From 63ae3c930de89af6f85229a467caa3f53cb844a2 Mon Sep 17 00:00:00 2001 From: Marcos Magueta Date: Fri, 3 Apr 2026 16:17:38 -0300 Subject: format --- lib/prelude/standard.ml | 332 ++++++++++++++++++++++-------------------------- 1 file changed, 154 insertions(+), 178 deletions(-) (limited to 'lib/prelude/standard.ml') diff --git a/lib/prelude/standard.ml b/lib/prelude/standard.ml index 68012fc..6bdab0c 100644 --- a/lib/prelude/standard.ml +++ b/lib/prelude/standard.ml @@ -7,22 +7,23 @@ 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]. *) +(** 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.empty + |> Schema.add "left" domain_name |> Schema.add "right" domain_name in let membership_criteria : Tuple.t -> bool = 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) + 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 Relation.make ~hash:None ~name ~schema ~tree:None ~constraints:None @@ -33,38 +34,35 @@ let make_comparison ~name ~domain_name ~pred ~cardinality ~generator = (** 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 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.)) + int_of_float (floor ((sqrt (float_of_int ((8 * n) + 1)) -. 1.) /. 2.)) in - let t = (w * (w + 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.t = 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 ) + 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." + 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) @@ -74,17 +72,16 @@ let less_than_or_equal_natural : Relation.t = 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 ) + 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" @@ -96,15 +93,14 @@ let greater_than_natural : Relation.t = 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 ) + 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" @@ -115,16 +111,15 @@ let greater_than_or_equal_natural : Relation.t = 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 ) + 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" @@ -136,12 +131,11 @@ let equal_natural : Relation.t = 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 ) + 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" @@ -152,21 +146,19 @@ let not_equal_natural : Relation.t = 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 ) + 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.t = let schema = Schema.empty |> Schema.add "a" "natural" |> Schema.add "b" "natural" @@ -175,175 +167,159 @@ let plus_natural : Relation.t = 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 ) + 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 = 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) + 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 Relation.make ~hash:None ~name:"natural_plus" ~schema ~tree:None - ~constraints:None - ~cardinality:Conventions.Cardinality.AlephZero + ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero ~generator:(Some generator) ~membership_criteria ~provenance:(Relation.Provenance.Base "plus") ~lineage:(Relation.Lineage.Base "plus") let times_natural : Relation.t = let schema = - Schema.empty |> Schema.add "a" "natural" - |> Schema.add "b" "natural" + 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 ) + 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 = 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) + 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 Relation.make ~hash:None ~name:"natural_times" ~schema ~tree:None - ~constraints:None - ~cardinality:Conventions.Cardinality.AlephZero + ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero ~generator:(Some generator) ~membership_criteria ~provenance:(Relation.Provenance.Base "times") ~lineage:(Relation.Lineage.Base "times") let minus_natural : Relation.t = let schema = - Schema.empty |> Schema.add "a" "natural" - |> Schema.add "b" "natural" + 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 ) + (* 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 = function | Tuple.Materialized m -> ( - 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) + 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) | Tuple.NonMaterialized _ -> false in Relation.make ~hash:None ~name:"natural_minus" ~schema ~tree:None - ~constraints:None - ~cardinality:Conventions.Cardinality.AlephZero + ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero ~generator:(Some generator) ~membership_criteria ~provenance:(Relation.Provenance.Base "minus") ~lineage:(Relation.Lineage.Base "minus") let divide_natural : Relation.t = let schema = - Schema.empty |> Schema.add "a" "natural" - |> Schema.add "b" "natural" + 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 ) + (* 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 = 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) + 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 Relation.make ~hash:None ~name:"natural_divide" ~schema ~tree:None - ~constraints:None - ~cardinality:Conventions.Cardinality.AlephZero + ~constraints:None ~cardinality:Conventions.Cardinality.AlephZero ~generator:(Some generator) ~membership_criteria ~provenance:(Relation.Provenance.Base "divide") ~lineage:(Relation.Lineage.Base "divide") -- cgit v1.2.3