type variable = string

val globalIdentifier : int ref

module VariableMap : Map.S with type key = variable
module VariableSet : Set.S with type elt = string

(* -------------------------------------------------------------------------- *)
(*                      polimporphic type checking types                      *)
(* -------------------------------------------------------------------------- *)

type id = int
type level = int

type type_f =
    IntegerTypeP
  | BooleanTypeP
  | TupleTypeP of type_f * type_f
  | VariableTypeP of variable_type ref
  | FunctionTypeP of type_f * type_f
  | ApplicationP of type_f * type_f
and variable_type =
    Unbound of id * level
  | Link of type_f
  | Generic of id

type env = type_f VariableMap.t
module IntegerMap : Map.S with type key = int

val pp_type_f : type_f -> string

(* -------------------------------------------------------------------------- *)

type ftype = (* type used for specification *)
    IntegerType
  | BooleanType
  | UnknownType
  | TupleType of ftype * ftype
  | FunctionType of ftype * ftype

type t_exp =
    Integer of int                                  (* x := a *)
  | Boolean of bool                                 (* v *)
  | Variable of variable                            (* x *)
  | Tuple of t_exp * t_exp                          (* (a, b) *)
  | Function of variable * ftype * t_exp            (* lambda x: t. x *)
  | Application of t_exp * t_exp                    (* x x *)
  | Plus of t_exp * t_exp                           (* x + x *)
  | Minus of t_exp * t_exp                          (* x - x *)
  | Times of t_exp * t_exp                          (* x * x *)
  | Division of t_exp * t_exp                       (* x / x *)
  | Modulo of t_exp * t_exp                         (* x % x *)
  | Power of t_exp * t_exp                          (* x ^ x *)
  | PowerMod of t_exp * t_exp * t_exp               (* (x ^ x) % x *)
  | Rand of t_exp                                   (* rand(0, x) *)
  | BAnd of t_exp * t_exp                           (* x && x *)
  | BOr of t_exp * t_exp                            (* x || x *)
  | BNot of t_exp                                   (* not x *)
  | First of t_exp                                  (* fst x *)
  | Second of t_exp                                 (* scn x *)
  | Cmp of t_exp * t_exp                            (* x == x *)
  | CmpLess of t_exp * t_exp                        (* x < x *)
  | CmpLessEq of t_exp * t_exp                      (* x <= x *)
  | CmpGreater of t_exp * t_exp                     (* x > x *)
  | CmpGreaterEq of t_exp * t_exp                   (* x >= x *)
  | IfThenElse of t_exp * t_exp * t_exp             (* if b then c else c *)
  | LetIn of variable * t_exp * t_exp               (* let x = x in x *)
  | LetFun of variable * variable * ftype * t_exp * t_exp
                                                    (* let rec x. y: t. x in x*)

type permitted_values =
    IntegerPermitted  of int
  | BooleanPermitted  of bool
  | TuplePermitted    of permitted_values * permitted_values
  | FunctionPermitted of closure
and closure = {
  input: variable;
  body: t_exp;
  assignments: permitted_values VariableMap.t;
  recursiveness: variable option
}

type memory = {
  assignments: permitted_values VariableMap.t
}


type base_error = [
    `AbsentAssignment of string
  | `WrongType of string
]

type typechecking_error = [
  | base_error
  | `WrongTypeSpecification of string
]

type polytypechecking_error = [
  | typechecking_error
  | `RecursionNotImplemented of string
]

type error = [
  | base_error
  | `DivisionByZero of string
]