(* Opening a library for generic programming (https://github.com/dboulytchev/GT).
   The library provides "@type ..." syntax extension and plugins like show, gmap, etc.
*)
open GT 
             
(* The type for the expression. Note, in regular OCaml there is no "@type..." notation, 
   it came from GT. *)
@type expr =
  (* integer constant *) | Const of int
  (* variable         *) | Var   of string
  (* binary operator  *) | Binop of string * expr * expr with show

(* Available binary operators:
    !!                   --- disjunction
    &&                   --- conjunction
    ==, !=, <=, <, >=, > --- comparisons
    +, -                 --- addition, subtraction
    *, /, %              --- multiplication, division, reminder
*)

(* State: a partial map from variables to integer values. *)
type state = string -> int

(* Empty state: maps every variable into nothing. *)
let empty = fun x -> failwith (Printf.sprintf "Undefined variable %s" x)

(* Update: non-destructively "modifies" the state s by binding the variable x to value v and 
   returns the new state.
*)
let update x v s = fun y -> if x = y then v else s y

(* An example of a non-trivial state: *)                                                   
let s = update "x" 1 @@ update "y" 2 @@ update "z" 3 @@ update "t" 4 empty

(* Some testing *)
let _ =
  List.iter
    (fun x ->
       try  Printf.printf "%s=%d\n" x @@ s x
       with Failure s -> Printf.printf "%s\n" s
    ) ["x"; "a"; "y"; "z"; "t"; "b"]