTrue
| CstFalse
| Times of exp * exp
| Sum of exp * exp
| Sub of exp * exp
| Eq of exp * exp
| Iszero of exp
| Or of exp * exp
| And of exp * exp
| Not of exp
| Ifthenelse of exp * exp * exp

type evT = Int of int | Bool of bool

let typecheck (x, y) = match x with
| "int" ->
(match y with
| Int(u) -> true
| _ -> false)
| "bool" ->
(match y with
| Bool(u) -> true
| _ -> false)
| _ -> failwith ("not a valid type");;

let is_zero x = match (typecheck("int",x), x) with
| (true, Int(y)) -> Bool(y=0)
| (_, _) -> failwith("run-time error");;
let int_eq(x,y) =
match (typecheck("int",x), typecheck("int",y), x, y) with
| (true, true, Int(v), Int(w)) -> Bool(v = w)
| (_,_,_,_) -> failwith("run-time error ");;
let int_plus(x, y) =
match(typecheck("int",x), typecheck("int",y), x, y) with
| (true, true, Int(v), Int(w)) -> Int(v + w)
| (_,_,_,_) -> failwith("run-time error ");;
let int_times(x, y) =
match(typecheck("int",x), typecheck("int",y), x, y) with
| (true, true, Int(v), Int(w)) -> Int(v * w)
| (_,_,_,_) -> failwith("run-time error ");;
let int_sub(x, y) =
match(typecheck("int",x), typecheck("int",y), x, y) with
| (true, true, Int(v), Int(w)) -> Int(v - w)
| (_,_,_,_) -> failwith("run-time error ");;
let bool_and(x, y) =
match(typecheck("bool",x),typecheck("bool",y), x, y) with
| (true, true, Bool(v), Bool(w)) -> Bool(v && w)
| (_,_,_,_) -> failwith("run-time error ");;
let bool_or(x, y) =
match(typecheck("bool",x),typecheck("bool",y), x, y) with
| (true, true, Bool(v), Bool(w)) -> Bool(v || w)
| (_,_,_,_) -> failwith("run-time error ");;
let bool_not(x) =
match(typecheck("bool",x), x) with
| (true, Bool(v)) -> Bool(not(v))
| (_,_) -> failwith("run-time error ");;

let rec eval e =
match e with
| CstInt(n) -> Int(n)
| CstTrue -> Bool(true)
| CstFalse -> Bool(false)
| Iszero(e1) -> is_zero(eval(e1))
| Eq(e1, e2) -> int_eq(eval(e1), eval(e2))
| Times(e1,e2) -> int_times(eval(e1), eval(e2))
| Sum(e1, e2) -> int_plus(eval(e1), eval(e2))
| Sub(e1, e2) -> int_sub(eval(e1), eval(e2))
| And(e1, e2) -> bool_and(eval(e1), eval(e2))
| Or(e1, e2) -> bool_or(eval(e1), eval(e2))
| Not(e1) -> bool_not(eval(e1))
| Ifthenelse(e1,e2,e3) ->
let g = eval(e1) in
(match (typecheck("bool", g), g) with
|(true, Bool(true)) -> eval(e2)
|(true, Bool(false)) -> eval(e3)
|(_, _) -> failwith ("nonboolean guard"))
| _ -> failwith ("run-time error");;


let e1= Eq(CstInt(5),CstInt(5));;
let e2 = Sum(CstInt(5),CstInt(1));;
let e3 = CstInt(2);;
let e = Ifthenelse(e1,e2,e3);;
eval e;;