module type Symantics = sig
    type 'a repr

    val int : int -> int repr
    val add : int repr -> int repr -> int repr
    val mul : int repr -> int repr -> int repr
    val app : ('a -> 'b) repr -> 'a repr -> 'b repr
    val lam : ('a repr -> 'b repr) -> ('a -> 'b) repr
end ;;

module Test(S:Symantics) = struct
    let test1 () = S.add (S.int 1) (S.int 2)
    let test2 () = S.mul (test1 ()) (S.int 2)
    let test3 () = S.lam (fun x -> S.add x (S.int 2))
    let test4 () = S.app (test3 ()) (test2 ())
end ;;

module Interp = struct
    type 'a repr = 'a

    let int i = i
    let add x y = x + y
    let mul x y = x * y
    let app f x = f x
    let lam f = f
end ;;

module Length = struct
    type 'a repr = int

    let int _ = 1
    let add x y = x + y
    let mul x y = x + y
    let app f x = f + x
    let lam f = f 0 + 1
end ;;

module T = Test(Interp);;

T.test1 ();;
T.test2 ();;
T.test3 ();;
T.test4 ();;

module T2 = Test(Length);;

T2.test1 ();;
T2.test2 ();;
T2.test3 ();;
T2.test4 ();;