(** Predefined fundamental domains, ported from the Erlang implementation.
    Each domain carries a generator (for enumeration) and membership criteria
    (for validation). Values are stored as {!Conventions.AbstractValue.t} via
    [Obj.magic], following the same convention as {!Standard}. *)

(** Bijection from natural number to integer: 0→0, 1→1, 2→-1, 3→2, 4→-2, … *)
let nat_to_int n =
  if n = 0 then 0
  else if n mod 2 = 1 then (n + 1) / 2
  else -(n / 2)

(** Cantor pairing inverse: given position [n], returns a pair [(a, b)] of
    natural numbers such that [a + b] lies on the [n]-th diagonal. *)
let cantor_unpair n =
  let w =
    int_of_float (floor ((sqrt (float_of_int (8 * n + 1)) -. 1.) /. 2.))
  in
  let t = (w * (w + 1)) / 2 in
  let b = n - t in
  let a = w - b in
  (a, b)

(** Integer domain: all integers, enumerated via a bijection from the naturals.
    Schema: [value: integer]. *)
let integer : Domain.t =
  let rec generator (position : int option) : Generator.result =
    match position with
    | Some n ->
      let v = nat_to_int n in
      let attributes = Tuple.AttributeMap.of_list [ ("value", Obj.magic v) ] in
      Generator.Value
        (Tuple.make_materialized ~relation:"integer" ~attributes, generator)
    | None ->
      Generator.Error
        "Cannot produce a randomly enumerated value for the integer domain."
  in
  let membership_criteria : Tuple.t -> bool = function
    | Tuple.Materialized _ -> true
    | Tuple.NonMaterialized _ -> false
  in
  Domain.make ~name:"integer" ~generator ~membership_criteria
    ~cardinality:Conventions.Cardinality.AlephZero
    ~compare:(fun a b -> Stdlib.compare (Obj.magic a : int) (Obj.magic b : int))

(** Natural number domain: non-negative integers (0, 1, 2, …).
    Schema: [value: natural]. *)
let natural : Domain.t =
  let rec generator (position : int option) : Generator.result =
    match position with
    | Some n ->
      let attributes = Tuple.AttributeMap.of_list [ ("value", Obj.magic n) ] in
      Generator.Value
        (Tuple.make_materialized ~relation:"natural" ~attributes, generator)
    | None ->
      Generator.Error
        "Cannot produce a randomly enumerated value for the natural domain."
  in
  let membership_criteria : Tuple.t -> bool = function
    | Tuple.Materialized m -> (
      match Tuple.AttributeMap.find_opt "value" m.attributes with
      | Some attr -> (Obj.magic attr : int) >= 0
      | None -> false)
    | Tuple.NonMaterialized _ -> false
  in
  Domain.make ~name:"natural" ~generator ~membership_criteria
    ~cardinality:Conventions.Cardinality.AlephZero
    ~compare:(fun a b -> Stdlib.compare (Obj.magic a : int) (Obj.magic b : int))

(** Rational number domain: pairs [(numerator, denominator)] where the
    denominator is never zero.  The generator enumerates all such pairs via
    Cantor pairing on the integers.
    Schema: [numerator: integer, denominator: integer]. *)
let rational : Domain.t =
  let rec generator (position : int option) : Generator.result =
    match position with
    | Some n ->
      let a, b = cantor_unpair n in
      let num = nat_to_int a in
      (* Map b → non-zero integer: 0→1, 1→-1, 2→2, 3→-2, … *)
      let den =
        if b mod 2 = 0 then b / 2 + 1 else -((b + 1) / 2)
      in
      let attributes =
        Tuple.AttributeMap.of_list
          [ ("numerator", Obj.magic num); ("denominator", Obj.magic den) ]
      in
      Generator.Value
        (Tuple.make_materialized ~relation:"rational" ~attributes, generator)
    | None ->
      Generator.Error
        "Cannot produce a randomly enumerated value for the rational domain."
  in
  let membership_criteria : Tuple.t -> bool = function
    | Tuple.Materialized m -> (
      match Tuple.AttributeMap.find_opt "denominator" m.attributes with
      | Some attr -> (Obj.magic attr : int) <> 0
      | None -> false)
    | Tuple.NonMaterialized _ -> false
  in
  Domain.make ~name:"rational" ~generator ~membership_criteria
    ~cardinality:Conventions.Cardinality.AlephZero
    ~compare:(fun a b ->
      Stdlib.compare (Obj.magic a : float) (Obj.magic b : float))

(** String domain: any string value.  Not enumerable.
    Schema: [value: string]. *)
let string : Domain.t =
  let generator (_ : int option) : Generator.result =
    Generator.Error "Strings are not enumerable."
  in
  let membership_criteria : Tuple.t -> bool = function
    | Tuple.Materialized _ -> true
    | Tuple.NonMaterialized _ -> false
  in
  Domain.make ~name:"string" ~generator ~membership_criteria
    ~cardinality:Conventions.Cardinality.AlephZero
    ~compare:(fun a b ->
      String.compare (Obj.magic a : string) (Obj.magic b : string))