Quelle hConstr.ml Sprache: SML

(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Util
open Names
open Constr
open Context

(** Provide caching and hashconsing dependent on the local context used by a term.

    We want to cache the results of typechecking a term (at constant
    global environment).

    To do this, we need a map [constr -> result of typechecking], and

    - it must distinguish alpha equal terms (to get the desired names
      in the result of checking "fun x:nat => eq_refl x" and
      "fun y:nat => eq_refl y").

    - it must distinguish terms which only differ in "cached" data
      like relevance marks (if we typecheck "fun x :(*Relevant*)
      cache the result then check "fun x :(*Irrelevant*) nat => x" we must fail).

    - actually the map should be [(rel_context * constr) -> result] as
      the result of checking a bound variable depends on the context.

      To be more precise we only need to depend on the minimal context
      needed for the term, ie the context filtered to only the
      variables which appear in the term and recursively in the types
      and bodies of needed variables.

      Also note that we don't care about the names of local variables
      here, they only appear in error messages and since we stop at
      the first error there is no caching issue.

      (NB we need bodies as while the result of checking [Rel 1] does
      not depend on the body of rel 1, checking [eq_refl (Rel 1) : Rel 1 = 0]
      does need the body.)

    - the map should be fast.

    The first 2 points just mean we need a sufficiently precise equality test.

    To distinguish terms according to their context, we annotate each
    [Rel] subterm with their corresponding (recursively annotated)
    binder (ignoring the name).

    In practice we have an indirection such that each annotated binder
    is associated with a unique [int]. It's not clear how useful this
    is vs annotating with the actual binder data but it does allow
    handling unknow binders by just generating a fresh int (cf [push_unknown_rel]).

    While annotating [Rel]s we also share identical (for our equality)
    subterms and annotate each subterm with its hash, ie we hashcons
    according to our finer-than-[Constr.equal] equality. This means we
    can lookup by hash, and since identical subterms are shared we can
    compare them by [(==)] (in practice [hasheq_kind] which does
    [(==)] on immediate subterms) instead of structural equality
    (which would be O(size of term)).

    Finally we keep a reference count so that we can avoid caching
    subterms which aren't repeated.
*)

module Self = struct

type t = {
  self : constr;
  kind : (t,t,Sorts.t,UVars.Instance.t,Sorts.relevance) kind_of_term;
  isRel : int (* 0 -> not a rel, otherwise unique identifier of that binder *);
  hash : int;
  mutable refcount : int;
}

(* XXX possibly should be just physical equality since we use
   [raw_equal] on not-yet-hashconsed terms *)
let equal a b =
  a.isRel == b.isRel
  && hasheq_kind a.kind b.kind

let hash x = x.hash

end

include Self

let raw_equal a ~isRel ~kind =
  a.isRel == isRel
  && hasheq_kind a.kind kind

let self x = x.self

let refcount x = x.refcount

module Tbl = struct
  type key = t

  (* The API looks like Hashtbl but implemented using Int.Map ref.

     We don't use Hashtbl for 2 reasons:
     - to provide the pre-hashconsing leaf lookup (not sure why it's so fast but it seems to be)
       (although note we could do this with Hashtbl by using something like
       [type key = Real of t | Fake of int (* hash *)
       equality between [Real] and [Fake] uses the predicate in [Fake],
       wrap [add] so that we only add [Real] keys,
       then [raw_find] is [Hashtbl.find_opt] using [Fake].)

     - for unclear reasons Int.Map ref is dramatically faster on an artificial example
       (balanced binary tree whose leaves are all different primitive ints,
        such that there is no sharing).
       It is a bit slower in the real world.
       It seems that hashtbl produces overly large buckets which then need to be linearly scanned.
       hconsing doesn't seem to have this problem,
       perhaps because of differences between hashtbl and our hashset implementation. *)
  type 'a t = (key * 'a) list Int.Map.t ref

  let create () = ref Int.Map.empty

  let add tbl key v =
    tbl := Int.Map.update key.hash (function
        | None -> Some [(key,v)]
        | Some l -> Some ((key,v)::l))
        !tbl

  let raw_find tbl h p =
    match Int.Map.find_opt h !tbl with
    | None -> None
    | Some l -> List.find_map (fun (k,v) -> if p k then Some v else None) l

  let find_opt tbl key =
    match Int.Map.find_opt key.hash !tbl with
    | None -> None
    | Some l ->
      List.find_map (fun (k',v) ->
          if equal key k' then Some v else None)
        l

  type stats = {
    hashes : int;
    bindings : int;
    most_collisions : int;
  }

  let empty_stats = {
    hashes = 0;
    bindings = 0;
    most_collisions = 0;
  }

  let stats tbl =
    Int.Map.fold (fun _ l acc ->
        let len = List.length l in
        {
          hashes = acc.hashes + 1;
          bindings = acc.bindings + len;
          most_collisions = max acc.most_collisions len;
        }
      )
      !tbl
      empty_stats

end

type henv = {
  (* only used for globals, rel context is not correct *)
  globals : Environ.env;
  (* table of reified terms *)
  tbl : t Tbl.t;
  (* debug counter *)
  steps : int ref;
  (* unique identifiers for each binder crossed *)
  rels : int Range.t;
  (* counter to generate uids for binders *)
  binder_cnt : int ref;
  (* how many unknown_rel we have seen *)
  unknown_cnt : int ref;
  assum_uids : int Tbl.t;
  (* the surrounding table is for the body, the inner table for the type *)
  letin_uids : int Tbl.t Tbl.t;
}

let empty_env env = {
  globals = env;
  tbl = Tbl.create ();
  steps = ref 0;
  rels = Range.empty;
  binder_cnt = ref 0;
  unknown_cnt = ref 0;
  assum_uids = Tbl.create ();
  letin_uids = Tbl.create ();
}

(* still used in fixpoint *)
let push_unknown_rel env =
  incr env.binder_cnt;
  incr env.unknown_cnt;
  { env with rels = Range.cons !(env.binder_cnt) env.rels }

let push_assum t env =
  let uid = match Tbl.find_opt env.assum_uids t with
  | Some uid -> uid
  | None ->
    incr env.binder_cnt;
    let uid = !(env.binder_cnt) in
    Tbl.add env.assum_uids t uid;
    uid
  in
  { env with rels = Range.cons uid env.rels }

let push_rec ts env =
  (* handling the lifting for mutual fixpoints doesn't seem worth the effort *)
  Array.fold_left_i (fun i env t ->
      if i = 0 then push_assum t env
      else push_unknown_rel env)
    env
    ts

let push_letin ~body ~typ env =
  let uid = match Tbl.find_opt env.letin_uids body with
    | Some tbl -> begin match Tbl.find_opt tbl typ with
        | Some uid -> uid
        | None ->
          incr env.binder_cnt;
          let uid = !(env.binder_cnt) in
          Tbl.add tbl typ uid;
          uid
      end
    | None ->
      incr env.binder_cnt;
      let uid = !(env.binder_cnt) in
      let tbl = Tbl.create () in
      Tbl.add tbl typ uid;
      Tbl.add env.letin_uids body tbl;
      uid
  in
  { env with rels = Range.cons uid env.rels }

module RelDecl = Context.Rel.Declaration

let push_decl d env = match d with
  | RelDecl.LocalAssum (_,t) -> push_assum t env
  | RelDecl.LocalDef (_,body,typ) -> push_letin ~body ~typ env

let hash_annot = hash_annot Name.hash

let hash_array hashf a = Array.fold_left (fun hash x -> Hashset.Combine.combine hash (hashf x)) 0 a

let hash_kind = let open Hashset.Combine in function
  | Var i -> combinesmall 1 (Id.hash i)
  | Sort s -> combinesmall 2 (Sorts.hash s)
  | Cast (c,k,t) -> combinesmall 3 (combine3 c.hash (hash_cast_kind k) t.hash)
  | Prod (na,t,c) -> combinesmall 4 (combine3 (hash_annot na) t.hash c.hash)
  | Lambda (na,t,c) -> combinesmall 5 (combine3 (hash_annot na) t.hash c.hash)
  | LetIn (na,b,t,c) -> combinesmall 6 (combine4 (hash_annot na) b.hash t.hash c.hash)
  | App (h,args) -> combinesmall 7 (Array.fold_left (fun hash c -> combine hash c.hash) h.hash args)
  | Evar _ -> assert false
  | Const (c,u) -> combinesmall 9 (combine (Constant.SyntacticOrd.hash c) (UVars.Instance.hash u))
  | Ind (ind,u) -> combinesmall 10 (combine (Ind.SyntacticOrd.hash ind) (UVars.Instance.hash u))
  | Construct (c,u) -> combinesmall 11 (combine (Construct.SyntacticOrd.hash c) (UVars.Instance.hash u))
  | Case (_,u,pms,(p,_),_,c,bl) ->
    let hash_ctx (bnd,c) =
      Array.fold_left (fun hash na -> combine (hash_annot na) hash) c.hash bnd
    in
    let hpms = hash_array hash pms in
    let hbl = hash_array hash_ctx bl in
    let h = combine5 (UVars.Instance.hash u)
        c.hash hpms (hash_ctx p) hbl
    in
    combinesmall 12 h
  | Fix (_,(lna,tl,bl)) ->
    combinesmall 13 (combine3 (hash_array hash_annot lna) (hash_array hash tl) (hash_array hash bl))
  | CoFix (_,(lna,tl,bl)) ->
    combinesmall 14 (combine3 (hash_array hash_annot lna) (hash_array hash tl) (hash_array hash bl))
  | Meta _ -> assert false
  | Rel n -> combinesmall 16 n
  | Proj (p,_,c) -> combinesmall 17 (combine (Projection.SyntacticOrd.hash p) c.hash)
  | Int i -> combinesmall 18 (Uint63.hash i)
  | Float f -> combinesmall 19 (Float64.hash f)
  | String s -> combinesmall 20 (Pstring.hash s)
  | Array (u,t,def,ty) -> combinesmall 21 (combine4 (UVars.Instance.hash u) (hash_array hash t) def.hash ty.hash)

let kind_to_constr = function
  | Rel n -> mkRel n
  | Var i -> mkVar i
  | Meta _ | Evar _ -> assert false
  | Sort s -> mkSort s
  | Cast (c,k,t) -> mkCast (c.self,k,t.self)
  | Prod (na,t,c) -> mkProd (na,t.self,c.self)
  | Lambda (na,t,c) -> mkLambda (na,t.self,c.self)
  | LetIn (na,b,t,c) -> mkLetIn (na,b.self,t.self,c.self)
  | App (h,args) -> mkApp (h.self, Array.map self args)
  | Const cu -> mkConstU cu
  | Ind iu -> mkIndU iu
  | Construct cu -> mkConstructU cu
  | Case (ci,u,pms,(p,r),iv,c,bl) ->
    let to_ctx (bnd,c) = bnd, c.self in
    let iv = match iv with
      | NoInvert -> NoInvert
      | CaseInvert x -> CaseInvert {indices=Array.map self x.indices}
    in
    mkCase (ci,u,Array.map self pms,(to_ctx p,r),iv,c.self,Array.map to_ctx bl)
  | Fix (ln,(lna,tl,bl)) ->
    mkFix (ln,(lna,Array.map self tl,Array.map self bl))
  | CoFix (ln,(lna,tl,bl)) ->
    mkCoFix (ln,(lna,Array.map self tl,Array.map self bl))
  | Proj (p,r,c) -> mkProj (p,r,c.self)
  | Int i -> mkInt i
  | Float f -> mkFloat f
  | String s -> mkString s
  | Array (u,t,def,ty) -> mkArray (u,Array.map self t,def.self,ty.self)

let of_kind_nohashcons = function
  | App (c, [||]) -> c
  | kind ->
  let self = kind_to_constr kind in
  let hash = hash_kind kind in
  let () = match kind with
    | Rel _ -> assert false
    | _ -> ()
  in
  { self; kind; hash; isRel = 0; refcount = 1 }

let eq_leaf c c' = match kind c, c'.kind with
  | Var i, Var i' -> Id.equal i i'
  | Const (c,u), Const (c',u') -> Constant.SyntacticOrd.equal c c' && UVars.Instance.equal u u'
  | Ind (i,u), Ind (i',u') -> Ind.SyntacticOrd.equal i i' && UVars.Instance.equal u u'
  | Construct (c,u), Construct (c',u') -> Construct.SyntacticOrd.equal c c' && UVars.Instance.equal u u'
  | _ -> false

let nonrel_leaf tbl c = match kind c with
  | Rel _ -> None
  | Var _ | Const _ | Ind _ | Construct _ as k ->
    let h = hash_kind k in
    Tbl.raw_find tbl h (fun c' -> eq_leaf c c')
  | _ -> None

let rec of_constr henv c =
  incr henv.steps;
  match nonrel_leaf henv.tbl c with
  | Some v -> v
  | None ->
    let kind = of_constr_aux henv c in
    let hash = hash_kind kind in
    let isRel, hash = match kind with
      | Rel n ->
        let uid = Range.get henv.rels (n-1) in
        assert (uid <> 0);
        uid, Hashset.Combine.combine uid hash
      | _ -> 0, hash
    in
    match Tbl.raw_find henv.tbl hash (fun c' -> raw_equal c' ~isRel ~kind) with
    | Some c' -> c'.refcount <- c'.refcount + 1; c'
    | None ->
      let c =
        let self = kind_to_constr kind in
        let self = if hasheq_kind (Constr.kind self) (Constr.kind c) then c else self in
        { self; kind; hash; isRel; refcount = 1 }
      in
    Tbl.add henv.tbl c c; c

and of_constr_aux henv c =
  match kind c with
  | Var i ->
    let _, i = Id.hcons i in
    Var i
  | Rel _ as t -> t
  | Sort s ->
    let _, s = Sorts.hcons s in
    Sort s
  | Cast (c,k,t) ->
    let c = of_constr henv c in
    let t = of_constr henv t in
    Cast (c, k, t)
  | Prod (na,t,c) ->
    let _, na = hcons_annot na in
    let t = of_constr henv t in
    let c = of_constr (push_assum t henv) c in
    Prod (na, t, c)
  | Lambda (na, t, c) ->
    let _, na = hcons_annot na in
    let t = of_constr henv t in
    let c = of_constr (push_assum t henv) c in
    Lambda (na,t,c)
  | LetIn (na,b,t,c) ->
    let _, na = hcons_annot na in
    let b = of_constr henv b in
    let t = of_constr henv t in
    let c = of_constr (push_letin ~body:b ~typ:t henv) c in
    LetIn (na,b,t,c)
  | App (h,args) ->
    let h = of_constr henv h in
    let args = Array.map (of_constr henv) args in
    App (h, args)
  | Evar _ -> CErrors.anomaly Pp.(str "evar in typeops")
  | Meta _ -> CErrors.anomaly Pp.(str "meta in typeops")
  | Const (c,u) ->
    let _, c = hcons_con c in
    let _, u = UVars.Instance.hcons u in
    Const (c,u)
  | Ind (ind,u) ->
    let _, ind = hcons_ind ind in
    let _, u = UVars.Instance.hcons u in
    Ind (ind,u)
  | Construct (c,u) ->
    let _, c = hcons_construct c in
    let _, u = UVars.Instance.hcons u in
    Construct (c,u)
  | Case (ci,u,pms,(p,r),iv,c,bl) ->
    let pctx, blctx =
      let specif = Inductive.lookup_mind_specif henv.globals ci.ci_ind in
      let pctx = Inductive.expand_arity specif (ci.ci_ind,u) pms (fst p) in
      let blctx = Inductive.expand_branch_contexts specif u pms bl in
      pctx, blctx
    in
    let of_ctx (bnd, c) bnd' =
      let _, bnd = Hashcons.hashcons_array hcons_annot bnd in
      let henv = push_rel_context henv bnd' in
      let c = of_constr henv c in
      bnd, c
    in
    let _, ci = hcons_caseinfo ci in
    let _, u = UVars.Instance.hcons u in
    let pms = Array.map (of_constr henv) pms in
    let p = of_ctx p pctx in
    let iv = match iv with
      | NoInvert -> NoInvert
      | CaseInvert {indices} -> CaseInvert {indices=Array.map (of_constr henv) indices}
    in
    let c = of_constr henv c in
    let bl = Array.map2 of_ctx bl blctx in
    Case (ci,u,pms,(p,r),iv,c,bl)
  | Fix (ln,(lna,tl,bl)) ->
    let _, lna = Hashcons.hashcons_array hcons_annot lna in
    let tl = Array.map (of_constr henv) tl in
    let body_env = push_rec tl henv in
    let bl = Array.map (of_constr body_env) bl in
    Fix (ln,(lna,tl,bl))
  | CoFix (ln,(lna,tl,bl)) ->
    let _, lna = Hashcons.hashcons_array hcons_annot lna in
    let tl = Array.map (of_constr henv) tl in
    let body_env = push_rec tl henv in
    let bl = Array.map (of_constr body_env) bl in
    CoFix (ln,(lna,tl,bl))
  | Proj (p,r,c) ->
    let _, p = Projection.hcons p in
    let c = of_constr henv c in
    Proj (p,r,c)
  | Int _ as t -> t
  | Float _ as t -> t
  | String _ as t -> t
  | Array (u,t,def,ty) ->
    let _, u = UVars.Instance.hcons u in
    let t = Array.map (of_constr henv) t in
    let def = of_constr henv def in
    let ty = of_constr henv ty in
    Array (u,t,def,ty)

and push_rel_context henv ctx =
  List.fold_right (fun d henv ->
      let d = RelDecl.map_constr_het (fun r -> r) (of_constr henv) d in
      push_decl d henv)
    ctx
    henv

let dbg = CDebug.create ~name:"hconstr" ()

let tree_size c =
  let rec aux size c =
    Constr.fold aux (size+1) c
  in
  aux 0 c

let of_constr env c =
  let henv = empty_env env in
  let henv = iterate push_unknown_rel (Environ.nb_rel env) henv in
  let c = NewProfile.profile "HConstr.of_constr" (fun () -> of_constr henv c) () in
  dbg Pp.(fun () ->
      let stats = Tbl.stats henv.tbl in
      let tree_size = tree_size (self c) in
      v 0 (
        str "steps = " ++ int !(henv.steps) ++ spc() ++
        str "rel cnt = " ++ int !(henv.binder_cnt) ++ spc() ++
        str "unknwown rels = " ++ int !(henv.unknown_cnt) ++ spc() ++
        str "hashes = " ++ int stats.Tbl.hashes ++ spc() ++
        str "bindings = " ++ int stats.Tbl.bindings ++ spc() ++
        str "tree size = " ++ int tree_size ++ spc() ++
        str "most_collisions = " ++ int stats.Tbl.most_collisions
    )
    );
  c

let kind x = x.kind

let hcons x =
  let tbl = Tbl.create () in
  let module HCons = GenHCons(struct
      type nonrec t = t
      let kind = kind
      let self = self
      let refcount = refcount
        let via_hconstr = true
      module Tbl = struct
        let find_opt x = Tbl.find_opt tbl x
        let add x y = Tbl.add tbl x y
      end
    end) in
  HCons.hcons x

quality99%

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Cephes Mathematical Library

Wiener Entwicklungsmethode

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