domains

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diff --git a/lib/prelude/domains.ml b/lib/prelude/domains.ml
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+(** 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
+
+(** 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
+
+(** 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
+
+(** 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