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Diffstat (limited to 'engine/universes.ml')
| -rw-r--r-- | engine/universes.ml | 1136 |
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diff --git a/engine/universes.ml b/engine/universes.ml new file mode 100644 index 00000000..fb64a642 --- /dev/null +++ b/engine/universes.ml @@ -0,0 +1,1136 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \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 Sorts +open Util +open Pp +open Names +open Constr +open Environ +open Univ +open Globnames +open Nametab + +module UPairs = OrderedType.UnorderedPair(Univ.Level) +module UPairSet = Set.Make (UPairs) + +let reference_of_level l = CAst.make @@ + match Level.name l with + | Some (d, n as na) -> + let qid = + try Nametab.shortest_qualid_of_universe na + with Not_found -> + let name = Id.of_string_soft (string_of_int n) in + Libnames.make_qualid d name + in Libnames.Qualid qid + | None -> Libnames.Ident Id.(of_string_soft (Level.to_string l)) + +let pr_with_global_universes l = Libnames.pr_reference (reference_of_level l) + +(** Global universe information outside the kernel, to handle + polymorphic universe names in sections that have to be discharged. *) + +let universe_map = (Summary.ref UnivIdMap.empty ~name:"global universe info" : bool Nametab.UnivIdMap.t ref) + +let add_global_universe u p = + match Level.name u with + | Some n -> universe_map := Nametab.UnivIdMap.add n p !universe_map + | None -> () + +let is_polymorphic l = + match Level.name l with + | Some n -> + (try Nametab.UnivIdMap.find n !universe_map + with Not_found -> false) + | None -> false + +(** Local universe names of polymorphic references *) + +type universe_binders = Univ.Level.t Names.Id.Map.t + +let empty_binders = Id.Map.empty + +let universe_binders_table = Summary.ref Refmap.empty ~name:"universe binders" + +let universe_binders_of_global ref : universe_binders = + try + let l = Refmap.find ref !universe_binders_table in l + with Not_found -> Names.Id.Map.empty + +let cache_ubinder (_,(ref,l)) = + universe_binders_table := Refmap.add ref l !universe_binders_table + +let subst_ubinder (subst,(ref,l as orig)) = + let ref' = fst (Globnames.subst_global subst ref) in + if ref == ref' then orig else ref', l + +let discharge_ubinder (_,(ref,l)) = + Some (Lib.discharge_global ref, l) + +let ubinder_obj : Globnames.global_reference * universe_binders -> Libobject.obj = + let open Libobject in + declare_object { (default_object "universe binder") with + cache_function = cache_ubinder; + load_function = (fun _ x -> cache_ubinder x); + classify_function = (fun x -> Substitute x); + subst_function = subst_ubinder; + discharge_function = discharge_ubinder; + rebuild_function = (fun x -> x); } + +let register_universe_binders ref ubinders = + let open Names in + (* Add the polymorphic (section) universes *) + let ubinders = UnivIdMap.fold (fun lvl poly ubinders -> + let qid = Nametab.shortest_qualid_of_universe lvl in + let level = Level.make (fst lvl) (snd lvl) in + if poly then Id.Map.add (snd (Libnames.repr_qualid qid)) level ubinders + else ubinders) + !universe_map ubinders + in + if not (Id.Map.is_empty ubinders) + then Lib.add_anonymous_leaf (ubinder_obj (ref,ubinders)) + +type univ_name_list = Misctypes.lname list + +let universe_binders_with_opt_names ref levels = function + | None -> universe_binders_of_global ref + | Some udecl -> + if Int.equal(List.length levels) (List.length udecl) + then + List.fold_left2 (fun acc { CAst.v = na} lvl -> match na with + | Anonymous -> acc + | Name na -> Names.Id.Map.add na lvl acc) + empty_binders udecl levels + else + CErrors.user_err ~hdr:"universe_binders_with_opt_names" + Pp.(str "Universe instance should have length " ++ int (List.length levels)) + +(* To disallow minimization to Set *) + +let set_minimization = ref true +let is_set_minimization () = !set_minimization + +type universe_constraint = + | ULe of Universe.t * Universe.t + | UEq of Universe.t * Universe.t + | ULub of Level.t * Level.t + | UWeak of Level.t * Level.t + +module Constraints = struct + module S = Set.Make( + struct + type t = universe_constraint + + let compare x y = + match x, y with + | ULe (u, v), ULe (u', v') -> + let i = Universe.compare u u' in + if Int.equal i 0 then Universe.compare v v' + else i + | UEq (u, v), UEq (u', v') -> + let i = Universe.compare u u' in + if Int.equal i 0 then Universe.compare v v' + else if Universe.equal u v' && Universe.equal v u' then 0 + else i + | ULub (u, v), ULub (u', v') | UWeak (u, v), UWeak (u', v') -> + let i = Level.compare u u' in + if Int.equal i 0 then Level.compare v v' + else if Level.equal u v' && Level.equal v u' then 0 + else i + | ULe _, _ -> -1 + | _, ULe _ -> 1 + | UEq _, _ -> -1 + | _, UEq _ -> 1 + | ULub _, _ -> -1 + | _, ULub _ -> 1 + end) + + include S + + let is_trivial = function + | ULe (u, v) | UEq (u, v) -> Universe.equal u v + | ULub (u, v) | UWeak (u, v) -> Level.equal u v + + let add cst s = + if is_trivial cst then s + else add cst s + + let pr_one = function + | ULe (u, v) -> Universe.pr u ++ str " <= " ++ Universe.pr v + | UEq (u, v) -> Universe.pr u ++ str " = " ++ Universe.pr v + | ULub (u, v) -> Level.pr u ++ str " /\\ " ++ Level.pr v + | UWeak (u, v) -> Level.pr u ++ str " ~ " ++ Level.pr v + + let pr c = + fold (fun cst pp_std -> + pp_std ++ pr_one cst ++ fnl ()) c (str "") + + let equal x y = + x == y || equal x y + +end + +type universe_constraints = Constraints.t +type 'a constraint_accumulator = universe_constraints -> 'a -> 'a option +type 'a universe_constrained = 'a * universe_constraints + +type 'a universe_constraint_function = 'a -> 'a -> universe_constraints -> universe_constraints + +let enforce_eq_instances_univs strict x y c = + let mk u v = if strict then ULub (u, v) else UEq (Universe.make u, Universe.make v) in + let ax = Instance.to_array x and ay = Instance.to_array y in + if Array.length ax != Array.length ay then + CErrors.anomaly (Pp.str "Invalid argument: enforce_eq_instances_univs called with" ++ + Pp.str " instances of different lengths."); + CArray.fold_right2 + (fun x y -> Constraints.add (mk x y)) + ax ay c + +let enforce_univ_constraint (u,d,v) = + match d with + | Eq -> enforce_eq u v + | Le -> enforce_leq u v + | Lt -> enforce_leq (super u) v + +let subst_univs_level fn l = + try Some (fn l) + with Not_found -> None + +let subst_univs_constraint fn (u,d,v as c) cstrs = + let u' = subst_univs_level fn u in + let v' = subst_univs_level fn v in + match u', v' with + | None, None -> Constraint.add c cstrs + | Some u, None -> enforce_univ_constraint (u,d,Universe.make v) cstrs + | None, Some v -> enforce_univ_constraint (Universe.make u,d,v) cstrs + | Some u, Some v -> enforce_univ_constraint (u,d,v) cstrs + +let subst_univs_constraints subst csts = + Constraint.fold + (fun c cstrs -> subst_univs_constraint subst c cstrs) + csts Constraint.empty + +let level_subst_of f = + fun l -> + try let u = f l in + match Universe.level u with + | None -> l + | Some l -> l + with Not_found -> l + +let subst_univs_universe_constraint fn = function + | ULe (u, v) -> + let u' = subst_univs_universe fn u and v' = subst_univs_universe fn v in + if Universe.equal u' v' then None + else Some (ULe (u',v')) + | UEq (u, v) -> + let u' = subst_univs_universe fn u and v' = subst_univs_universe fn v in + if Universe.equal u' v' then None + else Some (ULe (u',v')) + | ULub (u, v) -> + let u' = level_subst_of fn u and v' = level_subst_of fn v in + if Level.equal u' v' then None + else Some (ULub (u',v')) + | UWeak (u, v) -> + let u' = level_subst_of fn u and v' = level_subst_of fn v in + if Level.equal u' v' then None + else Some (UWeak (u',v')) + +let subst_univs_universe_constraints subst csts = + Constraints.fold + (fun c -> Option.fold_right Constraints.add (subst_univs_universe_constraint subst c)) + csts Constraints.empty + +let to_constraints ~force_weak g s = + let invalid () = + raise (Invalid_argument "to_constraints: non-trivial algebraic constraint between universes") + in + let tr cst acc = + match cst with + | ULub (l, l') -> Constraint.add (l, Eq, l') acc + | UWeak (l, l') when force_weak -> Constraint.add (l, Eq, l') acc + | UWeak _-> acc + | ULe (l, l') -> + begin match Universe.level l, Universe.level l' with + | Some l, Some l' -> Constraint.add (l, Le, l') acc + | None, Some _ -> enforce_leq l l' acc + | _, None -> + if UGraph.check_leq g l l' + then acc + else invalid () + end + | UEq (l, l') -> + begin match Universe.level l, Universe.level l' with + | Some l, Some l' -> Constraint.add (l, Eq, l') acc + | None, _ | _, None -> + if UGraph.check_eq g l l' + then acc + else invalid () + end + in + Constraints.fold tr s Constraint.empty + +(** Variant of [eq_constr_univs_infer] taking kind-of-term functions, + to expose subterms of [m] and [n], arguments. *) +let eq_constr_univs_infer_with kind1 kind2 univs fold m n accu = + (* spiwack: duplicates the code of [eq_constr_univs_infer] because I + haven't find a way to factor the code without destroying + pointer-equality optimisations in [eq_constr_univs_infer]. + Pointer equality is not sufficient to ensure equality up to + [kind1,kind2], because [kind1] and [kind2] may be different, + typically evaluating [m] and [n] in different evar maps. *) + let cstrs = ref accu in + let eq_universes _ _ = UGraph.check_eq_instances univs in + let eq_sorts s1 s2 = + if Sorts.equal s1 s2 then true + else + let u1 = Sorts.univ_of_sort s1 and u2 = Sorts.univ_of_sort s2 in + match fold (Constraints.singleton (UEq (u1, u2))) !cstrs with + | None -> false + | Some accu -> cstrs := accu; true + in + let rec eq_constr' nargs m n = + Constr.compare_head_gen_with kind1 kind2 eq_universes eq_sorts eq_constr' nargs m n + in + let res = Constr.compare_head_gen_with kind1 kind2 eq_universes eq_sorts eq_constr' 0 m n in + if res then Some !cstrs else None + +(* Generator of levels *) +type universe_id = DirPath.t * int + +let new_univ_id, set_remote_new_univ_id = + RemoteCounter.new_counter ~name:"Universes" 0 ~incr:((+) 1) + ~build:(fun n -> Global.current_dirpath (), n) + +let new_univ_level () = + let dp, id = new_univ_id () in + Univ.Level.make dp id + +let fresh_level () = new_univ_level () + +(* TODO: remove *) +let new_univ dp = Univ.Universe.make (new_univ_level dp) +let new_Type dp = mkType (new_univ dp) +let new_Type_sort dp = Type (new_univ dp) + +let fresh_universe_instance ctx = + let init _ = new_univ_level () in + Instance.of_array (Array.init (AUContext.size ctx) init) + +let fresh_instance_from_context ctx = + let inst = fresh_universe_instance ctx in + let constraints = AUContext.instantiate inst ctx in + inst, constraints + +let fresh_instance ctx = + let ctx' = ref LSet.empty in + let init _ = + let u = new_univ_level () in + ctx' := LSet.add u !ctx'; u + in + let inst = Instance.of_array (Array.init (AUContext.size ctx) init) + in !ctx', inst + +let existing_instance ctx inst = + let () = + let len1 = Array.length (Instance.to_array inst) + and len2 = AUContext.size ctx in + if not (len1 == len2) then + CErrors.user_err ~hdr:"Universes" + (str "Polymorphic constant expected " ++ int len2 ++ + str" levels but was given " ++ int len1) + else () + in LSet.empty, inst + +let fresh_instance_from ctx inst = + let ctx', inst = + match inst with + | Some inst -> existing_instance ctx inst + | None -> fresh_instance ctx + in + let constraints = AUContext.instantiate inst ctx in + inst, (ctx', constraints) + +(** Fresh universe polymorphic construction *) + +let fresh_constant_instance env c inst = + let cb = lookup_constant c env in + match cb.Declarations.const_universes with + | Declarations.Monomorphic_const _ -> ((c,Instance.empty), ContextSet.empty) + | Declarations.Polymorphic_const auctx -> + let inst, ctx = + fresh_instance_from auctx inst + in + ((c, inst), ctx) + +let fresh_inductive_instance env ind inst = + let mib, mip = Inductive.lookup_mind_specif env ind in + match mib.Declarations.mind_universes with + | Declarations.Monomorphic_ind _ -> + ((ind,Instance.empty), ContextSet.empty) + | Declarations.Polymorphic_ind uactx -> + let inst, ctx = (fresh_instance_from uactx) inst in + ((ind,inst), ctx) + | Declarations.Cumulative_ind acumi -> + let inst, ctx = + fresh_instance_from (Univ.ACumulativityInfo.univ_context acumi) inst + in ((ind,inst), ctx) + +let fresh_constructor_instance env (ind,i) inst = + let mib, mip = Inductive.lookup_mind_specif env ind in + match mib.Declarations.mind_universes with + | Declarations.Monomorphic_ind _ -> (((ind,i),Instance.empty), ContextSet.empty) + | Declarations.Polymorphic_ind auctx -> + let inst, ctx = fresh_instance_from auctx inst in + (((ind,i),inst), ctx) + | Declarations.Cumulative_ind acumi -> + let inst, ctx = fresh_instance_from (ACumulativityInfo.univ_context acumi) inst in + (((ind,i),inst), ctx) + +open Globnames + +let fresh_global_instance ?names env gr = + match gr with + | VarRef id -> mkVar id, ContextSet.empty + | ConstRef sp -> + let c, ctx = fresh_constant_instance env sp names in + mkConstU c, ctx + | ConstructRef sp -> + let c, ctx = fresh_constructor_instance env sp names in + mkConstructU c, ctx + | IndRef sp -> + let c, ctx = fresh_inductive_instance env sp names in + mkIndU c, ctx + +let fresh_constant_instance env sp = + fresh_constant_instance env sp None + +let fresh_inductive_instance env sp = + fresh_inductive_instance env sp None + +let fresh_constructor_instance env sp = + fresh_constructor_instance env sp None + +let constr_of_global gr = + let c, ctx = fresh_global_instance (Global.env ()) gr in + if not (Univ.ContextSet.is_empty ctx) then + if Univ.LSet.is_empty (Univ.ContextSet.levels ctx) then + (* Should be an error as we might forget constraints, allow for now + to make firstorder work with "using" clauses *) + c + else CErrors.user_err ~hdr:"constr_of_global" + Pp.(str "globalization of polymorphic reference " ++ Nametab.pr_global_env Id.Set.empty gr ++ + str " would forget universes.") + else c + +let constr_of_reference = constr_of_global + +let constr_of_global_univ (gr,u) = + match gr with + | VarRef id -> mkVar id + | ConstRef sp -> mkConstU (sp,u) + | ConstructRef sp -> mkConstructU (sp,u) + | IndRef sp -> mkIndU (sp,u) + +let fresh_global_or_constr_instance env = function + | IsConstr c -> c, ContextSet.empty + | IsGlobal gr -> fresh_global_instance env gr + +let global_of_constr c = + match kind c with + | Const (c, u) -> ConstRef c, u + | Ind (i, u) -> IndRef i, u + | Construct (c, u) -> ConstructRef c, u + | Var id -> VarRef id, Instance.empty + | _ -> raise Not_found + +open Declarations + +let type_of_reference env r = + match r with + | VarRef id -> Environ.named_type id env, ContextSet.empty + | ConstRef c -> + let cb = Environ.lookup_constant c env in + let ty = cb.const_type in + begin + match cb.const_universes with + | Monomorphic_const _ -> ty, ContextSet.empty + | Polymorphic_const auctx -> + let inst, ctx = fresh_instance_from auctx None in + Vars.subst_instance_constr inst ty, ctx + end + | IndRef ind -> + let (mib, oib as specif) = Inductive.lookup_mind_specif env ind in + begin + match mib.mind_universes with + | Monomorphic_ind _ -> + let ty = Inductive.type_of_inductive env (specif, Univ.Instance.empty) in + ty, ContextSet.empty + | Polymorphic_ind auctx -> + let inst, ctx = fresh_instance_from auctx None in + let ty = Inductive.type_of_inductive env (specif, inst) in + ty, ctx + | Cumulative_ind cumi -> + let inst, ctx = + fresh_instance_from (ACumulativityInfo.univ_context cumi) None + in + let ty = Inductive.type_of_inductive env (specif, inst) in + ty, ctx + end + + | ConstructRef cstr -> + let (mib,oib as specif) = + Inductive.lookup_mind_specif env (inductive_of_constructor cstr) + in + begin + match mib.mind_universes with + | Monomorphic_ind _ -> + Inductive.type_of_constructor (cstr,Instance.empty) specif, ContextSet.empty + | Polymorphic_ind auctx -> + let inst, ctx = fresh_instance_from auctx None in + Inductive.type_of_constructor (cstr,inst) specif, ctx + | Cumulative_ind cumi -> + let inst, ctx = + fresh_instance_from (ACumulativityInfo.univ_context cumi) None + in + Inductive.type_of_constructor (cstr,inst) specif, ctx + end + +let type_of_global t = type_of_reference (Global.env ()) t + +let fresh_sort_in_family env = function + | InProp -> Sorts.prop, ContextSet.empty + | InSet -> Sorts.set, ContextSet.empty + | InType -> + let u = fresh_level () in + Type (Univ.Universe.make u), ContextSet.singleton u + +let new_sort_in_family sf = + fst (fresh_sort_in_family (Global.env ()) sf) + +let extend_context (a, ctx) (ctx') = + (a, ContextSet.union ctx ctx') + +let new_global_univ () = + let u = fresh_level () in + (Univ.Universe.make u, ContextSet.singleton u) + +(** Simplification *) + +module LevelUnionFind = Unionfind.Make (Univ.LSet) (Univ.LMap) + +let add_list_map u t map = + try + let l = LMap.find u map in + LMap.set u (t :: l) map + with Not_found -> + LMap.add u [t] map + +module UF = LevelUnionFind + +(** Precondition: flexible <= ctx *) +let choose_canonical ctx flexible algs s = + let global = LSet.diff s ctx in + let flexible, rigid = LSet.partition flexible (LSet.inter s ctx) in + (** If there is a global universe in the set, choose it *) + if not (LSet.is_empty global) then + let canon = LSet.choose global in + canon, (LSet.remove canon global, rigid, flexible) + else (** No global in the equivalence class, choose a rigid one *) + if not (LSet.is_empty rigid) then + let canon = LSet.choose rigid in + canon, (global, LSet.remove canon rigid, flexible) + else (** There are only flexible universes in the equivalence + class, choose a non-algebraic. *) + let algs, nonalgs = LSet.partition (fun x -> LSet.mem x algs) flexible in + if not (LSet.is_empty nonalgs) then + let canon = LSet.choose nonalgs in + canon, (global, rigid, LSet.remove canon flexible) + else + let canon = LSet.choose algs in + canon, (global, rigid, LSet.remove canon flexible) + +let subst_univs_fn_constr f c = + let changed = ref false in + let fu = Univ.subst_univs_universe f in + let fi = Univ.Instance.subst_fn (level_subst_of f) in + let rec aux t = + match kind t with + | Sort (Sorts.Type u) -> + let u' = fu u in + if u' == u then t else + (changed := true; mkSort (Sorts.sort_of_univ u')) + | Const (c, u) -> + let u' = fi u in + if u' == u then t + else (changed := true; mkConstU (c, u')) + | Ind (i, u) -> + let u' = fi u in + if u' == u then t + else (changed := true; mkIndU (i, u')) + | Construct (c, u) -> + let u' = fi u in + if u' == u then t + else (changed := true; mkConstructU (c, u')) + | _ -> map aux t + in + let c' = aux c in + if !changed then c' else c + +let subst_univs_constr subst c = + if Univ.is_empty_subst subst then c + else + let f = Univ.make_subst subst in + subst_univs_fn_constr f c + +let subst_univs_constr = + if Flags.profile then + let subst_univs_constr_key = CProfile.declare_profile "subst_univs_constr" in + CProfile.profile2 subst_univs_constr_key subst_univs_constr + else subst_univs_constr + +let fresh_universe_context_set_instance ctx = + if ContextSet.is_empty ctx then LMap.empty, ctx + else + let (univs, cst) = ContextSet.levels ctx, ContextSet.constraints ctx in + let univs',subst = LSet.fold + (fun u (univs',subst) -> + let u' = fresh_level () in + (LSet.add u' univs', LMap.add u u' subst)) + univs (LSet.empty, LMap.empty) + in + let cst' = subst_univs_level_constraints subst cst in + subst, (univs', cst') + +let normalize_univ_variable ~find ~update = + let rec aux cur = + let b = find cur in + let b' = subst_univs_universe aux b in + if Universe.equal b' b then b + else update cur b' + in aux + +let normalize_univ_variable_opt_subst ectx = + let find l = + match Univ.LMap.find l !ectx with + | Some b -> b + | None -> raise Not_found + in + let update l b = + assert (match Universe.level b with Some l' -> not (Level.equal l l') | None -> true); + try ectx := Univ.LMap.add l (Some b) !ectx; b with Not_found -> assert false + in normalize_univ_variable ~find ~update + +let normalize_univ_variable_subst subst = + let find l = Univ.LMap.find l !subst in + let update l b = + assert (match Universe.level b with Some l' -> not (Level.equal l l') | None -> true); + try subst := Univ.LMap.set l b !subst; b with Not_found -> assert false in + normalize_univ_variable ~find ~update + +let normalize_universe_opt_subst subst = + let normlevel = normalize_univ_variable_opt_subst subst in + subst_univs_universe normlevel + +let normalize_universe_subst subst = + let normlevel = normalize_univ_variable_subst subst in + subst_univs_universe normlevel + +let normalize_opt_subst ctx = + let ectx = ref ctx in + let normalize = normalize_univ_variable_opt_subst ectx in + let () = + Univ.LMap.iter (fun u v -> + if Option.is_empty v then () + else try ignore(normalize u) with Not_found -> assert(false)) ctx + in !ectx + +type universe_opt_subst = Universe.t option universe_map + +let subst_univs_fn_puniverses f (c, u as cu) = + let u' = Instance.subst_fn f u in + if u' == u then cu else (c, u') + +let nf_evars_and_universes_opt_subst f subst = + let subst = normalize_univ_variable_opt_subst (ref subst) in + let lsubst = level_subst_of subst in + let rec aux c = + match kind c with + | Evar (evk, args) -> + let args = Array.map aux args in + (match try f (evk, args) with Not_found -> None with + | None -> mkEvar (evk, args) + | Some c -> aux c) + | Const pu -> + let pu' = subst_univs_fn_puniverses lsubst pu in + if pu' == pu then c else mkConstU pu' + | Ind pu -> + let pu' = subst_univs_fn_puniverses lsubst pu in + if pu' == pu then c else mkIndU pu' + | Construct pu -> + let pu' = subst_univs_fn_puniverses lsubst pu in + if pu' == pu then c else mkConstructU pu' + | Sort (Type u) -> + let u' = Univ.subst_univs_universe subst u in + if u' == u then c else mkSort (sort_of_univ u') + | _ -> Constr.map aux c + in aux + +let make_opt_subst s = + fun x -> + (match Univ.LMap.find x s with + | Some u -> u + | None -> raise Not_found) + +let subst_opt_univs_constr s = + let f = make_opt_subst s in + subst_univs_fn_constr f + +let normalize_univ_variables ctx = + let ctx = normalize_opt_subst ctx in + let undef, def, subst = + Univ.LMap.fold (fun u v (undef, def, subst) -> + match v with + | None -> (Univ.LSet.add u undef, def, subst) + | Some b -> (undef, Univ.LSet.add u def, Univ.LMap.add u b subst)) + ctx (Univ.LSet.empty, Univ.LSet.empty, Univ.LMap.empty) + in ctx, undef, def, subst + +let pr_universe_body = function + | None -> mt () + | Some v -> str" := " ++ Univ.Universe.pr v + +let pr_universe_opt_subst = Univ.LMap.pr pr_universe_body + +let compare_constraint_type d d' = + match d, d' with + | Eq, Eq -> 0 + | Eq, _ -> -1 + | _, Eq -> 1 + | Le, Le -> 0 + | Le, _ -> -1 + | _, Le -> 1 + | Lt, Lt -> 0 + +type lowermap = constraint_type LMap.t + +let lower_union = + let merge k a b = + match a, b with + | Some _, None -> a + | None, Some _ -> b + | None, None -> None + | Some l, Some r -> + if compare_constraint_type l r >= 0 then a + else b + in LMap.merge merge + +let lower_add l c m = + try let c' = LMap.find l m in + if compare_constraint_type c c' > 0 then + LMap.add l c m + else m + with Not_found -> LMap.add l c m + +let lower_of_list l = + List.fold_left (fun acc (d,l) -> LMap.add l d acc) LMap.empty l + +exception Found of Level.t * lowermap +let find_inst insts v = + try LMap.iter (fun k (enf,alg,v',lower) -> + if not alg && enf && Universe.equal v' v then raise (Found (k, lower))) + insts; raise Not_found + with Found (f,l) -> (f,l) + +let compute_lbound left = + (** The universe variable was not fixed yet. + Compute its level using its lower bound. *) + let sup l lbound = + match lbound with + | None -> Some l + | Some l' -> Some (Universe.sup l l') + in + List.fold_left (fun lbound (d, l) -> + if d == Le (* l <= ?u *) then sup l lbound + else (* l < ?u *) + (assert (d == Lt); + if not (Universe.level l == None) then + sup (Universe.super l) lbound + else None)) + None left + +let instantiate_with_lbound u lbound lower alg enforce (ctx, us, algs, insts, cstrs) = + if enforce then + let inst = Universe.make u in + let cstrs' = enforce_leq lbound inst cstrs in + (ctx, us, LSet.remove u algs, + LMap.add u (enforce,alg,lbound,lower) insts, cstrs'), + (enforce, alg, inst, lower) + else (* Actually instantiate *) + (Univ.LSet.remove u ctx, Univ.LMap.add u (Some lbound) us, algs, + LMap.add u (enforce,alg,lbound,lower) insts, cstrs), + (enforce, alg, lbound, lower) + +type constraints_map = (Univ.constraint_type * Univ.LMap.key) list Univ.LMap.t + +let _pr_constraints_map (cmap:constraints_map) = + LMap.fold (fun l cstrs acc -> + Level.pr l ++ str " => " ++ + prlist_with_sep spc (fun (d,r) -> pr_constraint_type d ++ Level.pr r) cstrs ++ + fnl () ++ acc) + cmap (mt ()) + +let remove_alg l (ctx, us, algs, insts, cstrs) = + (ctx, us, LSet.remove l algs, insts, cstrs) + +let remove_lower u lower = + let levels = Universe.levels u in + LSet.fold (fun l acc -> LMap.remove l acc) levels lower + +let minimize_univ_variables ctx us algs left right cstrs = + let left, lbounds = + Univ.LMap.fold (fun r lower (left, lbounds as acc) -> + if Univ.LMap.mem r us || not (Univ.LSet.mem r ctx) then acc + else (* Fixed universe, just compute its glb for sharing *) + let lbounds' = + match compute_lbound (List.map (fun (d,l) -> d, Universe.make l) lower) with + | None -> lbounds + | Some lbound -> LMap.add r (true, false, lbound, lower_of_list lower) + lbounds + in (Univ.LMap.remove r left, lbounds')) + left (left, Univ.LMap.empty) + in + let rec instance (ctx', us, algs, insts, cstrs as acc) u = + let acc, left, lower = + try + let l = LMap.find u left in + let acc, left, newlow, lower = + List.fold_left + (fun (acc, left', newlow, lower') (d, l) -> + let acc', (enf,alg,l',lower) = aux acc l in + let l' = + if enf then Universe.make l + else l' + in acc', (d, l') :: left', + lower_add l d newlow, lower_union lower lower') + (acc, [], LMap.empty, LMap.empty) l + in + let not_lower (d,l) = + (* We're checking if (d,l) is already implied by the lower + constraints on some level u. If it represents l < u (d is Lt + or d is Le and i > 0, the i < 0 case is impossible due to + invariants of Univ), and the lower constraints only have l <= + u then it is not implied. *) + Univ.Universe.exists + (fun (l,i) -> + let d = + if i == 0 then d + else match d with + | Le -> Lt + | d -> d + in + try let d' = LMap.find l lower in + (* If d is stronger than the already implied lower + * constraints we must keep it. *) + compare_constraint_type d d' > 0 + with Not_found -> + (** No constraint existing on l *) true) l + in + let left = List.uniquize (List.filter not_lower left) in + (acc, left, LMap.union newlow lower) + with Not_found -> acc, [], LMap.empty + and right = + try Some (LMap.find u right) + with Not_found -> None + in + let instantiate_lbound lbound = + let alg = LSet.mem u algs in + if alg then + (* u is algebraic: we instantiate it with its lower bound, if any, + or enforce the constraints if it is bounded from the top. *) + let lower = remove_lower lbound lower in + instantiate_with_lbound u lbound lower true false acc + else (* u is non algebraic *) + match Universe.level lbound with + | Some l -> (* The lowerbound is directly a level *) + (* u is not algebraic but has no upper bounds, + we instantiate it with its lower bound if it is a + different level, otherwise we keep it. *) + let lower = LMap.remove l lower in + if not (Level.equal l u) then + (* Should check that u does not + have upper constraints that are not already in right *) + let acc' = remove_alg l acc in + instantiate_with_lbound u lbound lower false false acc' + else acc, (true, false, lbound, lower) + | None -> + try + (* Another universe represents the same lower bound, + we can share them with no harm. *) + let can, lower = find_inst insts lbound in + let lower = LMap.remove can lower in + instantiate_with_lbound u (Universe.make can) lower false false acc + with Not_found -> + (* We set u as the canonical universe representing lbound *) + instantiate_with_lbound u lbound lower false true acc + in + let acc' acc = + match right with + | None -> acc + | Some cstrs -> + let dangling = List.filter (fun (d, r) -> not (LMap.mem r us)) cstrs in + if List.is_empty dangling then acc + else + let ((ctx', us, algs, insts, cstrs), (enf,_,inst,lower as b)) = acc in + let cstrs' = List.fold_left (fun cstrs (d, r) -> + if d == Univ.Le then + enforce_leq inst (Universe.make r) cstrs + else + try let lev = Option.get (Universe.level inst) in + Constraint.add (lev, d, r) cstrs + with Option.IsNone -> failwith "") + cstrs dangling + in + (ctx', us, algs, insts, cstrs'), b + in + if not (LSet.mem u ctx) then acc' (acc, (true, false, Universe.make u, lower)) + else + let lbound = compute_lbound left in + match lbound with + | None -> (* Nothing to do *) + acc' (acc, (true, false, Universe.make u, lower)) + | Some lbound -> + try acc' (instantiate_lbound lbound) + with Failure _ -> acc' (acc, (true, false, Universe.make u, lower)) + and aux (ctx', us, algs, seen, cstrs as acc) u = + try acc, LMap.find u seen + with Not_found -> instance acc u + in + LMap.fold (fun u v (ctx', us, algs, seen, cstrs as acc) -> + if v == None then fst (aux acc u) + else LSet.remove u ctx', us, LSet.remove u algs, seen, cstrs) + us (ctx, us, algs, lbounds, cstrs) + +let normalize_context_set g ctx us algs weak = + let (ctx, csts) = ContextSet.levels ctx, ContextSet.constraints ctx in + let uf = UF.create () in + (** Keep the Prop/Set <= i constraints separate for minimization *) + let smallles, csts = + Constraint.fold (fun (l,d,r as cstr) (smallles, noneqs) -> + if d == Le then + if Univ.Level.is_small l then + if is_set_minimization () && LSet.mem r ctx then + (Constraint.add cstr smallles, noneqs) + else (smallles, noneqs) + else if Level.is_small r then + if Level.is_prop r then + raise (Univ.UniverseInconsistency + (Le,Universe.make l,Universe.make r,None)) + else (smallles, Constraint.add (l,Eq,r) noneqs) + else (smallles, Constraint.add cstr noneqs) + else (smallles, Constraint.add cstr noneqs)) + csts (Constraint.empty, Constraint.empty) + in + let csts = + (* We first put constraints in a normal-form: all self-loops are collapsed + to equalities. *) + let g = Univ.LSet.fold (fun v g -> UGraph.add_universe v false g) + ctx UGraph.initial_universes + in + let g = + Univ.Constraint.fold + (fun (l, d, r) g -> + let g = + if not (Level.is_small l || LSet.mem l ctx) then + try UGraph.add_universe l false g + with UGraph.AlreadyDeclared -> g + else g + in + let g = + if not (Level.is_small r || LSet.mem r ctx) then + try UGraph.add_universe r false g + with UGraph.AlreadyDeclared -> g + else g + in g) csts g + in + let g = Univ.Constraint.fold UGraph.enforce_constraint csts g in + UGraph.constraints_of_universes g + in + let noneqs = + Constraint.fold (fun (l,d,r as cstr) noneqs -> + if d == Eq then (UF.union l r uf; noneqs) + else (* We ignore the trivial Prop/Set <= i constraints. *) + if d == Le && Univ.Level.is_small l then noneqs + else if Univ.Level.is_prop l && d == Lt && Univ.Level.is_set r + then noneqs + else Constraint.add cstr noneqs) + csts Constraint.empty + in + let noneqs = Constraint.union noneqs smallles in + let partition = UF.partition uf in + let flex x = LMap.mem x us in + let ctx, us, eqs = List.fold_left (fun (ctx, us, cstrs) s -> + let canon, (global, rigid, flexible) = choose_canonical ctx flex algs s in + (* Add equalities for globals which can't be merged anymore. *) + let cstrs = LSet.fold (fun g cst -> + Constraint.add (canon, Univ.Eq, g) cst) global + cstrs + in + (* Also add equalities for rigid variables *) + let cstrs = LSet.fold (fun g cst -> + Constraint.add (canon, Univ.Eq, g) cst) rigid + cstrs + in + let canonu = Some (Universe.make canon) in + let us = LSet.fold (fun f -> LMap.add f canonu) flexible us in + (LSet.diff ctx flexible, us, cstrs)) + (ctx, us, Constraint.empty) partition + in + (* Process weak constraints: when one side is flexible and the 2 + universes are unrelated unify them. *) + let ctx, us, g = UPairSet.fold (fun (u,v) (ctx, us, g as acc) -> + let norm = let us = ref us in level_subst_of (normalize_univ_variable_opt_subst us) in + let u = norm u and v = norm v in + let set_to a b = + (LSet.remove a ctx, + LMap.add a (Some (Universe.make b)) us, + UGraph.enforce_constraint (a,Eq,b) g) + in + if UGraph.check_constraint g (u,Le,v) || UGraph.check_constraint g (v,Le,u) + then acc + else + if LMap.mem u us + then set_to u v + else if LMap.mem v us + then set_to v u + else acc) + weak (ctx, us, g) in + (* Noneqs is now in canonical form w.r.t. equality constraints, + and contains only inequality constraints. *) + let noneqs = + let us = ref us in + let norm = level_subst_of (normalize_univ_variable_opt_subst us) in + Constraint.fold (fun (u,d,v) noneqs -> + let u = norm u and v = norm v in + if d != Lt && Level.equal u v then noneqs + else Constraint.add (u,d,v) noneqs) + noneqs Constraint.empty + in + (* Compute the left and right set of flexible variables, constraints + mentionning other variables remain in noneqs. *) + let noneqs, ucstrsl, ucstrsr = + Constraint.fold (fun (l,d,r as cstr) (noneq, ucstrsl, ucstrsr) -> + let lus = LMap.mem l us and rus = LMap.mem r us in + let ucstrsl' = + if lus then add_list_map l (d, r) ucstrsl + else ucstrsl + and ucstrsr' = + add_list_map r (d, l) ucstrsr + in + let noneqs = + if lus || rus then noneq + else Constraint.add cstr noneq + in (noneqs, ucstrsl', ucstrsr')) + noneqs (Constraint.empty, LMap.empty, LMap.empty) + in + (* Now we construct the instantiation of each variable. *) + let ctx', us, algs, inst, noneqs = + minimize_univ_variables ctx us algs ucstrsr ucstrsl noneqs + in + let us = normalize_opt_subst us in + (us, algs), (ctx', Constraint.union noneqs eqs) + +(* let normalize_conkey = CProfile.declare_profile "normalize_context_set" *) +(* let normalize_context_set a b c = CProfile.profile3 normalize_conkey normalize_context_set a b c *) + +let is_trivial_leq (l,d,r) = + Univ.Level.is_prop l && (d == Univ.Le || (d == Univ.Lt && Univ.Level.is_set r)) + +(* Prop < i <-> Set+1 <= i <-> Set < i *) +let translate_cstr (l,d,r as cstr) = + if Level.equal Level.prop l && d == Univ.Lt && not (Level.equal Level.set r) then + (Level.set, d, r) + else cstr + +let refresh_constraints univs (ctx, cstrs) = + let cstrs', univs' = + Univ.Constraint.fold (fun c (cstrs', univs as acc) -> + let c = translate_cstr c in + if is_trivial_leq c then acc + else (Univ.Constraint.add c cstrs', UGraph.enforce_constraint c univs)) + cstrs (Univ.Constraint.empty, univs) + in ((ctx, cstrs'), univs') + + +(**********************************************************************) +(* Tools for sort-polymorphic inductive types *) + +(* Miscellaneous functions to remove or test local univ assumed to + occur only in the le constraints *) + +(* + Solve a system of universe constraint of the form + + u_s11, ..., u_s1p1, w1 <= u1 + ... + u_sn1, ..., u_snpn, wn <= un + +where + + - the ui (1 <= i <= n) are universe variables, + - the sjk select subsets of the ui for each equations, + - the wi are arbitrary complex universes that do not mention the ui. +*) + +let is_direct_sort_constraint s v = match s with + | Some u -> univ_level_mem u v + | None -> false + +let solve_constraints_system levels level_bounds level_min = + let open Univ in + let levels = + Array.mapi (fun i o -> + match o with + | Some u -> + (match Universe.level u with + | Some u -> Some u + | _ -> level_bounds.(i) <- Universe.sup level_bounds.(i) u; None) + | None -> None) + levels in + let v = Array.copy level_bounds in + let nind = Array.length v in + let clos = Array.map (fun _ -> Int.Set.empty) levels in + (* First compute the transitive closure of the levels dependencies *) + for i=0 to nind-1 do + for j=0 to nind-1 do + if not (Int.equal i j) && is_direct_sort_constraint levels.(j) v.(i) then + clos.(i) <- Int.Set.add j clos.(i); + done; + done; + let rec closure () = + let continue = ref false in + Array.iteri (fun i deps -> + let deps' = + Int.Set.fold (fun j acc -> Int.Set.union acc clos.(j)) deps deps + in + if Int.Set.equal deps deps' then () + else (clos.(i) <- deps'; continue := true)) + clos; + if !continue then closure () + else () + in + closure (); + for i=0 to nind-1 do + for j=0 to nind-1 do + if not (Int.equal i j) && Int.Set.mem j clos.(i) then + (v.(i) <- Universe.sup v.(i) level_bounds.(j)); + done; + done; + v |