further deletions on drl and prelude

3 files changed, 0 insertions, 577 deletions

diff --git a/lib/prelude/catalog.ml b/lib/prelude/catalog.ml
deleted file mode 100644
index 26fe30c..0000000
--- a/lib/prelude/catalog.ml
+++ /dev/null
@@ -1,158 +0,0 @@
-(** System catalog helpers. Pure definitions — no storage access, no
-    manipulation dependency. Consumed by {!Manipulation.Make} and
-    {!Catalog.Make} to bootstrap the catalog relations that make each multigroup
-    self-describing. *)
-
-(* TODO: on_rel_name and timing_rel_name are defined and seeded but never
-   written to by any executor. They appear to be stubs for trigger/timing
-   metadata that was never implemented. *)
-
-(** Dedicated multigroup hosting the system catalog. The catalog's relation
-    names keep the [public:] prefix — that prefix is part of the relation name
-    inside this mg, not a separate namespace. *)
-let prelude_mg = "sakura"
-
-let catalog_prefix = "public:"
-let relation_rel_name = catalog_prefix ^ "relation"
-let domain_rel_name = catalog_prefix ^ "domain"
-let attribute_rel_name = catalog_prefix ^ "attribute"
-let constraint_rel_name = catalog_prefix ^ "constraint"
-let on_rel_name = catalog_prefix ^ "on"
-let timing_rel_name = catalog_prefix ^ "timing"
-let branch_rel_name = catalog_prefix ^ "branch"
-let head_rel_name = catalog_prefix ^ "head"
-let multigroup_rel_name = catalog_prefix ^ "multigroup"
-let schema_rel_name = catalog_prefix ^ "schema"
-let function_predicate_rel_name = catalog_prefix ^ "function_predicate"
-let loaded_library_rel_name = catalog_prefix ^ "loaded_library"
-
-(** Relations present in every multigroup's catalog. *)
-let catalog_relation_names =
-  [ relation_rel_name;
-    domain_rel_name;
-    attribute_rel_name;
-    constraint_rel_name;
-    on_rel_name;
-    timing_rel_name;
-    schema_rel_name;
-    function_predicate_rel_name;
-    loaded_library_rel_name ]
-
-(** Relations exclusive to the sakura meta-multigroup. *)
-let sakura_only_relation_names = [multigroup_rel_name]
-
-let all_catalog_relation_names = catalog_relation_names @ sakura_only_relation_names
-let is_catalog_relation name = List.mem name all_catalog_relation_names
-let relation_schema : Schema.t = Schema.empty |> Schema.add "name" "string"
-let domain_schema : Schema.t = Schema.empty |> Schema.add "name" "string"
-
-let attribute_schema : Schema.t =
-  Schema.empty
-  |> Schema.add "relation_name" "string"
-  |> Schema.add "attr_name" "string"
-  |> Schema.add "domain_name" "string"
-
-let constraint_schema : Schema.t =
-  Schema.empty |> Schema.add "name" "string" |> Schema.add "relation_name" "string"
-
-let on_schema : Schema.t = Schema.empty |> Schema.add "event" "string"
-let timing_schema : Schema.t = Schema.empty |> Schema.add "timing" "string"
-let multigroup_schema : Schema.t = Schema.empty |> Schema.add "name" "string"
-let schema_schema : Schema.t = Schema.empty |> Schema.add "name" "string"
-
-let function_predicate_schema : Schema.t =
-  Schema.empty
-  |> Schema.add "name" "string"
-  |> Schema.add "symbol" "string"
-  |> Schema.add "cardinality" "string"
-  |> Schema.add "purity" "string"
-
-let loaded_library_schema : Schema.t = Schema.empty |> Schema.add "path" "string"
-
-(** Definitions seeded into every multigroup. *)
-let catalog_definitions =
-  [ relation_rel_name, relation_schema;
-    domain_rel_name, domain_schema;
-    attribute_rel_name, attribute_schema;
-    constraint_rel_name, constraint_schema;
-    on_rel_name, on_schema;
-    timing_rel_name, timing_schema;
-    schema_rel_name, schema_schema;
-    function_predicate_rel_name, function_predicate_schema;
-    loaded_library_rel_name, loaded_library_schema ]
-
-(** Extra definitions seeded only into the sakura meta-multigroup. *)
-let sakura_only_definitions = [multigroup_rel_name, multigroup_schema]
-
-(* TODO: all tuple builders use Obj.magic to coerce string values into
-   Attribute.value (Obj.t). This is the same UB pattern fixed in standard.ml;
-   should use Obj.repr instead. *)
-
-let build_relation_tuple rel_name : Tuple.materialized =
-  { Tuple.relation= relation_rel_name;
-    attributes= Tuple.AttributeMap.singleton "name" {Attribute.value= Obj.magic rel_name} }
-
-let build_domain_tuple dom_name : Tuple.materialized =
-  { Tuple.relation= domain_rel_name;
-    attributes= Tuple.AttributeMap.singleton "name" {Attribute.value= Obj.magic dom_name} }
-
-let build_attribute_tuples ~relation_name (schema : Schema.t) : Tuple.materialized list =
-  List.map
-    (fun (attr_n, dom_n) ->
-      { Tuple.relation= attribute_rel_name;
-        attributes=
-          Tuple.AttributeMap.of_list
-            [ "relation_name", {Attribute.value= Obj.magic relation_name};
-              "attr_name", {Attribute.value= Obj.magic attr_n};
-              "domain_name", {Attribute.value= Obj.magic dom_n} ] } )
-    schema
-
-let build_constraint_tuple cname rel_name : Tuple.materialized =
-  { Tuple.relation= constraint_rel_name;
-    attributes=
-      Tuple.AttributeMap.of_list
-        [ "name", {Attribute.value= Obj.magic cname};
-          "relation_name", {Attribute.value= Obj.magic rel_name} ] }
-
-let build_on_tuple event : Tuple.materialized =
-  { Tuple.relation= on_rel_name;
-    attributes= Tuple.AttributeMap.singleton "event" {Attribute.value= Obj.magic event} }
-
-let build_timing_tuple timing : Tuple.materialized =
-  { Tuple.relation= timing_rel_name;
-    attributes= Tuple.AttributeMap.singleton "timing" {Attribute.value= Obj.magic timing} }
-
-let build_multigroup_tuple mg_name : Tuple.materialized =
-  { Tuple.relation= multigroup_rel_name;
-    attributes= Tuple.AttributeMap.singleton "name" {Attribute.value= Obj.magic mg_name} }
-
-let build_schema_tuple schema_name : Tuple.materialized =
-  { Tuple.relation= schema_rel_name;
-    attributes= Tuple.AttributeMap.singleton "name" {Attribute.value= Obj.magic schema_name} }
-
-let purity_to_string p = Sexplib.Sexp.to_string (Conventions.Purity.sexp_of_t p)
-
-let purity_of_string s =
-  match Conventions.Purity.t_of_sexp (Sexplib.Sexp.of_string s) with
-  | p -> Some p
-  | exception _ -> None
-
-let cardinality_to_string c = Sexplib.Sexp.to_string (Conventions.Cardinality.sexp_of_t c)
-
-let cardinality_of_string s =
-  match Conventions.Cardinality.t_of_sexp (Sexplib.Sexp.of_string s) with
-  | c -> Some c
-  | exception _ -> None
-
-let build_function_predicate_tuple ~name ~symbol ~cardinality ~purity : Tuple.materialized =
-  { Tuple.relation= function_predicate_rel_name;
-    attributes=
-      Tuple.AttributeMap.of_list
-        [ "name", {Attribute.value= Obj.magic name};
-          "symbol", {Attribute.value= Obj.magic symbol};
-          "cardinality", {Attribute.value= Obj.magic (cardinality_to_string cardinality)};
-          "purity", {Attribute.value= Obj.magic (purity_to_string purity)} ] }
-
-let build_loaded_library_tuple path : Tuple.materialized =
-  { Tuple.relation= loaded_library_rel_name;
-    attributes= Tuple.AttributeMap.singleton "path" {Attribute.value= Obj.magic path} }
diff --git a/lib/prelude/domains.ml b/lib/prelude/domains.ml
deleted file mode 100644
index 264bf03..0000000
--- a/lib/prelude/domains.ml
+++ /dev/null
@@ -1,118 +0,0 @@
-(** Predefined fundamental domains. 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 : Relation.domain =
-  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
-  let schema = Schema.empty |> Schema.add "value" "integer" in
-  new Relation.domain
-    ~name:"integer" ~generator ~membership_criteria ~schema ~constraints:None
-    ~cardinality:Conventions.Cardinality.AlephZero ~lineage:None ~provenance:None
-
-(** Natural number domain: non-negative integers (0, 1, 2, …). Schema:
-    [value: natural]. *)
-let natural : Relation.domain =
-  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
-  let schema = Schema.empty |> Schema.add "value" "natural" in
-  new Relation.domain
-    ~name:"natural" ~generator ~membership_criteria ~schema ~constraints:None
-    ~cardinality:Conventions.Cardinality.AlephZero ~lineage:None ~provenance:None
-
-(** 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 : Relation.domain =
-  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
-  (* Note: Additionally to the membership criteria, we add the constraint here as this relation
-     can be further dismembered, rendering the denominator into a lone integer, that should
-     propagate the constraint `integer <> 0`. If we declared a domain `integer_without_zero`,
-     then this constraint would not be needed as the domain would not be dissociated from the value. *)
-  let constraints : Relation.RelationConstraint.t option =
-    let denominator_not_zero =
-      let open Constraint in
-      Not {body= Eq {left= Var "denominator"; right= Const (Obj.magic 0)}; universe= "integer"}
-    in
-    Some (("DENOMINATOR_DIFFERENT_FROM_ZERO", denominator_not_zero) |> List.singleton)
-  in
-  let schema =
-    Schema.empty |> Schema.add "numerator" "integer" |> Schema.add "denominator" "integer"
-  in
-  new Relation.domain
-    ~name:"rational" ~generator ~membership_criteria ~schema ~constraints
-    ~cardinality:Conventions.Cardinality.AlephZero ~lineage:None ~provenance:None
-
-(** String domain: any string value. Not enumerable. Schema: [value: string]. *)
-let string : Relation.domain =
-  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
-  let schema = Schema.empty |> Schema.add "value" "string" in
-  new Relation.domain
-    ~name:"string" ~generator ~membership_criteria ~schema
-    ~constraints:None
-      (* TODO: Implement some form of enumeration for strings with a bijection on naturals. *)
-    ~cardinality:Conventions.Cardinality.Continuum ~lineage:None ~provenance:None
diff --git a/lib/prelude/standard.ml b/lib/prelude/standard.ml
deleted file mode 100644
index 3822700..0000000
--- a/lib/prelude/standard.ml
+++ /dev/null
@@ -1,301 +0,0 @@
-(** Comparison and arithmetic relations over the natural domain. *)
-
-(* TODO: all relations here are hardcoded to naturals. The make_comparison
-   factory accepts a domain_name string but membership_criteria always uses
-   Stdlib.compare on Obj.t, which only works correctly for unboxed integers.
-   Extending to other domains requires a proper typed comparison dispatch. *)
-
-let mk v = {Attribute.value= Obj.repr v}
-
-(** Build a comparison relation over a single domain. [pred] receives the result
-    of [Stdlib.compare left right]. *)
-let make_comparison ~name ~domain_name ~pred ~cardinality ~generator =
-  let schema = Schema.empty |> Schema.add "left" domain_name |> Schema.add "right" domain_name in
-  let membership_criteria : (*(string -> Merkle.t option) ->*) Tuple.t -> bool =
-    (* fun _tree_of -> function *)
-    function
-    | Tuple.Materialized m -> (
-      match
-        ( Tuple.AttributeMap.find_opt "left" m.attributes,
-          Tuple.AttributeMap.find_opt "right" m.attributes )
-      with
-      | Some l, Some r -> pred (Stdlib.compare l.Attribute.value r.Attribute.value)
-      | _ -> false )
-    | Tuple.NonMaterialized _ -> false
-  in
-  new Relation.ephemeral
-    ~name ~schema ~constraints:None ~cardinality ~generator ~membership_criteria ~provenance:None
-    ~lineage:None
-
-(** Enumerate pairs (a, b) where a < b using triangular indexing. *)
-let pair_of_nat_lt n =
-  let nf = float_of_int n in
-  let r = int_of_float (floor ((1. +. sqrt (1. +. (8. *. nf))) /. 2.)) in
-  let t_prev = r * (r - 1) / 2 in
-  let left = n - t_prev in
-  left, r
-
-(** Enumerate all pairs (a, b) via Cantor pairing. *)
-let cantor_pair_of_nat 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
-
-let less_than_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some position ->
-        let left, right = pair_of_nat_lt position in
-        let attributes : Attribute.materialized Tuple.AttributeMap.t =
-          Tuple.AttributeMap.of_list ["left", mk left; "right", mk right]
-        in
-        Generator.Value (Tuple.make_materialized ~relation:"less_than" ~attributes, generator)
-    | None -> Error "Cannot produce a randomly enumerated value for less_than over naturals."
-  in
-  make_comparison ~name:"natural_natural_less_than" ~domain_name:"natural"
-    ~pred:(fun c -> c < 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let less_than_or_equal_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let a, b = cantor_pair_of_nat n in
-        (* a <= b is always true when a <= b; we enumerate all (a, b) with a <= b *)
-        let left = min a b in
-        let right = max a b in
-        let attributes = Tuple.AttributeMap.of_list ["left", mk left; "right", mk right] in
-        Generator.Value
-          (Tuple.make_materialized ~relation:"less_than_or_equal" ~attributes, generator)
-    | None -> Error "Cannot enumerate less_than_or_equal randomly."
-  in
-  make_comparison ~name:"natural_natural_less_than_or_equal" ~domain_name:"natural"
-    ~pred:(fun c -> c <= 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let greater_than_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let left, right = pair_of_nat_lt n in
-        (* Swap: right > left *)
-        let attributes = Tuple.AttributeMap.of_list ["left", mk right; "right", mk left] in
-        Generator.Value (Tuple.make_materialized ~relation:"greater_than" ~attributes, generator)
-    | None -> Error "Cannot enumerate greater_than randomly."
-  in
-  make_comparison ~name:"natural_natural_greater_than" ~domain_name:"natural"
-    ~pred:(fun c -> c > 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let greater_than_or_equal_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let a, b = cantor_pair_of_nat n in
-        let left = max a b in
-        let right = min a b in
-        let attributes = Tuple.AttributeMap.of_list ["left", mk left; "right", mk right] in
-        Generator.Value
-          (Tuple.make_materialized ~relation:"greater_than_or_equal" ~attributes, generator)
-    | None -> Error "Cannot enumerate greater_than_or_equal randomly."
-  in
-  make_comparison ~name:"natural_natural_greater_than_or_equal" ~domain_name:"natural"
-    ~pred:(fun c -> c >= 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let equal_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let attributes = Tuple.AttributeMap.of_list ["left", mk n; "right", mk n] in
-        Generator.Value (Tuple.make_materialized ~relation:"equal" ~attributes, generator)
-    | None -> Error "Cannot enumerate equal randomly."
-  in
-  make_comparison ~name:"natural_natural_equal" ~domain_name:"natural"
-    ~pred:(fun c -> c = 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let not_equal_natural : Relation.ephemeral =
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let a, b = cantor_pair_of_nat n in
-        let left, right = if a = b then a, b + 1 else a, b in
-        let attributes = Tuple.AttributeMap.of_list ["left", mk left; "right", mk right] in
-        Generator.Value (Tuple.make_materialized ~relation:"not_equal" ~attributes, generator)
-    | None -> Error "Cannot enumerate not_equal randomly."
-  in
-  make_comparison ~name:"natural_natural_not_equal" ~domain_name:"natural"
-    ~pred:(fun c -> c <> 0)
-    ~cardinality:Conventions.Cardinality.AlephZero ~generator
-
-let plus_natural : Relation.ephemeral =
-  let schema =
-    Schema.empty
-    |> Schema.add "a" "natural"
-    |> Schema.add "b" "natural"
-    |> Schema.add "sum" "natural"
-  in
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let a, b = cantor_pair_of_nat n in
-        let s = a + b in
-        let attributes = Tuple.AttributeMap.of_list ["a", mk a; "b", mk b; "sum", mk s] in
-        Generator.Value (Tuple.make_materialized ~relation:"plus" ~attributes, generator)
-    | None -> Error "Cannot enumerate plus randomly."
-  in
-  let membership_criteria : Tuple.t -> bool =
-    (* fun _tree_of ->  *)
-    function
-    | Tuple.Materialized m -> (
-      match
-        ( Tuple.AttributeMap.find_opt "a" m.attributes,
-          Tuple.AttributeMap.find_opt "b" m.attributes,
-          Tuple.AttributeMap.find_opt "sum" m.attributes )
-      with
-      | Some a, Some b, Some s ->
-          (Obj.magic a.Attribute.value : int) + (Obj.magic b.Attribute.value : int)
-          = (Obj.magic s.Attribute.value : int)
-      | _ -> false )
-    | Tuple.NonMaterialized _ -> false
-  in
-  new Relation.ephemeral
-    ~name:"natural_plus" ~schema ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero
-    ~generator ~membership_criteria ~provenance:None ~lineage:None
-
-let times_natural : Relation.ephemeral =
-  let schema =
-    Schema.empty
-    |> Schema.add "a" "natural"
-    |> Schema.add "b" "natural"
-    |> Schema.add "product" "natural"
-  in
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        let a, b = cantor_pair_of_nat n in
-        let p = a * b in
-        let attributes = Tuple.AttributeMap.of_list ["a", mk a; "b", mk b; "product", mk p] in
-        Generator.Value (Tuple.make_materialized ~relation:"times" ~attributes, generator)
-    | None -> Error "Cannot enumerate times randomly."
-  in
-  let membership_criteria : Tuple.t -> bool =
-    (* fun _tree_of -> *)
-    function
-    | Tuple.Materialized m -> (
-      match
-        ( Tuple.AttributeMap.find_opt "a" m.attributes,
-          Tuple.AttributeMap.find_opt "b" m.attributes,
-          Tuple.AttributeMap.find_opt "product" m.attributes )
-      with
-      | Some a, Some b, Some p ->
-          (Obj.magic a.Attribute.value : int) * (Obj.magic b.Attribute.value : int)
-          = (Obj.magic p.Attribute.value : int)
-      | _ -> false )
-    | Tuple.NonMaterialized _ -> false
-  in
-  new Relation.ephemeral
-    ~name:"natural_times" ~schema ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero
-    ~generator ~membership_criteria ~provenance:None ~lineage:None
-
-let minus_natural : Relation.ephemeral =
-  let schema =
-    Schema.empty
-    |> Schema.add "a" "natural"
-    |> Schema.add "b" "natural"
-    |> Schema.add "difference" "natural"
-  in
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        (* Enumerate pairs where a >= b, so difference >= 0 *)
-        let b, diff = cantor_pair_of_nat n in
-        let a = b + diff in
-        let attributes = Tuple.AttributeMap.of_list ["a", mk a; "b", mk b; "difference", mk diff] in
-        Generator.Value (Tuple.make_materialized ~relation:"minus" ~attributes, generator)
-    | None -> Error "Cannot enumerate minus randomly."
-  in
-  let membership_criteria : Tuple.t -> bool =
-    (* fun _tree_of ->  *)
-    function
-    | Tuple.Materialized m ->
-      begin match
-        ( Tuple.AttributeMap.find_opt "a" m.attributes,
-          Tuple.AttributeMap.find_opt "b" m.attributes,
-          Tuple.AttributeMap.find_opt "difference" m.attributes )
-      with
-      | Some a, Some b, Some d ->
-          let av = (Obj.magic a.Attribute.value : int) in
-          let bv = (Obj.magic b.Attribute.value : int) in
-          let dv = (Obj.magic d.Attribute.value : int) in
-          av - bv = dv && dv >= 0
-      | _ -> false
-      end
-    | Tuple.NonMaterialized _ -> false
-  in
-  new Relation.ephemeral
-    ~name:"natural_minus" ~schema ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero
-    ~generator ~membership_criteria ~provenance:None ~lineage:None
-
-let divide_natural : Relation.ephemeral =
-  let schema =
-    Schema.empty
-    |> Schema.add "a" "natural"
-    |> Schema.add "b" "natural"
-    |> Schema.add "quotient" "natural"
-    |> Schema.add "remainder" "natural"
-  in
-  let rec generator (position : int option) : Generator.result =
-    match position with
-    | Some n ->
-        (* Enumerate (b, q, r) triples where b > 0, then a = b*q + r, 0 <= r < b *)
-        (* We use a nested Cantor pairing: n -> (b_idx, qr_idx) -> (q, r) *)
-        let b_idx, qr_idx = cantor_pair_of_nat n in
-        let b = b_idx + 1 in
-        (* b > 0 *)
-        let q, r_raw = cantor_pair_of_nat qr_idx in
-        let r = r_raw mod b in
-        let a = (b * q) + r in
-        let attributes =
-          Tuple.AttributeMap.of_list ["a", mk a; "b", mk b; "quotient", mk q; "remainder", mk r]
-        in
-        Generator.Value (Tuple.make_materialized ~relation:"divide" ~attributes, generator)
-    | None -> Error "Cannot enumerate divide randomly."
-  in
-  let membership_criteria : Tuple.t -> bool =
-    (* fun _tree_of ->  *)
-    function
-    | Tuple.Materialized m -> (
-      match
-        ( Tuple.AttributeMap.find_opt "a" m.attributes,
-          Tuple.AttributeMap.find_opt "b" m.attributes,
-          Tuple.AttributeMap.find_opt "quotient" m.attributes,
-          Tuple.AttributeMap.find_opt "remainder" m.attributes )
-      with
-      | Some a, Some b, Some q, Some r ->
-          let av = (Obj.magic a.Attribute.value : int) in
-          let bv = (Obj.magic b.Attribute.value : int) in
-          let qv = (Obj.magic q.Attribute.value : int) in
-          let rv = (Obj.magic r.Attribute.value : int) in
-          bv > 0 && av = (bv * qv) + rv && rv >= 0 && rv < bv
-      | _ -> false )
-    | Tuple.NonMaterialized _ -> false
-  in
-  new Relation.ephemeral
-    ~name:"natural_divide" ~schema ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero
-    ~generator ~membership_criteria ~provenance:None ~lineage:None
-
-let prelude_relations =
-  [ less_than_natural;
-    less_than_or_equal_natural;
-    greater_than_natural;
-    greater_than_or_equal_natural;
-    equal_natural;
-    not_equal_natural;
-    plus_natural;
-    times_natural;
-    minus_natural;
-    divide_natural ]