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-rw-r--r--lib/prelude/domains.ml133
1 files changed, 40 insertions, 93 deletions
diff --git a/lib/prelude/domains.ml b/lib/prelude/domains.ml
index 9dc9c86..264bf03 100644
--- a/lib/prelude/domains.ml
+++ b/lib/prelude/domains.ml
@@ -1,22 +1,20 @@
-(** 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}. *)
+(** 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)
+(** 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 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)
+ a, b
(** Integer domain: all integers, enumerated via a bijection from the naturals.
Schema: [value: integer]. *)
@@ -25,32 +23,18 @@ let integer : Relation.domain =
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."
+ 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
+ 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
+ ~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]. *)
@@ -58,35 +42,21 @@ 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."
+ 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)
+ 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
+ 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
+ ~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
@@ -101,50 +71,35 @@ let rational : Relation.domain =
(* 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) ]
+ 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."
+ 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)
+ 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 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" }
+ Not {body= Eq {left= Var "denominator"; right= Const (Obj.magic 0)}; universe= "integer"}
in
- Some (("DENOMINATOR_DIFFERENT_FROM_ZERO", denominator_not_zero)
- |> List.singleton)
+ Some (("DENOMINATOR_DIFFERENT_FROM_ZERO", denominator_not_zero) |> List.singleton)
in
let schema =
- Schema.empty
- |> Schema.add "numerator" "integer"
- |> Schema.add "denominator" "integer"
+ 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
+ ~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 =
@@ -155,17 +110,9 @@ let string : Relation.domain =
| Tuple.Materialized _ -> true
| Tuple.NonMaterialized _ -> false
in
- let schema =
- Schema.empty
- |> Schema.add "value" "string"
- in
+ let schema = Schema.empty |> Schema.add "value" "string" in
new Relation.domain
- ~name:"string"
- ~generator
- ~membership_criteria
- ~schema
+ ~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
+ (* TODO: Implement some form of enumeration for strings with a bijection on naturals. *)
+ ~cardinality:Conventions.Cardinality.Continuum ~lineage:None ~provenance:None
generated by cgit v1.2.3 (git 2.25.1) at 2026-11-04 05:26:43 +0000