diff options
Diffstat (limited to '')
| -rw-r--r-- | lib/prelude/standard.ml | 304 |
1 files changed, 117 insertions, 187 deletions
diff --git a/lib/prelude/standard.ml b/lib/prelude/standard.ml index f38ee40..3822700 100644 --- a/lib/prelude/standard.ml +++ b/lib/prelude/standard.ml @@ -5,37 +5,26 @@ 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 } +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 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 + (* 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 + ~name ~schema ~constraints:None ~cardinality ~generator ~membership_criteria ~provenance:None ~lineage:None (** Enumerate pairs (a, b) where a < b using triangular indexing. *) @@ -44,17 +33,15 @@ let pair_of_nat_lt n = 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) + 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 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 let less_than_natural : Relation.ephemeral = let rec generator (position : int option) : Generator.result = @@ -62,14 +49,10 @@ let less_than_natural : Relation.ephemeral = | 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) ] + 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." + 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) @@ -83,16 +66,12 @@ let less_than_or_equal_natural : Relation.ephemeral = (* 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 + 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 ) + (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" + make_comparison ~name:"natural_natural_less_than_or_equal" ~domain_name:"natural" ~pred:(fun c -> c <= 0) ~cardinality:Conventions.Cardinality.AlephZero ~generator @@ -102,12 +81,8 @@ let greater_than_natural : Relation.ephemeral = | 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 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" @@ -121,16 +96,12 @@ let greater_than_or_equal_natural : Relation.ephemeral = 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 + 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 ) + (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" + make_comparison ~name:"natural_natural_greater_than_or_equal" ~domain_name:"natural" ~pred:(fun c -> c >= 0) ~cardinality:Conventions.Cardinality.AlephZero ~generator @@ -138,11 +109,8 @@ 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) + 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" @@ -154,12 +122,9 @@ let not_equal_natural : Relation.ephemeral = 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 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" @@ -168,7 +133,9 @@ let not_equal_natural : Relation.ephemeral = let plus_natural : Relation.ephemeral = let schema = - Schema.empty |> Schema.add "a" "natural" |> Schema.add "b" "natural" + Schema.empty + |> Schema.add "a" "natural" + |> Schema.add "b" "natural" |> Schema.add "sum" "natural" in let rec generator (position : int option) : Generator.result = @@ -176,42 +143,34 @@ let plus_natural : Relation.ephemeral = | 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 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 -> *) + (* 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 + | 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 + ~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.empty + |> Schema.add "a" "natural" + |> Schema.add "b" "natural" |> Schema.add "product" "natural" in let rec generator (position : int option) : Generator.result = @@ -219,43 +178,34 @@ let times_natural : Relation.ephemeral = | 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 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 -> *) + (* 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 + | 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 + ~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.empty + |> Schema.add "a" "natural" + |> Schema.add "b" "natural" |> Schema.add "difference" "natural" in let rec generator (position : int option) : Generator.result = @@ -264,45 +214,37 @@ let minus_natural : Relation.ephemeral = (* 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) + 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 -> *) + (* 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 + | 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 + ~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.empty + |> Schema.add "a" "natural" + |> Schema.add "b" "natural" |> Schema.add "quotient" "natural" |> Schema.add "remainder" "natural" in @@ -318,47 +260,36 @@ let divide_natural : Relation.ephemeral = 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); - ] + 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) + 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 -> *) + (* 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 + | 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 + ~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_natural; less_than_or_equal_natural; greater_than_natural; greater_than_or_equal_natural; @@ -367,5 +298,4 @@ let prelude_relations = plus_natural; times_natural; minus_natural; - divide_natural; - ] + divide_natural ] |