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 *)
and b_exp =
    Boolean of bool                     (* v *)
  | BAnd of b_exp * b_exp               (* b and b *)
  | BNot of b_exp                       (* not b *)
  | BCmpLess 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 *)



module VariableMap : Map.S with type key = variable

type memory = {
  assignments: int VariableMap.t
}

exception AbsentAssignment of string

val reduce : int -> p_exp -> int