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Diffstat (limited to 'library/universes.ml')
| -rw-r--r-- | library/universes.ml | 1162 |
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diff --git a/library/universes.ml b/library/universes.ml deleted file mode 100644 index 112b20a4..00000000 --- a/library/universes.ml +++ /dev/null @@ -1,1162 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -open Util -open Pp -open Names -open Term -open Environ -open Univ -open Globnames -open Decl_kinds - -(** Global universe names *) -type universe_names = - (polymorphic * Univ.universe_level) Idmap.t * Id.t Univ.LMap.t - -let global_universes = - Summary.ref ~name:"Global universe names" - ((Idmap.empty, Univ.LMap.empty) : universe_names) - -let global_universe_names () = !global_universes -let set_global_universe_names s = global_universes := s - -let pr_with_global_universes l = - try Nameops.pr_id (LMap.find l (snd !global_universes)) - with Not_found -> Level.pr l - -(** Local universe names of polymorphic references *) - -type universe_binders = (Id.t * Univ.universe_level) list - -let universe_binders_table = Summary.ref Refmap.empty ~name:"universe binders" - -let universe_binders_of_global ref = - try - let l = Refmap.find ref !universe_binders_table in l - with Not_found -> [] - -let register_universe_binders ref l = - universe_binders_table := Refmap.add ref l !universe_binders_table - -(* To disallow minimization to Set *) - -let set_minimization = ref true -let is_set_minimization () = !set_minimization - -type universe_constraint_type = ULe | UEq | ULub - -type universe_constraint = universe * universe_constraint_type * universe - -module Constraints = struct - module S = Set.Make( - struct - type t = universe_constraint - - let compare_type c c' = - match c, c' with - | ULe, ULe -> 0 - | ULe, _ -> -1 - | _, ULe -> 1 - | UEq, UEq -> 0 - | UEq, _ -> -1 - | ULub, ULub -> 0 - | ULub, _ -> 1 - - let compare (u,c,v) (u',c',v') = - let i = compare_type c c' in - if Int.equal i 0 then - let i' = Universe.compare u u' in - if Int.equal i' 0 then Universe.compare v v' - else - if c != ULe && Universe.compare u v' = 0 && Universe.compare v u' = 0 then 0 - else i' - else i - end) - - include S - - let add (l,d,r as cst) s = - if Universe.equal l r then s - else add cst s - - let tr_dir = function - | ULe -> Le - | UEq -> Eq - | ULub -> Eq - - let op_str = function ULe -> " <= " | UEq -> " = " | ULub -> " /\\ " - - let pr c = - fold (fun (u1,op,u2) pp_std -> - pp_std ++ Universe.pr u1 ++ str (op_str op) ++ - Universe.pr u2 ++ 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 d = if strict then ULub else UEq 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 (Universe.make x, d, Universe.make y)) - ax ay c - -let subst_univs_universe_constraint fn (u,d,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 (u',d,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 g s = - let tr (x,d,y) acc = - let add l d l' acc = Constraint.add (l,Constraints.tr_dir d,l') acc in - match Universe.level x, d, Universe.level y with - | Some l, (ULe | UEq | ULub), Some l' -> add l d l' acc - | _, ULe, Some l' -> enforce_leq x y acc - | _, ULub, _ -> acc - | _, d, _ -> - let f = if d == ULe then UGraph.check_leq else UGraph.check_eq in - if f g x y then acc else - raise (Invalid_argument - "to_constraints: non-trivial algebraic constraint between universes") - in Constraints.fold tr s Constraint.empty - -let eq_constr_univs_infer univs fold m n accu = - if m == n then Some accu - else - let cstrs = ref accu in - let eq_universes strict = 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 (u1, UEq, u2)) !cstrs with - | None -> false - | Some accu -> cstrs := accu; true - in - let rec eq_constr' m n = - m == n || Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n - in - let res = Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n in - if res then Some !cstrs else None - -(** 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 strict = 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 (u1, UEq, u2)) !cstrs with - | None -> false - | Some accu -> cstrs := accu; true - in - let rec eq_constr' m n = - Constr.compare_head_gen_with kind1 kind2 eq_universes eq_sorts eq_constr' m n - in - let res = Constr.compare_head_gen_with kind1 kind2 eq_universes eq_sorts eq_constr' m n in - if res then Some !cstrs else None - -let leq_constr_univs_infer univs fold m n accu = - if m == n then Some accu - else - let cstrs = ref accu in - let eq_universes strict l l' = UGraph.check_eq_instances univs l l' 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 (u1, UEq, u2)) !cstrs with - | None -> false - | Some accu -> cstrs := accu; true - in - let leq_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 (u1, ULe, u2)) !cstrs with - | None -> false - | Some accu -> cstrs := accu; true - in - let rec eq_constr' m n = - m == n || Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n - in - let rec compare_leq m n = - Constr.compare_head_gen_leq eq_universes leq_sorts - eq_constr' leq_constr' m n - and leq_constr' m n = m == n || compare_leq m n in - let res = compare_leq m n in - if res then Some !cstrs else None - -let eq_constr_universes m n = - if m == n then true, Constraints.empty - else - let cstrs = ref Constraints.empty in - let eq_universes strict l l' = - cstrs := enforce_eq_instances_univs strict l l' !cstrs; true in - let eq_sorts s1 s2 = - if Sorts.equal s1 s2 then true - else - (cstrs := Constraints.add - (Sorts.univ_of_sort s1, UEq, Sorts.univ_of_sort s2) !cstrs; - true) - in - let rec eq_constr' m n = - m == n || Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n - in - let res = Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n in - res, !cstrs - -let leq_constr_universes m n = - if m == n then true, Constraints.empty - else - let cstrs = ref Constraints.empty in - let eq_universes strict l l' = - cstrs := enforce_eq_instances_univs strict l l' !cstrs; true in - let eq_sorts s1 s2 = - if Sorts.equal s1 s2 then true - else (cstrs := Constraints.add - (Sorts.univ_of_sort s1,UEq,Sorts.univ_of_sort s2) !cstrs; - true) - in - let leq_sorts s1 s2 = - if Sorts.equal s1 s2 then true - else - (cstrs := Constraints.add - (Sorts.univ_of_sort s1,ULe,Sorts.univ_of_sort s2) !cstrs; - true) - in - let rec eq_constr' m n = - m == n || Constr.compare_head_gen eq_universes eq_sorts eq_constr' m n - in - let rec compare_leq m n = - Constr.compare_head_gen_leq eq_universes leq_sorts eq_constr' leq_constr' m n - and leq_constr' m n = m == n || compare_leq m n in - let res = compare_leq m n in - res, !cstrs - -let compare_head_gen_proj env equ eqs eqc' m n = - match kind_of_term m, kind_of_term n with - | Proj (p, c), App (f, args) - | App (f, args), Proj (p, c) -> - (match kind_of_term f with - | Const (p', u) when eq_constant (Projection.constant p) p' -> - let pb = Environ.lookup_projection p env in - let npars = pb.Declarations.proj_npars in - if Array.length args == npars + 1 then - eqc' c args.(npars) - else false - | _ -> false) - | _ -> Constr.compare_head_gen equ eqs eqc' m n - -let eq_constr_universes_proj env m n = - if m == n then true, Constraints.empty - else - let cstrs = ref Constraints.empty in - let eq_universes strict l l' = - cstrs := enforce_eq_instances_univs strict l l' !cstrs; true in - let eq_sorts s1 s2 = - if Sorts.equal s1 s2 then true - else - (cstrs := Constraints.add - (Sorts.univ_of_sort s1, UEq, Sorts.univ_of_sort s2) !cstrs; - true) - in - let rec eq_constr' m n = - m == n || compare_head_gen_proj env eq_universes eq_sorts eq_constr' m n - in - let res = eq_constr' m n in - res, !cstrs - -(* Generator of levels *) -let new_univ_level, set_remote_new_univ_level = - RemoteCounter.new_counter ~name:"Universes" 0 ~incr:((+) 1) - ~build:(fun n -> Univ.Level.make (Global.current_dirpath ()) n) - -let new_univ_level _ = new_univ_level () - (* Univ.Level.make db (new_univ_level ()) *) - -let fresh_level () = new_univ_level (Global.current_dirpath ()) - -(* 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 = - Instance.subst_fn (fun _ -> new_univ_level (Global.current_dirpath ())) - (UContext.instance ctx) - -let fresh_instance_from_context ctx = - let inst = fresh_universe_instance ctx in - let constraints = instantiate_univ_constraints inst ctx in - inst, constraints - -let fresh_instance ctx = - let ctx' = ref LSet.empty in - let inst = - Instance.subst_fn (fun v -> - let u = new_univ_level (Global.current_dirpath ()) in - ctx' := LSet.add u !ctx'; u) - (UContext.instance ctx) - in !ctx', inst - -let existing_instance ctx inst = - let () = - let a1 = Instance.to_array inst - and a2 = Instance.to_array (UContext.instance ctx) in - let len1 = Array.length a1 and len2 = Array.length a2 in - if not (len1 == len2) then - CErrors.errorlabstrm "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 = instantiate_univ_constraints inst ctx in - inst, (ctx', constraints) - -let unsafe_instance_from ctx = - (Univ.UContext.instance ctx, ctx) - -(** Fresh universe polymorphic construction *) - -let fresh_constant_instance env c inst = - let cb = lookup_constant c env in - if cb.Declarations.const_polymorphic then - let inst, ctx = - fresh_instance_from - (Declareops.universes_of_constant (Environ.opaque_tables env) cb) inst - in - ((c, inst), ctx) - else ((c,Instance.empty), ContextSet.empty) - -let fresh_inductive_instance env ind inst = - let mib, mip = Inductive.lookup_mind_specif env ind in - if mib.Declarations.mind_polymorphic then - let inst, ctx = fresh_instance_from mib.Declarations.mind_universes inst in - ((ind,inst), ctx) - else ((ind,Instance.empty), ContextSet.empty) - -let fresh_constructor_instance env (ind,i) inst = - let mib, mip = Inductive.lookup_mind_specif env ind in - if mib.Declarations.mind_polymorphic then - let inst, ctx = fresh_instance_from mib.Declarations.mind_universes inst in - (((ind,i),inst), ctx) - else (((ind,i),Instance.empty), ContextSet.empty) - -let unsafe_constant_instance env c = - let cb = lookup_constant c env in - if cb.Declarations.const_polymorphic then - let inst, ctx = unsafe_instance_from - (Declareops.universes_of_constant (Environ.opaque_tables env) cb) in - ((c, inst), ctx) - else ((c,Instance.empty), UContext.empty) - -let unsafe_inductive_instance env ind = - let mib, mip = Inductive.lookup_mind_specif env ind in - if mib.Declarations.mind_polymorphic then - let inst, ctx = unsafe_instance_from mib.Declarations.mind_universes in - ((ind,inst), ctx) - else ((ind,Instance.empty), UContext.empty) - -let unsafe_constructor_instance env (ind,i) = - let mib, mip = Inductive.lookup_mind_specif env ind in - if mib.Declarations.mind_polymorphic then - let inst, ctx = unsafe_instance_from mib.Declarations.mind_universes in - (((ind,i),inst), ctx) - else (((ind,i),Instance.empty), UContext.empty) - -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 unsafe_global_instance env gr = - match gr with - | VarRef id -> mkVar id, UContext.empty - | ConstRef sp -> - let c, ctx = unsafe_constant_instance env sp in - mkConstU c, ctx - | ConstructRef sp -> - let c, ctx = unsafe_constructor_instance env sp in - mkConstructU c, ctx - | IndRef sp -> - let c, ctx = unsafe_inductive_instance env sp in - mkIndU c, ctx - -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 raise (Invalid_argument - ("constr_of_global: globalization of polymorphic reference " ^ - Pp.string_of_ppcmds (Nametab.pr_global_env Id.Set.empty gr) ^ - " would forget universes.")) - else c - -let constr_of_reference = constr_of_global - -let unsafe_constr_of_global gr = - unsafe_global_instance (Global.env ()) gr - -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_of_term 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 - -let global_app_of_constr c = - match kind_of_term c with - | Const (c, u) -> (ConstRef c, u), None - | Ind (i, u) -> (IndRef i, u), None - | Construct (c, u) -> (ConstructRef c, u), None - | Var id -> (VarRef id, Instance.empty), None - | Proj (p, c) -> (ConstRef (Projection.constant p), Instance.empty), Some c - | _ -> 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 = Typeops.type_of_constant_type env cb.const_type in - if cb.const_polymorphic then - let inst, ctx = fresh_instance_from (Declareops.universes_of_constant (Environ.opaque_tables env) cb) None in - Vars.subst_instance_constr inst ty, ctx - else ty, ContextSet.empty - - | IndRef ind -> - let (mib, oib as specif) = Inductive.lookup_mind_specif env ind in - if mib.mind_polymorphic then - let inst, ctx = fresh_instance_from mib.mind_universes None in - let ty = Inductive.type_of_inductive env (specif, inst) in - ty, ctx - else - let ty = Inductive.type_of_inductive env (specif, Univ.Instance.empty) in - ty, ContextSet.empty - | ConstructRef cstr -> - let (mib,oib as specif) = Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in - if mib.mind_polymorphic then - let inst, ctx = fresh_instance_from mib.mind_universes None in - Inductive.type_of_constructor (cstr,inst) specif, ctx - else Inductive.type_of_constructor (cstr,Instance.empty) specif, ContextSet.empty - -let type_of_global t = type_of_reference (Global.env ()) t - -let unsafe_type_of_reference env r = - match r with - | VarRef id -> Environ.named_type id env - | ConstRef c -> - let cb = Environ.lookup_constant c env in - Typeops.type_of_constant_type env cb.const_type - - | IndRef ind -> - let (mib, oib as specif) = Inductive.lookup_mind_specif env ind in - let (_, inst), _ = unsafe_inductive_instance env ind in - Inductive.type_of_inductive env (specif, inst) - - | ConstructRef (ind, _ as cstr) -> - let (mib,oib as specif) = Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in - let (_, inst), _ = unsafe_inductive_instance env ind in - Inductive.type_of_constructor (cstr,inst) specif - -let unsafe_type_of_global t = unsafe_type_of_reference (Global.env ()) t - -let fresh_sort_in_family env = function - | InProp -> prop_sort, ContextSet.empty - | InSet -> set_sort, 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.update 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_puniverses lsubst (c, u as cu) = - let u' = Instance.subst_fn lsubst u in - if u' == u then cu else (c, u') - -let nf_evars_and_universes_opt_subst f subst = - let subst = fun l -> match LMap.find l subst with None -> raise Not_found | Some l' -> l' in - let lsubst = Univ.level_subst_of subst in - let rec aux c = - match kind_of_term c with - | Evar (evk, args) -> - let args = Array.map aux args in - (match try f (evk, args) with Not_found -> None with - | None -> c - | 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') - | _ -> map_constr aux c - in aux - -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.update 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 option universe_map - -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 - Vars.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 = - 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 ctx us algs = - 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.empty_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, subst, us, eqs = List.fold_left (fun (ctx, subst, 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 subst = LSet.fold (fun f -> LMap.add f canon) rigid subst in - let subst = LSet.fold (fun f -> LMap.add f canon) flexible subst 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, subst, us, cstrs)) - (ctx, LMap.empty, us, Constraint.empty) partition - in - (* Noneqs is now in canonical form w.r.t. equality constraints, - and contains only inequality constraints. *) - let noneqs = subst_univs_level_constraints subst noneqs 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 = Profile.declare_profile "normalize_context_set" *) -(* let normalize_context_set a b c = Profile.profile3 normalize_conkey normalize_context_set a b c *) - -let universes_of_constr c = - let rec aux s c = - match kind_of_term c with - | Const (_, u) | Ind (_, u) | Construct (_, u) -> - LSet.fold LSet.add (Instance.levels u) s - | Sort u when not (Sorts.is_small u) -> - let u = univ_of_sort u in - LSet.fold LSet.add (Universe.levels u) s - | _ -> fold_constr aux s c - in aux LSet.empty c - -let restrict_universe_context (univs,csts) s = - (* Universes that are not necessary to typecheck the term. - E.g. univs introduced by tactics and not used in the proof term. *) - let diff = LSet.diff univs s in - let rec aux diff candid univs ness = - let (diff', candid', univs', ness') = - Constraint.fold - (fun (l, d, r as c) (diff, candid, univs, csts) -> - if not (LSet.mem l diff) then - (LSet.remove r diff, candid, univs, Constraint.add c csts) - else if not (LSet.mem r diff) then - (LSet.remove l diff, candid, univs, Constraint.add c csts) - else (diff, Constraint.add c candid, univs, csts)) - candid (diff, Constraint.empty, univs, ness) - in - if ness' == ness then (LSet.diff univs diff', ness) - else aux diff' candid' univs' ness' - in aux diff csts univs Constraint.empty - -let simplify_universe_context (univs,csts) = - let uf = UF.create () in - let noneqs = - Constraint.fold (fun (l,d,r) noneqs -> - if d == Eq && (LSet.mem l univs || LSet.mem r univs) then - (UF.union l r uf; noneqs) - else Constraint.add (l,d,r) noneqs) - csts Constraint.empty - in - let partition = UF.partition uf in - let flex x = LSet.mem x univs in - let subst, univs', csts' = List.fold_left (fun (subst, univs, cstrs) s -> - let canon, (global, rigid, flexible) = choose_canonical univs flex LSet.empty 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) (LSet.union global rigid) - cstrs - in - let subst = LSet.fold (fun f -> LMap.add f canon) - flexible subst - in (subst, LSet.diff univs flexible, cstrs)) - (LMap.empty, univs, noneqs) partition - in - (* Noneqs is now in canonical form w.r.t. equality constraints, - and contains only inequality constraints. *) - let csts' = subst_univs_level_constraints subst csts' in - (univs', csts'), subst - -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 |