Source file uState.ml
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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;
}
type quality = QVar of Sorts.QVar.t | QProp | QSProp | QType
let sort_inconsistency ?explain cst l r =
let explain = Option.map (fun p -> UGraph.Other p) explain in
raise (UGraph.UniverseInconsistency (cst, l, r, explain))
let pr_quality = function
| QVar v -> Sorts.QVar.pr v
| QProp -> Pp.str "Prop"
| QSProp -> Pp.str "SProp"
| QType -> Pp.str "Type"
module QState : sig
type t
type elt = Sorts.QVar.t
val empty : t
val union : fail:(t -> quality -> quality -> t) -> t -> t -> t
val add : elt -> t -> t
val repr : elt -> t -> quality
val unify_quality : fail:(unit -> t) -> Conversion.conv_pb -> quality -> quality -> t -> t
val is_above_prop : elt -> t -> bool
val collapse : t -> t
val pr : t -> Pp.t
end =
struct
module QSet = Set.Make(Sorts.QVar)
module QMap = Map.Make(Sorts.QVar)
type t = {
qmap : quality option QMap.t;
above : QSet.t;
(** Set of quality variables known to be either in Prop or Type.
If q ∈ above then it must map to None in qmap. *)
}
type elt = Sorts.QVar.t
let empty = { qmap = QMap.empty; above = QSet.empty }
let quality_eq a b = match a, b with
| QProp, QProp | QSProp, QSProp | QType, QType -> true
| QVar q1, QVar q2 -> Sorts.QVar.equal q1 q2
| (QVar _ | QProp | QSProp | QType), _ -> false
let rec repr q m = match QMap.find q m.qmap with
| None -> QVar q
| Some (QVar q) -> repr q m
| Some (QProp | QSProp | QType as q) -> q
| exception Not_found ->
QVar q
let is_above_prop q m = QSet.mem q m.above
let set q qv m =
let q = repr q m in
let q = match q with QVar q -> q | QProp | QSProp | QType -> assert false in
let qv = match qv with QVar qv -> repr qv m | (QSProp | QProp | QType as qv) -> qv in
match q, qv with
| q, QVar qv ->
if Sorts.QVar.equal q qv then Some m
else
let above =
if QSet.mem q m.above then QSet.add qv (QSet.remove q m.above)
else m.above
in
Some { qmap = QMap.add q (Some (QVar qv)) m.qmap; above }
| q, (QProp | QSProp | QType as qv) ->
if qv == QSProp && QSet.mem q m.above then None
else Some { qmap = QMap.add q (Some qv) m.qmap; above = QSet.remove q m.above }
let set_above_prop q m =
let q = repr q m in
let q = match q with QVar q -> q | QProp | QSProp | QType -> assert false in
{ qmap = m.qmap; above = QSet.add q m.above }
let unify_quality ~fail c q1 q2 local = match q1, q2 with
| QType, QType | QProp, QProp | QSProp, QSProp -> local
| QProp, QVar q when c == Conversion.CUMUL ->
set_above_prop q local
| QVar q, (QType | QProp | QSProp | QVar _ as qv)
| (QType | QProp | QSProp as qv), QVar q ->
begin match set q qv local with
| Some local -> local
| None -> fail ()
end
| (QType, (QProp | QSProp)) -> fail ()
| (QProp, QType) ->
begin match c with
| CONV -> fail ()
| CUMUL -> local
end
| (QSProp, (QType | QProp)) -> fail ()
| (QProp, QSProp) -> fail ()
let nf_quality m = function
| QSProp | QProp | QType as q -> q
| QVar q -> repr q m
let union ~fail s1 s2 =
let = ref [] in
let qmap = QMap.union (fun qk q1 q2 ->
match q1, q2 with
| Some q, None | None, Some q -> Some (Some q)
| None, None -> Some None
| Some q1, Some q2 ->
let () = if not (quality_eq q1 q2) then extra := (q1,q2) :: !extra in
Some (Some q1))
s1.qmap s2.qmap
in
let = !extra in
let filter q = match QMap.find q qmap with
| None -> true
| Some _ -> false
| exception Not_found -> false
in
let above = QSet.filter filter @@ QSet.union s1.above s2.above in
let s = { qmap; above } in
List.fold_left (fun s (q1,q2) ->
let q1 = nf_quality s q1 and q2 = nf_quality s q2 in
unify_quality ~fail:(fun () -> fail s q1 q2) CONV q1 q2 s)
s
extra
let add q m = { qmap = QMap.add q None m.qmap; above = m.above }
let collapse m =
let map q v = match v with
| None -> Some QType
| Some _ -> v
in
{ qmap = QMap.mapi map m.qmap; above = QSet.empty }
let pr { qmap; above } =
let open Pp in
let prbody u = function
| None ->
if QSet.mem u above then str " >= Prop"
else mt ()
| Some q ->
let q = pr_quality q in
str " := " ++ q
in
h (prlist_with_sep fnl (fun (u, v) -> Sorts.QVar.pr u ++ prbody u v) (QMap.bindings qmap))
end
module UPairSet = UnivMinim.UPairSet
type univ_names = UnivNames.universe_binders * uinfo Level.Map.t
type t =
{ names : univ_names; (** 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. *)
sort_variables : QState.t;
(** Local quality variables. *)
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 *)
minim_extra : UnivMinim.extra;
}
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;
sort_variables = QState.empty;
universes = UGraph.initial_universes;
universes_lbound = UGraph.Bound.Set;
initial_universes = UGraph.initial_universes;
minim_extra = UnivMinim.empty_extra; }
let make ~lbound univs =
{ 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 = UnivMinim.extra_union uctx.minim_extra uctx'.minim_extra in
let declarenew g =
Level.Set.fold (fun u g -> UGraph.add_universe u ~lbound:uctx.universes_lbound ~strict:false g) newus g
in
let fail_union s q1 q2 =
if UGraph.type_in_type uctx.universes then s
else CErrors.user_err
Pp.(str "Could not merge universe contexts: could not unify" ++ spc() ++
pr_quality q1 ++ strbrk " and " ++ pr_quality q2 ++ str ".")
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;
sort_variables = QState.union ~fail:fail_union uctx.sort_variables uctx'.sort_variables;
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;
minim_extra = extra}
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 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_names (ubind,revubind) =
let revubind = Level.Map.map (fun id -> { uname = Some id; uloc = None }) revubind in
{empty with names = (ubind,revubind)}
let universe_of_name uctx s =
UNameMap.find s (fst uctx.names)
let name_level level id uctx =
assert(not(Names.Id.Map.mem id (fst uctx.names)));
{ uctx with names = (Names.Id.Map.add id level (fst uctx.names), Univ.Level.Map.add level { uname = Some id; uloc = None } (snd uctx.names)) }
let universe_binders uctx =
let named, _ = uctx.names in
named
let nf_qvar uctx q = QState.repr q uctx.sort_variables
let instantiate_variable l (b : Universe.t) v =
try v := Level.Map.set l (Some b) !v
with Not_found -> assert false
exception UniversesDiffer
let { Goptions.get = drop_weak_constraints } =
Goptions.declare_bool_option_and_ref
~key:["Cumulativity";"Weak";"Constraints"]
~value:false
()
let level_inconsistency cst l r =
let mk u = Sorts.sort_of_univ @@ Universe.make u in
raise (UGraph.UniverseInconsistency (cst, mk l, mk r, None))
let subst_univs_sort normalize qnormalize s = match s with
| Sorts.Set | Sorts.Prop | Sorts.SProp -> s
| Sorts.Type u -> Sorts.sort_of_univ (UnivSubst.subst_univs_universe normalize u)
| Sorts.QSort (q, u) ->
match qnormalize q with
| QSProp -> Sorts.sprop
| QProp -> Sorts.prop
| QType -> Sorts.sort_of_univ (UnivSubst.subst_univs_universe normalize u)
| QVar q -> Sorts.qsort q (UnivSubst.subst_univs_universe normalize u)
let nf_sort uctx s =
let normalize u = UnivSubst.normalize_univ_variable_opt_subst uctx.univ_variables u in
let qnormalize q = QState.repr q uctx.sort_variables in
subst_univs_sort normalize qnormalize s
let nf_relevance uctx r = match r with
| Sorts.Relevant | Sorts.Irrelevant -> r
| Sorts.RelevanceVar q ->
match nf_qvar uctx q with
| QSProp -> Sorts.Irrelevant
| QProp | QType -> Sorts.Relevant
| QVar q' ->
if QState.is_above_prop q' uctx.sort_variables then Relevant
else if Sorts.QVar.equal q q' then r
else Sorts.RelevanceVar q'
let nf_universes uctx c =
let lsubst = uctx.univ_variables in
let level_value l =
UnivSubst.level_subst_of (fun l -> UnivSubst.normalize_univ_variable_opt_subst lsubst l) l
in
let sort_value s = nf_sort uctx s in
let rel_value r = nf_relevance uctx r in
UnivSubst.nf_evars_and_universes_opt_subst (fun _ -> None) level_value sort_value rel_value c
type small_universe = USet | UProp | USProp
let is_uset = function USet -> true | UProp | USProp -> false
type sort_classification =
| USmall of small_universe
| ULevel of Level.t
| UMax of Universe.t * Level.Set.t
| UAlgebraic of Universe.t
let classify s = match s with
| Sorts.Prop -> USmall UProp
| Sorts.SProp -> USmall USProp
| Sorts.Set -> USmall USet
| Sorts.Type u | Sorts.QSort (_, u) ->
if Universe.is_levels u then match Universe.level u with
| None -> UMax (u, Universe.levels u)
| Some u -> ULevel u
else UAlgebraic u
type local = {
local_cst : Constraints.t;
local_above_prop : Level.Set.t;
local_weak : UPairSet.t;
local_sorts : QState.t;
}
let add_local cst local =
{ local with local_cst = Constraints.add cst local.local_cst }
let enforce_leq_up u v local =
{ local with local_cst = UnivSubst.enforce_leq u (Universe.make v) local.local_cst }
let quality_of_sort = function
| Sorts.Set | Sorts.Type _ -> QType
| Sorts.Prop -> QProp
| Sorts.SProp -> QSProp
| Sorts.QSort (q, _) -> QVar q
let get_constraint = function
| Conversion.CONV -> Eq
| Conversion.CUMUL -> Le
let unify_quality univs c s1 s2 l =
let fail () = if UGraph.type_in_type univs then l.local_sorts
else sort_inconsistency (get_constraint c) s1 s2
in
{ l with
local_sorts = QState.unify_quality ~fail
c (quality_of_sort s1) (quality_of_sort s2) l.local_sorts;
}
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 normalize u = normalize_univ_variable_opt_subst !vars u in
let normalize_sort sorts s =
let qnormalize q = QState.repr q sorts in
subst_univs_sort normalize qnormalize s
in
let nf_constraint sorts = 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 (normalize_sort sorts u, normalize_sort sorts v)
| ULe (u, v) -> ULe (normalize_sort sorts u, normalize_sort sorts v)
in
let is_local l = Level.Map.mem l !vars in
let equalize_small l s local =
let ls = match l with
| USProp -> Sorts.sprop
| UProp -> Sorts.prop
| USet -> Sorts.set
in
if UGraph.check_eq_sort univs ls s then local
else if is_uset l then match classify s with
| USmall _ -> sort_inconsistency Eq Sorts.set s
| ULevel r ->
if is_local r then
let () = instantiate_variable r Universe.type0 vars in
add_local (Level.set, Eq, r) local
else
sort_inconsistency Eq Sorts.set s
| UMax (u, _)| UAlgebraic u ->
if univ_level_mem Level.set u then
let inst = univ_level_rem Level.set u u in
enforce_leq_up inst Level.set local
else
sort_inconsistency Eq ls s
else sort_inconsistency Eq ls s
in
let equalize_variables fo l' r' local =
if Level.equal l' r' then local
else
let () =
if is_local l' then
instantiate_variable l' (Universe.make r') vars
else if is_local r' then
instantiate_variable r' (Universe.make l') vars
else if not (UnivProblem.check_eq_level univs l' r') then
if Level.is_set l' || Level.is_set r' then
level_inconsistency Eq l' r'
else if fo then
raise UniversesDiffer
in
add_local (l', Eq, r') local
in
let equalize_algebraic l ru local =
let alg = Level.Set.mem l uctx.univ_algebraic in
let inst = univ_level_rem l ru ru in
if alg && not (Level.Set.mem l (Universe.levels inst)) then
let () = instantiate_variable l inst vars in
local
else
if univ_level_mem l ru then
enforce_leq_up inst l local
else sort_inconsistency Eq (Sorts.sort_of_univ (Universe.make l)) (Sorts.sort_of_univ ru)
in
let equalize_universes l r local = match classify l, classify r with
| USmall l', (USmall _ | ULevel _ | UMax _ | UAlgebraic _) ->
equalize_small l' r local
| (ULevel _ | UMax _ | UAlgebraic _), USmall r' ->
equalize_small r' l local
| ULevel l', ULevel r' ->
equalize_variables false l' r' local
| ULevel l', (UAlgebraic r | UMax (r, _)) | (UAlgebraic r | UMax (r, _)), ULevel l' ->
equalize_algebraic l' r local
| (UAlgebraic _ | UMax _), (UAlgebraic _ | UMax _) ->
if UGraph.check_eq_sort univs l r then local
else sort_inconsistency Eq l r
in
let unify_universes cst local =
let cst = nf_constraint local.local_sorts cst in
if UnivProblem.is_trivial cst then local
else match cst with
| ULe (l, r) ->
let local = unify_quality univs CUMUL l r local in
let l = normalize_sort local.local_sorts l in
let r = normalize_sort local.local_sorts r in
begin match classify r with
| UAlgebraic _ | UMax _ ->
if UGraph.check_leq_sort univs l r then local
else
sort_inconsistency Le l r
~explain:(Pp.str "(cannot handle algebraic on the right)")
| USmall r' ->
if UGraph.type_in_type univs then local
else begin match classify l with
| UAlgebraic _ ->
sort_inconsistency Le l r
| USmall l' ->
if UGraph.check_leq_sort univs l r then local
else sort_inconsistency Le l r
| ULevel l' ->
if is_uset r' && is_local l' then
let () = instantiate_variable l' Universe.type0 vars in
add_local (l', Eq, Level.set) local
else
sort_inconsistency Le l r
| UMax (_, levels) ->
if is_uset r' then
let fold l' local =
let l = Sorts.sort_of_univ @@ Universe.make l' in
if Level.is_set l' || is_local l' then
equalize_variables false l' Level.set local
else sort_inconsistency Le l r
in
Level.Set.fold fold levels local
else
sort_inconsistency Le l r
end
| ULevel r' ->
match classify l with
| USmall UProp ->
{ local with local_above_prop = Level.Set.add r' local.local_above_prop }
| USmall USProp ->
if UGraph.type_in_type univs then local
else sort_inconsistency Le l r
| USmall USet ->
add_local (Level.set, Le, r') local
| ULevel l' ->
add_local (l', Le, r') local
| UAlgebraic l ->
enforce_leq_up l r' local
| UMax (_, l) ->
Univ.Level.Set.fold (fun l' accu -> add_local (l', Le, r') accu) l local
end
| ULub (l, r) ->
equalize_variables true l r local
| UWeak (l, r) ->
if not (drop_weak_constraints ())
then { local with local_weak = UPairSet.add (l, r) local.local_weak }
else local
| UEq (l, r) ->
let local = unify_quality univs CONV l r local in
let l = normalize_sort local.local_sorts l in
let r = normalize_sort local.local_sorts r in
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 UGraph.UniverseInconsistency _ -> local
in
let local = {
local_cst = Constraints.empty;
local_weak = uctx.minim_extra.UnivMinim.weak_constraints;
local_above_prop = uctx.minim_extra.UnivMinim.above_prop;
local_sorts = uctx.sort_variables;
} in
let local = UnivProblem.Set.fold unify_universes cstrs local in
let = { UnivMinim.above_prop = local.local_above_prop; UnivMinim.weak_constraints = local.local_weak } in
!vars, extra, local.local_cst, local.local_sorts
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, , cstrs', sorts = 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;
sort_variables = sorts;
minim_extra = extra; }
let add_universe_constraints uctx cstrs =
let univs, local = uctx.local in
let vars, , local', sorts = process_universe_constraints uctx cstrs in
{ uctx with
local = (univs, Constraints.union local local');
univ_variables = vars;
universes = UGraph.merge_constraints local' uctx.universes;
sort_variables = sorts;
minim_extra = extra; }
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_names (map, map_rev) l =
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 qualid_of_level uctx l = qualid_of_level_names uctx.names l
let pr_uctx_level_names names l =
match qualid_of_level_names names l with
| Some qid -> Libnames.pr_qualid qid
| None -> Level.raw_pr l
let pr_uctx_level uctx l = pr_uctx_level_names uctx.names l
type ('a, 'b) gen_universe_decl = {
univdecl_instance : 'a;
univdecl_extensible_instance : bool;
univdecl_constraints : 'b;
univdecl_extensible_constraints : bool }
type universe_decl =
(Level.t 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 names =
let open Pp in
let n = Level.Set.cardinal left in
let prlev u =
let info = Level.Map.find_opt u (snd names) in
h (pr_uctx_level_names names 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 * univ_names
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_inst ~prefix ~extensible levels names =
let left = List.fold_left (fun acc l -> Level.Set.remove l acc) levels prefix in
if not extensible && not (Level.Set.is_empty left)
then error_unbound_universes left names
else
let left = ContextSet.sort_levels (Array.of_list (Level.Set.elements left)) in
let inst = Array.append (Array.of_list prefix) left in
let inst = Instance.of_array inst in
inst
let check_universe_context_set ~prefix levels names =
let left =
List.fold_left (fun left l -> Level.Set.remove l left)
levels prefix
in
if not (Level.Set.is_empty left)
then error_unbound_universes left names
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 levels, csts = uctx.local in
let () =
let prefix = decl.univdecl_instance in
if not decl.univdecl_extensible_instance
then check_universe_context_set ~prefix levels uctx.names
in
if decl.univdecl_extensible_constraints then uctx.local
else begin
check_implication uctx
decl.univdecl_constraints
csts;
levels, decl.univdecl_constraints
end
let check_poly_univ_decl uctx decl =
let prefix = decl.univdecl_instance in
let extensible = decl.univdecl_extensible_instance in
let levels, csts = uctx.local in
let inst = universe_context_inst ~prefix ~extensible levels uctx.names in
let nas = compute_instance_binders (snd uctx.names) inst in
let csts = if decl.univdecl_extensible_constraints then csts
else begin
check_implication uctx
decl.univdecl_constraints
csts;
decl.univdecl_constraints
end
in
let uctx = UContext.make nas (inst, csts) in
uctx
let check_univ_decl ~poly uctx decl =
let entry =
if not poly then
let ctx = check_mono_univ_decl uctx decl in
Monomorphic_entry ctx
else
let ctx = check_poly_univ_decl uctx decl in
Polymorphic_entry ctx
in
entry, fst uctx.names
let is_bound l lbound = match lbound with
| UGraph.Bound.Prop -> false
| 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_set 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)) 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' }
let restrict_even_binders uctx vars =
let vars = Level.Set.union vars uctx.seff_univs 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 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 univs =
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_sort_variable uctx =
let q = UnivGen.new_sort_global () in
let sort_variables = QState.add q uctx.sort_variables in
{ uctx with sort_variables }, q
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)
| Sorts.QSort (q, u) ->
let q = nf_qvar uctx q in
(match q, Universe.level u with
| QType, Some l ->
if Level.Set.mem l (ContextSet.levels uctx.local) then Some l
else None
| (_, Some _ | _, 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 refresh_constraints univs (ctx, cstrs) =
let cstrs', univs' =
Constraints.fold (fun c (cstrs', univs) ->
(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 make_subst subst l = Level.Map.find_opt l subst 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 collapse_sort_variables uctx =
{ uctx with sort_variables = QState.collapse uctx.sort_variables }
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.minim_extra
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;
univ_variables = vars';
univ_algebraic = algs';
sort_variables = uctx.sort_variables;
universes = universes;
universes_lbound = lbound;
initial_universes = uctx.initial_universes;
minim_extra = UnivMinim.empty_extra; }
let pr_weak prl {minim_extra={UnivMinim.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 prl = function
| None -> Pp.mt ()
| Some x -> Pp.(str " := " ++ Univ.Universe.pr prl x)
let pr_universe_opt_subst prl = Univ.Level.Map.pr prl (pr_universe_body prl)
let pr_sort_opt_subst uctx = QState.pr uctx.sort_variables
module Internal =
struct
let reboot env uctx =
let uctx_global = from_env env in
{ uctx_global with univ_variables = uctx.univ_variables; sort_variables = uctx.sort_variables }
end