path: root/lib/algebra.ml

type error =
  | StorageError   of string
  | GeneratorError of string

module Make(Storage : Management.Physical.S) = struct
  module Ops = Manipulation.Make(Storage)
  type storage = Storage.t

  (* Internal generator utilities *)

  let rec list_generator : Tuple.t list -> Generator.t = function
    | []        -> (fun _pos -> Generator.Done)
    | t :: rest -> (fun _pos -> Generator.Value (t, list_generator rest))

  let drain gen =
    let rec go gen pos acc =
      match gen (Some pos) with
      | Generator.Done            -> Ok (List.rev acc)
      | Generator.Error e         -> Error (GeneratorError e)
      | Generator.Value (t, next) -> go next (pos + 1) (t :: acc)
    in go gen 0 []

  let to_generator (storage : storage) (rel : Relation.t) : Generator.t =
    match rel.Relation.generator with
    | Some gen -> gen
    | None ->
      (* TODO: Avoid materializing all tuple hashes/tuples at once.
         Current implementation calls tuple_hashes rel which loads all hashes
         into memory, then load_tuples which loads all tuples. This defeats
         lazy evaluation and scales badly (fails for billions of tuples).
         Replace with paginated tuple_hashes or Merkle streaming to load
         hashes/tuples on demand in chunks. *)
      let hashes = Ops.tuple_hashes rel in
      (match Ops.load_tuples storage hashes with
       | Error _ -> (fun _pos -> Generator.Error ("Failed to load: " ^ rel.Relation.name))
       | Ok ts -> list_generator (List.map (fun t -> Tuple.Materialized t) ts))

  let of_generator ~name ~schema ?constraints ?cardinality gen =
    let cardinality =
      match cardinality with
      | Some c -> c
      | None -> Conventions.Cardinality.AlephZero
    in
    Relation.make
      ~hash:None ~name ~schema ~tree:None ~constraints
      ~cardinality
      ~generator:(Some gen)
      ~membership_criteria:(fun _ -> true)
      ~provenance:Relation.Provenance.Undefined
      ~lineage:(Relation.Lineage.Base "derived")

  let const_relation (pairs : (string * Conventions.AbstractValue.t) list) : Relation.t =
    let attrs = List.fold_left (fun acc (k, v) ->
      Tuple.AttributeMap.add k { Attribute.value = v } acc)
      Tuple.AttributeMap.empty pairs
    in
    let tuple = Tuple.Materialized { Tuple.relation = "const"; attributes = attrs } in
    let schema = List.map (fun (k, _) -> (k, "abstract")) pairs in
    of_generator ~name:"const" ~schema (list_generator [tuple])

  (* Operators *)

  let select_fn storage predicate rel =
    let gen = to_generator storage rel in
    let lazy_gen =
      let rec go g pos =
        match g pos with
        | Generator.Done    -> Generator.Done
        | Generator.Error e -> Generator.Error e
        | Generator.Value (t, next) ->
          if predicate t then Generator.Value (t, go next)
          else go next (Option.map ((+) 1) pos)
      in fun pos -> go gen pos
    in
    Ok (of_generator ~name:("σ_" ^ rel.Relation.name) ~schema:rel.Relation.schema
           ?constraints:rel.Relation.constraints lazy_gen)

  let project storage (attrs : string list) rel =
    let gen = to_generator storage rel in
    let project_tuple = function
      | Tuple.Materialized t ->
        let attrs' = List.fold_left (fun acc k ->
          match Tuple.AttributeMap.find_opt k t.Tuple.attributes with
          | None   -> acc
          | Some v -> Tuple.AttributeMap.add k v acc)
          Tuple.AttributeMap.empty attrs in
        Tuple.Materialized { t with attributes = attrs' }
      | other -> other
    in
    let new_schema = List.filter (fun (n, _) -> List.mem n attrs) rel.Relation.schema in
    let lazy_gen =
      let rec go g pos = match g pos with
        | Generator.Done    -> Generator.Done
        | Generator.Error e -> Generator.Error e
        | Generator.Value (t, next) -> Generator.Value (project_tuple t, go next)
      in fun pos -> go gen pos
    in
    let filtered_constraints =
      match rel.Relation.constraints with
      | None | Some [] -> None
      | Some cs ->
        let kept =
          List.filter_map
            (fun (name, c) ->
              match Constraint.filter_by_attrs attrs c with
              | Some c' -> Some (name, c')
              | None -> None)
            cs
        in
        (match kept with [] -> None | _ -> Some kept)
    in
    Ok (of_generator ~name:("π_" ^ rel.Relation.name) ~schema:new_schema
           ?constraints:filtered_constraints lazy_gen)

  let rename storage (renames : (string * string) list) rel =
    let rename_key k = match List.assoc_opt k renames with Some k' -> k' | None -> k in
    let rename_tuple = function
      | Tuple.Materialized t ->
        let attrs' = Tuple.AttributeMap.fold (fun k v acc ->
          Tuple.AttributeMap.add (rename_key k) v acc)
          t.Tuple.attributes Tuple.AttributeMap.empty in
        Tuple.Materialized { t with attributes = attrs' }
      | other -> other
    in
    let gen = to_generator storage rel in
    let new_schema = List.map (fun (n, d) -> (rename_key n, d)) rel.Relation.schema in
    let lazy_gen =
      let rec go g pos = match g pos with
        | Generator.Done    -> Generator.Done
        | Generator.Error e -> Generator.Error e
        | Generator.Value (t, next) -> Generator.Value (rename_tuple t, go next)
      in fun pos -> go gen pos
    in
    let renamed_constraints =
      match rel.Relation.constraints with
      | None | Some [] -> None
      | Some cs ->
        Some
          (List.map
             (fun (name, c) -> (name, Constraint.rename_vars renames c))
             cs)
    in
    Ok (of_generator ~name:("ρ_" ^ rel.Relation.name) ~schema:new_schema
           ?constraints:renamed_constraints lazy_gen)

  let equijoin storage (attrs : string list) left right =
    let right_gen = to_generator storage right in
    match drain right_gen with
    | Error e -> Error e
    | Ok right_tuples ->
      let left_gen = to_generator storage left in
      let get_vals attr_list = function
        | Tuple.Materialized t ->
          List.map (fun a -> Tuple.AttributeMap.find_opt a t.Tuple.attributes) attr_list
        | _ -> List.map (fun _ -> None) attr_list
      in
      let merge lt rt = match lt, rt with
        | Tuple.Materialized l, Tuple.Materialized r ->
          Tuple.Materialized { l with attributes =
            Tuple.AttributeMap.union (fun _ a _ -> Some a)
              l.Tuple.attributes r.Tuple.attributes }
        | _ -> lt
      in
      let merged_schema =
        left.Relation.schema @
        List.filter (fun (n, _) ->
          not (List.mem n attrs) &&
          not (List.exists (fun (m, _) -> m = n) left.Relation.schema))
          right.Relation.schema
      in
      let join_gen =
        let rec chain_with_cont g cont pos =
          match g pos with
          | Generator.Done            -> cont pos
          | Generator.Value (t, next) -> Generator.Value (t, fun p -> chain_with_cont next cont p)
          | Generator.Error e         -> Generator.Error e
        in
        let rec from_left lgen lpos =
          fun pos ->
          match lgen (Some lpos) with
          | Generator.Done    -> Generator.Done
          | Generator.Error e -> Generator.Error e
          | Generator.Value (lt, next_left) ->
            let lv = get_vals attrs lt in
            let matches = List.filter_map (fun rt ->
              if get_vals attrs rt = lv then Some (merge lt rt) else None) right_tuples in
            (match matches with
             | [] -> from_left next_left (lpos + 1) pos
             | _  ->
               chain_with_cont (list_generator matches)
                 (from_left next_left (lpos + 1)) pos)
        in
        from_left left_gen 0
      in
      let merged_constraints =
        match left.Relation.constraints, right.Relation.constraints with
        | None, None -> None
        | Some cs, None | None, Some cs -> Some cs
        | Some cs1, Some cs2 -> Some (Constraint.merge cs1 cs2)
      in
      let name = "⋈_" ^ left.Relation.name ^ "_" ^ right.Relation.name in
      Ok (of_generator ~name ~schema:merged_schema
             ?constraints:merged_constraints join_gen)

  let union storage rel1 rel2 =
    let gen1 = to_generator storage rel1 in
    let gen2 = to_generator storage rel2 in
    let chain_gen =
      let rec go g1 g2 pos =
        match g1 pos with
        | Generator.Done    -> g2 pos
        | Generator.Error _ -> g2 pos
        | Generator.Value (t, next) -> Generator.Value (t, fun p -> go next g2 p)
      in fun pos -> go gen1 gen2 pos
    in
    let name = "∪_" ^ rel1.Relation.name ^ "_" ^ rel2.Relation.name in
    (* Conservative: drop constraints since they only hold if both inputs agree *)
    Ok (of_generator ~name ~schema:rel1.Relation.schema chain_gen)

  let attrs_equal
      (m1 : Attribute.materialized Tuple.AttributeMap.t)
      (m2 : Attribute.materialized Tuple.AttributeMap.t) =
    Tuple.AttributeMap.equal
      (fun a b -> Stdlib.(=) a.Attribute.value b.Attribute.value) m1 m2

  let diff storage rel1 rel2 =
    let right_gen = to_generator storage rel2 in
    match drain right_gen with
    | Error e -> Error e
    | Ok right_tuples ->
      let right_mats = List.filter_map (function
        | Tuple.Materialized t -> Some t | _ -> None) right_tuples in
      let left_gen = to_generator storage rel1 in
      let not_in_right = function
        | Tuple.Materialized t ->
          not (List.exists (fun r ->
            attrs_equal t.Tuple.attributes r.Tuple.attributes) right_mats)
        | _ -> true
      in
      let lazy_gen =
        let rec go g pos =
          match g pos with
          | Generator.Done    -> Generator.Done
          | Generator.Error e -> Generator.Error e
          | Generator.Value (t, next) ->
            if not_in_right t then Generator.Value (t, go next)
            else go next (Option.map ((+) 1) pos)
        in fun pos -> go left_gen pos
      in
      let name = "−_" ^ rel1.Relation.name ^ "_" ^ rel2.Relation.name in
      Ok (of_generator ~name ~schema:rel1.Relation.schema
             ?constraints:rel1.Relation.constraints lazy_gen)

  let take storage n rel =
    let gen = to_generator storage rel in
    let lazy_gen =
      let rec go g count pos =
        if count = 0 then Generator.Done
        else match g pos with
          | Generator.Done    -> Generator.Done
          | Generator.Error e -> Generator.Error e
          | Generator.Value (t, next) -> Generator.Value (t, go next (count - 1))
      in fun pos -> go gen n pos
    in
    Ok (of_generator ~name:("τ_" ^ rel.Relation.name) ~schema:rel.Relation.schema
           ?constraints:rel.Relation.constraints
           ~cardinality:(Conventions.Cardinality.Finite n) lazy_gen)

  let materialize storage rel : (Tuple.materialized list, error) Result.t =
    match drain (to_generator storage rel) with
    | Error e -> Error e
    | Ok tuples ->
      Ok (List.filter_map (function Tuple.Materialized t -> Some t | _ -> None) tuples)

end

module Memory = Make(Management.Physical.Memory)