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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \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 Context
open Environ
open Locus
open Univ
(* 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 subst = make_universe_subst inst ctx in
let constraints = instantiate_univ_context subst ctx in
(inst, subst), constraints
let fresh_instance ctx =
let s = ref LSet.empty in
let inst =
Instance.subst_fn (fun _ ->
let u = new_univ_level (Global.current_dirpath ()) in
s := LSet.add u !s; u)
(UContext.instance ctx)
in !s, inst
let fresh_instance_from ctx =
let ctx', inst = fresh_instance ctx in
let subst = make_universe_subst inst ctx in
let constraints = instantiate_univ_context subst ctx in
(inst, subst), (ctx', constraints)
(** Fresh universe polymorphic construction *)
let fresh_constant_instance env c =
let cb = lookup_constant c env in
if cb.Declarations.const_polymorphic then
let (inst,_), ctx = fresh_instance_from (Future.force cb.Declarations.const_universes) in
((c, inst), ctx)
else ((c,Instance.empty), ContextSet.empty)
let fresh_inductive_instance env ind =
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 in
((ind,inst), ctx)
else ((ind,Instance.empty), ContextSet.empty)
let fresh_constructor_instance env (ind,i) =
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 in
(((ind,i),inst), ctx)
else (((ind,i),Instance.empty), ContextSet.empty)
open Globnames
let fresh_global_instance env gr =
match gr with
| VarRef id -> mkVar id, ContextSet.empty
| ConstRef sp ->
let c, ctx = fresh_constant_instance env sp in
mkConstU c, ctx
| ConstructRef sp ->
let c, ctx = fresh_constructor_instance env sp in
mkConstructU c, ctx
| IndRef sp ->
let c, ctx = fresh_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 unsafe_constr_of_global gr =
let c, ctx = fresh_global_instance (Global.env ()) gr in
c
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 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
if cb.const_polymorphic then
let (inst, subst), ctx = fresh_instance_from (Future.force cb.const_universes) in
Vars.subst_univs_constr subst cb.const_type, ctx
else cb.const_type, ContextSet.empty
| IndRef ind ->
let (mib, oib) = Inductive.lookup_mind_specif env ind in
if mib.mind_polymorphic then
let (inst, subst), ctx = fresh_instance_from mib.mind_universes in
Vars.subst_univs_constr subst oib.mind_arity.mind_user_arity, ctx
else oib.mind_arity.mind_user_arity, 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, subst), ctx = fresh_instance_from mib.mind_universes 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 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 remove_trivial_constraints cst =
Constraint.fold (fun (l,d,r as cstr) nontriv ->
if d != Lt && eq_levels l r then nontriv
else if d == Le && is_type0m_univ (Univ.Universe.make l) then nontriv
else Constraint.add cstr nontriv)
cst Constraint.empty
let add_list_map u t map =
let l, d, r = LMap.split u map in
let d' = match d with None -> [t] | Some l -> t :: l in
let lr =
LMap.merge (fun k lm rm ->
match lm with Some t -> lm | None ->
match rm with Some t -> rm | None -> None) l r
in LMap.add u d' lr
let find_list_map u map =
try LMap.find u map with Not_found -> []
module UF = LevelUnionFind
type universe_full_subst = (universe_level * universe) list
(** Precondition: flexible <= ctx *)
let choose_canonical ctx flexible algs s =
let global = LSet.diff s ctx in
let flexible, rigid = LSet.partition (fun x -> LMap.mem x 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)
open Universe
let subst_puniverses subst (c, u as cu) =
let u' = Instance.subst subst u in
if u' == u then cu else (c, u')
let nf_evars_and_universes_local f subst =
let rec aux c =
match kind_of_term c with
| Evar (evdk, _ as ev) ->
(match f ev with
| None -> c
| Some c -> aux c)
| Const pu ->
let pu' = subst_puniverses subst pu in
if pu' == pu then c else mkConstU pu'
| Ind pu ->
let pu' = subst_puniverses subst pu in
if pu' == pu then c else mkIndU pu'
| Construct pu ->
let pu' = subst_puniverses subst pu in
if pu' == pu then c else mkConstructU pu'
| Sort (Type u) ->
let u' = Univ.subst_univs_level_universe subst u in
if u' == u then c else mkSort (sort_of_univ u')
| _ -> map_constr aux c
in aux
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 subst_univs_puniverses subst cu =
subst_univs_fn_puniverses (Univ.level_subst_of (Univ.make_subst subst)) cu
let nf_evars_and_universes_gen f subst =
let lsubst = Univ.level_subst_of subst in
let rec aux c =
match kind_of_term c with
| Evar (evdk, _ as ev) ->
(match try f ev 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 nf_evars_and_universes_subst f subst =
nf_evars_and_universes_gen f (Univ.make_subst subst)
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
nf_evars_and_universes_gen f subst
let subst_univs_full_constr subst c =
nf_evars_and_universes_subst (fun _ -> None) subst c
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.eq b' b then b
else update cur b'
in fun b -> try aux b with Not_found -> Universe.make b
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.eq l l') | None -> true);
ectx := Univ.LMap.add l (Some b) !ectx; b
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.eq l l') | None -> true);
subst := Univ.LMap.add l b !subst; b 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
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 ectx = ref ctx in
let normalize = normalize_univ_variable_opt_subst ectx in
let _ = Univ.LMap.iter (fun u _ -> ignore(normalize u)) 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))
!ectx (Univ.LSet.empty, Univ.LSet.empty, Univ.LMap.empty)
in !ectx, 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 is_defined_var u l =
try
match LMap.find u l with
| Some _ -> true
| None -> false
with Not_found -> false
let subst_univs_subst u l s =
LMap.add u l s
exception Found of Level.t
let find_inst insts v =
try LMap.iter (fun k (enf,alg,v') ->
if not alg && enf && Universe.eq v' v then raise (Found k))
insts; raise Not_found
with Found l -> l
let add_inst u (enf,b,lbound) insts =
match lbound with
| Some v -> LMap.add u (enf,b,v) insts
| None -> insts
exception Stays
let compute_lbound left =
(** The universe variable was not fixed yet.
Compute its level using its lower bound. *)
if CList.is_empty left then None
else
let lbound = List.fold_left (fun lbound (d, l) ->
if d == Le (* l <= ?u *) then (Universe.sup l lbound)
else (* l < ?u *)
(assert (d == Lt);
(Universe.sup (Universe.super l) lbound)))
Universe.type0m left
in
Some lbound
let maybe_enforce_leq lbound u cstrs =
match lbound with
| Some lbound -> enforce_leq lbound (Universe.make u) cstrs
| None -> cstrs
let instantiate_with_lbound u lbound 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) insts, cstrs'), (enforce, alg, inst)
else (* Actually instantiate *)
(Univ.LSet.remove u ctx, Univ.LMap.add u (Some lbound) us, algs,
LMap.add u (enforce,alg,lbound) insts, cstrs), (enforce, alg, lbound)
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 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) 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 =
try let l = LMap.find u left in
List.fold_left (fun (acc, left') (d, l) ->
let acc', (enf,alg,l') = aux acc l in
(* if alg then assert(not alg); *)
let l' =
if enf then Universe.make l
else l'
(* match Universe.level l' with Some _ -> l' | None -> Universe.make l *)
in
acc', (d, l') :: left') (acc, []) l
with Not_found -> acc, []
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 and has no upper bound constraints: we
instantiate it with it's lower bound, if any *)
instantiate_with_lbound u lbound 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. *)
if not (Level.eq l u) && not (LSet.mem l algs) then
(* if right = None then. Should check that u does not
have upper constraints that are not already in right *)
instantiate_with_lbound u lbound false false acc
(* else instantiate_with_lbound u lbound false true acc *)
else
(* assert false: l can't be alg *)
acc, (true, false, lbound)
| None ->
try
(* if right <> None then raise Not_found; *)
(* Another universe represents the same lower bound,
we can share them with no harm. *)
let can = find_inst insts lbound in
instantiate_with_lbound u (Universe.make can) false false acc
with Not_found ->
(* We set u as the canonical universe representing lbound *)
instantiate_with_lbound u lbound 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 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 -> assert false)
cstrs dangling
in
(ctx', us, algs, insts, cstrs'), b
in
if not (LSet.mem u ctx) then acc' (acc, (true, false, Universe.make u))
else
let lbound = compute_lbound left in
match lbound with
| None -> (* Nothing to do *)
acc' (acc, (true, false, Universe.make u))
| Some lbound ->
acc' (instantiate_lbound lbound)
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
let csts =
(* We first put constraints in a normal-form: all self-loops are collapsed
to equalities. *)
let g = Univ.merge_constraints csts Univ.empty_universes in
Univ.constraints_of_universes (Univ.normalize_universes g)
in
let noneqs =
Constraint.fold (fun (l,d,r) noneqs ->
if d == Eq 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 subst, eqs = List.fold_left (fun (subst, cstrs) s ->
let canon, (global, rigid, flexible) = choose_canonical ctx us 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
(** Should this really happen? *)
let subst' = LSet.fold (fun f -> LMap.add f canon)
(LSet.union rigid flexible) LMap.empty
in
let subst = LMap.union subst' subst in
(subst, cstrs))
(LMap.empty, 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
let us =
LMap.subst_union (LMap.map (fun v -> Some (Universe.make v)) subst) us
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 instanciation of each variable. *)
let ctx', us, algs, inst, noneqs =
minimize_univ_variables ctx us algs ucstrsr ucstrsl noneqs
in
let us = ref us in
let norm = normalize_univ_variable_opt_subst us in
let _normalize_subst = LMap.iter (fun u v -> ignore(norm u)) !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.union (Instance.levels u) s
| Sort u ->
let u = univ_of_sort u in
LSet.union (Universe.levels u) s
| _ -> fold_constr aux s c
in aux LSet.empty c
let shrink_universe_context (univs,csts) s =
let univs' = LSet.inter univs s in
Constraint.fold (fun (l,d,r as c) (univs',csts) ->
if LSet.mem l univs' then
let univs' = if LSet.mem r univs then LSet.add r univs' else univs' in
(univs', Constraint.add c csts)
else if LSet.mem r univs' then
let univs' = if LSet.mem l univs then LSet.add l univs' else univs' in
(univs', Constraint.add c csts)
else (univs', csts))
csts (univs',Constraint.empty)
let restrict_universe_context (univs,csts) s =
let univs' = LSet.inter univs s in
(* 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 csts' =
Constraint.fold (fun (l,d,r as c) csts ->
if LSet.mem l diff || LSet.mem r diff then csts
else Constraint.add c csts)
csts Constraint.empty
in (univs', csts')
let is_prop_leq (l,d,r) =
Level.eq Level.prop l && d == Univ.Le
(* Prop < i <-> Set+1 <= i <-> Set < i *)
let translate_cstr (l,d,r as cstr) =
if Level.eq Level.prop l && d == Univ.Lt 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 Univ.check_constraint univs c && not (is_prop_leq c) then acc
else (Univ.Constraint.add c cstrs', Univ.enforce_constraint c univs))
cstrs (Univ.Constraint.empty, univs)
in ((ctx, cstrs'), univs')
let remove_trivial_constraints (ctx, cstrs) =
let cstrs' =
Univ.Constraint.fold (fun c acc ->
if is_prop_leq c then Univ.Constraint.remove c acc
else acc) cstrs cstrs
in (ctx, cstrs')
|