type variable = string

type p_exp =
    Main of variable * variable * c_exp  (* def main with input x output y as c *)
and c_exp =
    Skip
  | Assignment of variable * a_exp       (* x := a *)
  | Sequence of c_exp * c_exp            (* c; c *)
  | If of b_exp * c_exp * c_exp          (* if b then c else c *)
  | While of b_exp * c_exp               (* while b do c *)
  | For of c_exp * b_exp * c_exp * c_exp (* for c; b; c do c *)
and b_exp =
    Boolean of bool                      (* v *)
  | BAnd of b_exp * b_exp                (* b and b *)
  | BOr of b_exp * b_exp                 (* b or b *)
  | BNot of b_exp                        (* not b *)
  | BCmp of a_exp * a_exp                (* a = a *)
  | BCmpLess of a_exp * a_exp            (* a < a *)
  | BCmpLessEq of a_exp * a_exp          (* a <= a *)
  | BCmpGreater of a_exp * a_exp         (* a > a *)
  | BCmpGreaterEq of a_exp * a_exp       (* a >= a *)
and a_exp =
    Variable of variable                 (* x *)
  | Integer of int                       (* n *)
  | Plus of a_exp * a_exp                (* a + a *)
  | Minus of a_exp * a_exp               (* a - a *)
  | Times of a_exp * a_exp               (* a * a *)
  | Division of a_exp * a_exp            (* a / a *)
  | Modulo of a_exp * a_exp              (* a % a *)
  | Power of a_exp * a_exp               (* a ^ a *)
  | PowerMod of a_exp * a_exp * a_exp    (* a ^ a % a *)
  | Rand of a_exp                        (* rand(0, a) *)



module VariableMap : Map.S with type key = variable

type memory = {
  assignments: int VariableMap.t
}

exception AbsentAssignment of string

val reduce : p_exp -> int -> int