/
uState.ml
766 lines (679 loc) · 27.9 KB
/
uState.ml
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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open CErrors
open Util
open Names
open Univ
type universes_entry =
| Monomorphic_entry of Univ.ContextSet.t
| Polymorphic_entry of Univ.UContext.t
module UNameMap = Names.Id.Map
type uinfo = {
uname : Id.t option;
uloc : Loc.t option;
}
module UPairSet = UnivMinim.UPairSet
(* 2nd part used to check consistency on the fly. *)
type t =
{ names : UnivNames.universe_binders * uinfo Level.Map.t; (** Printing/location information *)
local : ContextSet.t; (** The local graph of universes (variables and constraints) *)
seff_univs : Level.Set.t; (** Local universes used through private constants *)
univ_variables : UnivSubst.universe_opt_subst;
(** The local universes that are unification variables *)
univ_algebraic : Level.Set.t;
(** The subset of unification variables that can be instantiated with
algebraic universes as they appear in inferred types only. *)
universes : UGraph.t; (** The current graph extended with the local constraints *)
universes_lbound : UGraph.Bound.t; (** The lower bound on universes (e.g. Set or Prop) *)
initial_universes : UGraph.t; (** The graph at the creation of the evar_map *)
weak_constraints : UPairSet.t
}
let initial_sprop_cumulative = UGraph.set_cumulative_sprop true UGraph.initial_universes
let empty =
{ names = UNameMap.empty, Level.Map.empty;
local = ContextSet.empty;
seff_univs = Level.Set.empty;
univ_variables = Level.Map.empty;
univ_algebraic = Level.Set.empty;
universes = initial_sprop_cumulative;
universes_lbound = UGraph.Bound.Set;
initial_universes = initial_sprop_cumulative;
weak_constraints = UPairSet.empty; }
let elaboration_sprop_cumul =
Goptions.declare_bool_option_and_ref ~depr:false
~key:["Elaboration";"StrictProp";"Cumulativity"] ~value:true
let make ~lbound univs =
let univs = UGraph.set_cumulative_sprop (elaboration_sprop_cumul ()) univs in
{ empty with
universes = univs;
universes_lbound = lbound;
initial_universes = univs}
let is_empty uctx =
ContextSet.is_empty uctx.local &&
Level.Map.is_empty uctx.univ_variables
let uname_union s t =
if s == t then s
else
UNameMap.merge (fun k l r ->
match l, r with
| Some _, _ -> l
| _, _ -> r) s t
let union uctx uctx' =
if uctx == uctx' then uctx
else if is_empty uctx' then uctx
else
let local = ContextSet.union uctx.local uctx'.local in
let seff = Level.Set.union uctx.seff_univs uctx'.seff_univs in
let names = uname_union (fst uctx.names) (fst uctx'.names) in
let names_rev = Level.Map.lunion (snd uctx.names) (snd uctx'.names) in
let newus = Level.Set.diff (ContextSet.levels uctx'.local)
(ContextSet.levels uctx.local) in
let newus = Level.Set.diff newus (Level.Map.domain uctx.univ_variables) in
let weak = UPairSet.union uctx.weak_constraints uctx'.weak_constraints in
let declarenew g =
Level.Set.fold (fun u g -> UGraph.add_universe u ~lbound:uctx.universes_lbound ~strict:false g) newus g
in
{ names = (names, names_rev);
local = local;
seff_univs = seff;
univ_variables =
Level.Map.subst_union uctx.univ_variables uctx'.univ_variables;
univ_algebraic =
Level.Set.union uctx.univ_algebraic uctx'.univ_algebraic;
initial_universes = declarenew uctx.initial_universes;
universes =
(if local == uctx.local then uctx.universes
else
let cstrsr = ContextSet.constraints uctx'.local in
UGraph.merge_constraints cstrsr (declarenew uctx.universes));
universes_lbound = uctx.universes_lbound;
weak_constraints = weak}
let context_set uctx = uctx.local
let constraints uctx = snd uctx.local
let compute_instance_binders rbinders inst =
let map lvl =
try Name (Option.get (Level.Map.find lvl rbinders).uname)
with Option.IsNone | Not_found -> Anonymous
in
Array.map map (Instance.to_array inst)
let context uctx =
let (_, rbinders) = uctx.names in
ContextSet.to_context (compute_instance_binders rbinders) uctx.local
type named_universes_entry = universes_entry * UnivNames.universe_binders
let univ_entry ~poly uctx =
let (binders, _) = uctx.names in
let entry =
if poly then Polymorphic_entry (context uctx)
else Monomorphic_entry (context_set uctx) in
entry, binders
let of_context_set local = { empty with local }
type universe_opt_subst = UnivSubst.universe_opt_subst
let subst uctx = uctx.univ_variables
let nf_universes uctx c =
UnivSubst.nf_evars_and_universes_opt_subst (fun _ -> None) (subst uctx) c
let ugraph uctx = uctx.universes
let initial_graph uctx = uctx.initial_universes
let algebraics uctx = uctx.univ_algebraic
let add_names ?loc s l (names, names_rev) =
if UNameMap.mem s names
then user_err ?loc
Pp.(str "Universe " ++ Names.Id.print s ++ str" already bound.");
(UNameMap.add s l names, Level.Map.add l { uname = Some s; uloc = loc } names_rev)
let add_loc l loc (names, names_rev) =
match loc with
| None -> (names, names_rev)
| Some _ -> (names, Level.Map.add l { uname = None; uloc = loc } names_rev)
let of_binders names =
let rev_map =
UNameMap.fold (fun id l rmap ->
Level.Map.add l { uname = Some id; uloc = None } rmap)
names Level.Map.empty
in
{ empty with names = (names, rev_map) }
let universe_of_name uctx s =
UNameMap.find s (fst uctx.names)
let universe_binders uctx =
let named, _ = uctx.names in
named
let instantiate_variable l b v =
try v := Level.Map.set l (Some (Sorts.univ_of_sort b)) !v
with Not_found -> assert false
exception UniversesDiffer
let drop_weak_constraints =
Goptions.declare_bool_option_and_ref
~depr:false
~key:["Cumulativity";"Weak";"Constraints"]
~value:false
let sort_inconsistency cst l r =
raise (UniverseInconsistency (cst, Sorts.univ_of_sort l, Sorts.univ_of_sort r, None))
let subst_univs_sort normalize s =
Sorts.sort_of_univ (subst_univs_universe normalize (Sorts.univ_of_sort s))
let process_universe_constraints uctx cstrs =
let open UnivSubst in
let open UnivProblem in
let univs = uctx.universes in
let vars = ref uctx.univ_variables in
let weak = ref uctx.weak_constraints in
let normalize u = normalize_univ_variable_opt_subst !vars u in
let nf_constraint = function
| ULub (u, v) -> ULub (level_subst_of normalize u, level_subst_of normalize v)
| UWeak (u, v) -> UWeak (level_subst_of normalize u, level_subst_of normalize v)
| UEq (u, v) -> UEq (subst_univs_sort normalize u, subst_univs_sort normalize v)
| ULe (u, v) -> ULe (subst_univs_sort normalize u, subst_univs_sort normalize v)
in
let is_local l = Level.Map.mem l !vars in
let varinfo x =
match Universe.level (Sorts.univ_of_sort x) with
| None -> Inl x
| Some l -> Inr l
in
let equalize_variables fo l l' r r' local =
(* Assumes l = [l',0] and r = [r',0] *)
let () =
if is_local l' then
instantiate_variable l' r vars
else if is_local r' then
instantiate_variable r' l vars
else if not (UGraph.check_eq_level univs l' r') then
(* Two rigid/global levels, none of them being local,
one of them being Prop/Set, disallow *)
if Level.is_small l' || Level.is_small r' then
sort_inconsistency Eq l r
else if fo then
raise UniversesDiffer
in
enforce_eq_level l' r' local
in
let equalize_universes l r local = match varinfo l, varinfo r with
| Inr l', Inr r' -> equalize_variables false l l' r r' local
| Inr l, Inl r | Inl r, Inr l ->
let alg = Level.Set.mem l uctx.univ_algebraic in
let ru = Sorts.univ_of_sort r in
let inst = univ_level_rem l ru ru in
if alg && not (Level.Set.mem l (Universe.levels inst)) then
(instantiate_variable l (Sorts.sort_of_univ inst) vars; local)
else
let lu = Universe.make l in
if univ_level_mem l ru then
enforce_leq inst lu local
else sort_inconsistency Eq (Sorts.sort_of_univ lu) r
| Inl _, Inl _ (* both are algebraic *) ->
if Sorts.check_eq_sort univs l r then local
else sort_inconsistency Eq l r
in
let unify_universes cst local =
let cst = nf_constraint cst in
if UnivProblem.is_trivial cst then local
else
match cst with
| ULe (l, r) ->
begin match Univ.Universe.level (Sorts.univ_of_sort r) with
| None ->
if Sorts.check_leq_sort univs l r then local
else user_err Pp.(str "Algebraic universe on the right")
| Some r' ->
if Level.is_small r' then
if not (Universe.is_levels (Sorts.univ_of_sort l))
then (* l contains a +1 and r=r' small so l <= r impossible *)
sort_inconsistency Le l r
else
if Sorts.check_leq_sort univs l r then match Univ.Universe.level (Sorts.univ_of_sort l) with
| Some l ->
Univ.Constraints.add (l, Le, r') local
| None -> local
else
let levels = Sorts.levels l in
let fold l' local =
let l = Sorts.sort_of_univ @@ Universe.make l' in
if Level.is_small l' || is_local l' then
equalize_variables false l l' r r' local
else sort_inconsistency Le l r
in
Level.Set.fold fold levels local
else
match Univ.Universe.level (Sorts.univ_of_sort l) with
| Some l ->
Univ.Constraints.add (l, Le, r') local
| None ->
(* We insert the constraint in the graph even if the graph
already contains it. Indeed, checking the existance of the
constraint is costly when the constraint does not already
exist directly as a single edge in the graph, but adding an
edge in the graph which is implied by others is cheap.
Hence, by doing this, we avoid a costly check here, and
make further checks of this constraint easier since it will
exist directly in the graph. *)
Sorts.enforce_leq_sort l r local
end
| ULub (l, r) ->
equalize_variables true (Sorts.sort_of_univ (Universe.make l)) l (Sorts.sort_of_univ (Universe.make r)) r local
| UWeak (l, r) ->
if not (drop_weak_constraints ()) then weak := UPairSet.add (l,r) !weak; local
| UEq (l, r) -> equalize_universes l r local
in
let unify_universes cst local =
if not (UGraph.type_in_type univs) then unify_universes cst local
else try unify_universes cst local with UniverseInconsistency _ -> local
in
let local =
UnivProblem.Set.fold unify_universes cstrs Constraints.empty
in
!vars, !weak, local
let add_constraints uctx cstrs =
let univs, old_cstrs = uctx.local in
let cstrs' = Constraints.fold (fun (l,d,r) acc ->
let l = Universe.make l and r = Sorts.sort_of_univ @@ Universe.make r in
let cstr' = let open UnivProblem in
match d with
| Lt ->
ULe (Sorts.sort_of_univ @@ Universe.super l, r)
| Le -> ULe (Sorts.sort_of_univ l, r)
| Eq -> UEq (Sorts.sort_of_univ l, r)
in UnivProblem.Set.add cstr' acc)
cstrs UnivProblem.Set.empty
in
let vars, weak, cstrs' = process_universe_constraints uctx cstrs' in
{ uctx with
local = (univs, Constraints.union old_cstrs cstrs');
univ_variables = vars;
universes = UGraph.merge_constraints cstrs' uctx.universes;
weak_constraints = weak; }
let add_universe_constraints uctx cstrs =
let univs, local = uctx.local in
let vars, weak, local' = process_universe_constraints uctx cstrs in
{ uctx with
local = (univs, Constraints.union local local');
univ_variables = vars;
universes = UGraph.merge_constraints local' uctx.universes;
weak_constraints = weak; }
let constrain_variables diff uctx =
let univs, local = uctx.local in
let univs, vars, local =
Level.Set.fold
(fun l (univs, vars, cstrs) ->
try
match Level.Map.find l vars with
| Some u ->
(Level.Set.add l univs,
Level.Map.remove l vars,
Constraints.add (l, Eq, Option.get (Universe.level u)) cstrs)
| None -> (univs, vars, cstrs)
with Not_found | Option.IsNone -> (univs, vars, cstrs))
diff (univs, uctx.univ_variables, local)
in
{ uctx with local = (univs, local); univ_variables = vars }
let id_of_level uctx l =
try Some (Option.get (Level.Map.find l (snd uctx.names)).uname)
with Not_found | Option.IsNone ->
None
let qualid_of_level uctx l =
let map, map_rev = uctx.names in
try Some (Libnames.qualid_of_ident (Option.get (Level.Map.find l map_rev).uname))
with Not_found | Option.IsNone ->
UnivNames.qualid_of_level map l
let pr_uctx_level uctx l =
match qualid_of_level uctx l with
| Some qid -> Libnames.pr_qualid qid
| None -> Level.pr l
type ('a, 'b) gen_universe_decl = {
univdecl_instance : 'a; (* Declared universes *)
univdecl_extensible_instance : bool; (* Can new universes be added *)
univdecl_constraints : 'b; (* Declared constraints *)
univdecl_extensible_constraints : bool (* Can new constraints be added *) }
type universe_decl =
(lident list, Constraints.t) gen_universe_decl
let default_univ_decl =
{ univdecl_instance = [];
univdecl_extensible_instance = true;
univdecl_constraints = Constraints.empty;
univdecl_extensible_constraints = true }
let pr_error_unbound_universes left uctx =
let open Pp in
let n = Level.Set.cardinal left in
let prlev u =
let info = Level.Map.find_opt u (snd uctx.names) in
h (pr_uctx_level uctx u ++ (match info with
| None | Some {uloc=None} -> mt ()
| Some {uloc=Some loc} -> spc() ++ str"(" ++ Loc.pr loc ++ str")"))
in
(hv 0
(str (CString.plural n "Universe") ++ spc () ++
(prlist_with_sep spc prlev (Level.Set.elements left)) ++
spc () ++ str (CString.conjugate_verb_to_be n) ++ str" unbound."))
exception UnboundUnivs of Level.Set.t * t
(* Deliberately using no location as the location of the univs
doesn't correspond to the failing command. *)
let error_unbound_universes left uctx = raise (UnboundUnivs (left,uctx))
let _ = CErrors.register_handler (function
| UnboundUnivs (left,uctx) -> Some (pr_error_unbound_universes left uctx)
| _ -> None)
let universe_context ~names ~extensible uctx =
let levels = ContextSet.levels uctx.local in
let newinst, left =
List.fold_right
(fun { CAst.loc; v = id } (newinst, acc) ->
let l =
try universe_of_name uctx id
with Not_found -> assert false
in (l :: newinst, Level.Set.remove l acc))
names ([], levels)
in
if not extensible && not (Level.Set.is_empty left)
then error_unbound_universes left uctx
else
let left = ContextSet.sort_levels (Array.of_list (Level.Set.elements left)) in
let inst = Array.append (Array.of_list newinst) left in
let inst = Instance.of_array inst in
(inst, ContextSet.constraints uctx.local)
let check_universe_context_set ~names ~extensible uctx =
if extensible then ()
else
let left = List.fold_left (fun left { CAst.loc; v = id } ->
let l =
try universe_of_name uctx id
with Not_found -> assert false
in Level.Set.remove l left)
(ContextSet.levels uctx.local) names
in
if not (Level.Set.is_empty left)
then error_unbound_universes left uctx
let check_implication uctx cstrs cstrs' =
let gr = initial_graph uctx in
let grext = UGraph.merge_constraints cstrs gr in
let cstrs' = Constraints.filter (fun c -> not (UGraph.check_constraint grext c)) cstrs' in
if Constraints.is_empty cstrs' then ()
else CErrors.user_err
Pp.(str "Universe constraints are not implied by the ones declared: " ++
pr_constraints (pr_uctx_level uctx) cstrs')
let check_mono_univ_decl uctx decl =
let () =
let names = decl.univdecl_instance in
let extensible = decl.univdecl_extensible_instance in
check_universe_context_set ~names ~extensible uctx
in
if not decl.univdecl_extensible_constraints then
check_implication uctx
decl.univdecl_constraints
(ContextSet.constraints uctx.local);
uctx.local
let check_univ_decl ~poly uctx decl =
if not decl.univdecl_extensible_constraints then
check_implication uctx
decl.univdecl_constraints
(ContextSet.constraints uctx.local);
let names = decl.univdecl_instance in
let extensible = decl.univdecl_extensible_instance in
let (binders, rbinders) = uctx.names in
if poly then
let inst, csts = universe_context ~names ~extensible uctx in
let nas = compute_instance_binders rbinders inst in
let uctx = UContext.make nas (inst, csts) in
Polymorphic_entry uctx, binders
else
let () = check_universe_context_set ~names ~extensible uctx in
Monomorphic_entry uctx.local, binders
let is_bound l lbound = match lbound with
| UGraph.Bound.Prop -> Level.is_prop l
| UGraph.Bound.Set -> Level.is_set l
let restrict_universe_context ~lbound (univs, csts) keep =
let removed = Level.Set.diff univs keep in
if Level.Set.is_empty removed then univs, csts
else
let allunivs = Constraints.fold (fun (u,_,v) all -> Level.Set.add u (Level.Set.add v all)) csts univs in
let g = UGraph.initial_universes in
let g = Level.Set.fold (fun v g -> if Level.is_small v then g else
UGraph.add_universe v ~lbound ~strict:false g) allunivs g in
let g = UGraph.merge_constraints csts g in
let allkept = Level.Set.union (UGraph.domain UGraph.initial_universes) (Level.Set.diff allunivs removed) in
let csts = UGraph.constraints_for ~kept:allkept g in
let csts = Constraints.filter (fun (l,d,r) ->
not ((is_bound l lbound && d == Le) || (Level.is_prop l && d == Lt && Level.is_set r))) csts in
(Level.Set.inter univs keep, csts)
let restrict uctx vars =
let vars = Level.Set.union vars uctx.seff_univs in
let vars = Names.Id.Map.fold (fun na l vars -> Level.Set.add l vars)
(fst uctx.names) vars
in
let uctx' = restrict_universe_context ~lbound:uctx.universes_lbound uctx.local vars in
{ uctx with local = uctx' }
type rigid =
| UnivRigid
| UnivFlexible of bool (** Is substitution by an algebraic ok? *)
let univ_rigid = UnivRigid
let univ_flexible = UnivFlexible false
let univ_flexible_alg = UnivFlexible true
(** ~sideff indicates that it is ok to redeclare a universe.
~extend also merges the universe context in the local constraint structures
and not only in the graph. This depends if the
context we merge comes from a side effect that is already inlined
or defined separately. In the later case, there is no extension,
see [emit_side_effects] for example. *)
let merge ?loc ~sideff rigid uctx uctx' =
let levels = ContextSet.levels uctx' in
let uctx =
match rigid with
| UnivRigid -> uctx
| UnivFlexible b ->
let fold u accu =
if Level.Map.mem u accu then accu
else Level.Map.add u None accu
in
let uvars' = Level.Set.fold fold levels uctx.univ_variables in
if b then
{ uctx with univ_variables = uvars';
univ_algebraic = Level.Set.union uctx.univ_algebraic levels }
else { uctx with univ_variables = uvars' }
in
let local = ContextSet.append uctx' uctx.local in
let declare g =
Level.Set.fold (fun u g ->
try UGraph.add_universe ~lbound:uctx.universes_lbound ~strict:false u g
with UGraph.AlreadyDeclared when sideff -> g)
levels g
in
let names =
let fold u accu =
let modify _ info = match info.uloc with
| None -> { info with uloc = loc }
| Some _ -> info
in
try Level.Map.modify u modify accu
with Not_found -> Level.Map.add u { uname = None; uloc = loc } accu
in
(fst uctx.names, Level.Set.fold fold levels (snd uctx.names))
in
let initial = declare uctx.initial_universes in
let univs = declare uctx.universes in
let universes = UGraph.merge_constraints (ContextSet.constraints uctx') univs in
{ uctx with names; local; universes;
initial_universes = initial }
let merge_subst uctx s =
{ uctx with univ_variables = Level.Map.subst_union uctx.univ_variables s }
let demote_seff_univs univs uctx =
let seff = Level.Set.union uctx.seff_univs univs in
{ uctx with seff_univs = seff }
let demote_global_univs env uctx =
let env_ugraph = Environ.universes env in
let global_univs = UGraph.domain env_ugraph in
let global_constraints, _ = UGraph.constraints_of_universes env_ugraph in
let promoted_uctx =
ContextSet.(of_set global_univs |> add_constraints global_constraints) in
{ uctx with local = ContextSet.diff uctx.local promoted_uctx }
let merge_seff uctx uctx' =
let levels = ContextSet.levels uctx' in
let declare g =
Level.Set.fold (fun u g ->
try UGraph.add_universe ~lbound:uctx.universes_lbound ~strict:false u g
with UGraph.AlreadyDeclared -> g)
levels g
in
let initial_universes = declare uctx.initial_universes in
let univs = declare uctx.universes in
let universes = UGraph.merge_constraints (ContextSet.constraints uctx') univs in
{ uctx with universes; initial_universes }
let emit_side_effects eff u =
let uctx = Safe_typing.universes_of_private eff in
let u = demote_seff_univs (fst uctx) u in
merge_seff u uctx
let update_sigma_univs uctx ugraph =
let univs = UGraph.set_cumulative_sprop (elaboration_sprop_cumul()) ugraph in
let eunivs =
{ uctx with
initial_universes = univs;
universes = univs }
in
merge_seff eunivs eunivs.local
let add_universe ?loc name strict lbound uctx u =
let initial_universes = UGraph.add_universe ~lbound ~strict u uctx.initial_universes in
let universes = UGraph.add_universe ~lbound ~strict u uctx.universes in
let local = ContextSet.add_universe u uctx.local in
let names =
match name with
| Some n -> add_names ?loc n u uctx.names
| None -> add_loc u loc uctx.names
in
{ uctx with names; local; initial_universes; universes }
let new_univ_variable ?loc rigid name uctx =
let u = UnivGen.fresh_level () in
let uctx =
match rigid with
| UnivRigid -> uctx
| UnivFlexible allow_alg ->
let univ_variables = Level.Map.add u None uctx.univ_variables in
if allow_alg
then
let univ_algebraic = Level.Set.add u uctx.univ_algebraic in
{ uctx with univ_variables; univ_algebraic }
else
{ uctx with univ_variables }
in
let uctx = add_universe ?loc name false uctx.universes_lbound uctx u in
uctx, u
let add_global_univ uctx u = add_universe None true UGraph.Bound.Set uctx u
let make_with_initial_binders ~lbound univs us =
let uctx = make ~lbound univs in
List.fold_left
(fun uctx { CAst.loc; v = id } ->
fst (new_univ_variable ?loc univ_rigid (Some id) uctx))
uctx us
let from_env ?(binders=[]) env =
make_with_initial_binders ~lbound:(Environ.universes_lbound env) (Environ.universes env) binders
let make_flexible_variable uctx ~algebraic u =
let {local = cstrs; univ_variables = uvars;
univ_algebraic = avars; universes=g; } = uctx in
assert (try Level.Map.find u uvars == None with Not_found -> true);
match UGraph.choose (fun v -> not (Level.equal u v) && (algebraic || not (Level.Set.mem v avars))) g u with
| Some v ->
let uvars' = Level.Map.add u (Some (Universe.make v)) uvars in
{ uctx with univ_variables = uvars'; }
| None ->
let uvars' = Level.Map.add u None uvars in
let avars' =
if algebraic then
let uu = Universe.make u in
let substu_not_alg u' v =
Option.cata (fun vu -> Universe.equal uu vu && not (Level.Set.mem u' avars)) false v
in
let has_upper_constraint () =
Constraints.exists
(fun (l,d,r) -> d == Lt && Level.equal l u)
(ContextSet.constraints cstrs)
in
if not (Level.Map.exists substu_not_alg uvars || has_upper_constraint ())
then Level.Set.add u avars else avars
else avars
in
{ uctx with univ_variables = uvars'; univ_algebraic = avars' }
let make_nonalgebraic_variable uctx u =
{ uctx with univ_algebraic = Level.Set.remove u uctx.univ_algebraic }
let make_flexible_nonalgebraic uctx =
{ uctx with univ_algebraic = Level.Set.empty }
let is_sort_variable uctx s =
match s with
| Sorts.Type u ->
(match universe_level u with
| Some l as x ->
if Level.Set.mem l (ContextSet.levels uctx.local) then x
else None
| None -> None)
| _ -> None
let subst_univs_context_with_def def usubst (uctx, cst) =
(Level.Set.diff uctx def, UnivSubst.subst_univs_constraints usubst cst)
let is_trivial_leq (l,d,r) =
Level.is_prop l && (d == Le || d == Lt) && 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 == Lt && not (Level.equal Level.set r) then
(Level.set, d, r)
else cstr
let refresh_constraints univs (ctx, cstrs) =
let cstrs', univs' =
Constraints.fold (fun c (cstrs', univs as acc) ->
let c = translate_cstr c in
if is_trivial_leq c then acc
else (Constraints.add c cstrs', UGraph.enforce_constraint c univs))
cstrs (Constraints.empty, univs)
in ((ctx, cstrs'), univs')
let normalize_variables uctx =
let normalized_variables, def, subst =
UnivSubst.normalize_univ_variables uctx.univ_variables
in
let uctx_local = subst_univs_context_with_def def (make_subst subst) uctx.local in
let uctx_local', univs = refresh_constraints uctx.initial_universes uctx_local in
{ uctx with
local = uctx_local';
univ_variables = normalized_variables;
universes = univs }
let abstract_undefined_variables uctx =
let vars' =
Level.Map.fold (fun u v acc ->
if v == None then Level.Set.remove u acc
else acc)
uctx.univ_variables uctx.univ_algebraic
in { uctx with local = ContextSet.empty;
univ_algebraic = vars' }
let fix_undefined_variables uctx =
let algs', vars' =
Level.Map.fold (fun u v (algs, vars as acc) ->
if v == None then (Level.Set.remove u algs, Level.Map.remove u vars)
else acc)
uctx.univ_variables
(uctx.univ_algebraic, uctx.univ_variables)
in
{ uctx with univ_variables = vars';
univ_algebraic = algs' }
let minimize uctx =
let open UnivMinim in
let lbound = uctx.universes_lbound in
let ((vars',algs'), us') =
normalize_context_set ~lbound uctx.universes uctx.local uctx.univ_variables
uctx.univ_algebraic uctx.weak_constraints
in
if ContextSet.equal us' uctx.local then uctx
else
let us', universes =
refresh_constraints uctx.initial_universes us'
in
{ names = uctx.names;
local = us';
seff_univs = uctx.seff_univs; (* not sure about this *)
univ_variables = vars';
univ_algebraic = algs';
universes = universes;
universes_lbound = lbound;
initial_universes = uctx.initial_universes;
weak_constraints = UPairSet.empty; (* weak constraints are consumed *) }
let pr_weak prl {weak_constraints=weak} =
let open Pp in
prlist_with_sep fnl (fun (u,v) -> prl u ++ str " ~ " ++ prl v) (UPairSet.elements weak)
let pr_universe_body = function
| None -> Pp.mt ()
| Some x -> Pp.(str " := " ++ Univ.Universe.pr x)
let pr_universe_opt_subst = Univ.Level.Map.pr pr_universe_body