1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2019       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Univ

module G = AcyclicGraph.Make(struct
    type t = Level.t
    module Set = LSet
    module Map = LMap
    module Constraint = Constraint

    let equal = Level.equal
    let compare = Level.compare

    type explanation = Univ.explanation
    let error_inconsistency d u v p =
      raise (UniverseInconsistency (d,Universe.make u, Universe.make v, p))

    let pr = Level.pr
  end) [@@inlined] (* without inline, +1% ish on HoTT, compcert. See jenkins 594 vs 596 *)
(* Do not include G to make it easier to control universe specific
   code (eg add_universe with a constraint vs G.add with no
   constraint) *)

type t = { graph: G.t; sprop_cumulative : bool }
type 'a check_function = t -> 'a -> 'a -> bool

let g_map f g =
  let g' = f g.graph in
  if g.graph == g' then g
  else {g with graph=g'}

let make_sprop_cumulative g = {g with sprop_cumulative=true}

let check_smaller_expr g (u,n) (v,m) =
  let diff = n - m in
    match diff with
    | 0 -> G.check_leq g.graph u v
    | 1 -> G.check_lt g.graph u v
    | x when x < 0 -> G.check_leq g.graph u v
    | _ -> false

let exists_bigger g ul l =
  Universe.exists (fun ul' ->
    check_smaller_expr g ul ul') l

let real_check_leq g u v =
  Universe.for_all (fun ul -> exists_bigger g ul v) u

let check_leq g u v =
  Universe.equal u v || (g.sprop_cumulative && Universe.is_sprop u) ||
  (not (Universe.is_sprop u) && not (Universe.is_sprop v) &&
    (is_type0m_univ u ||
     real_check_leq g u v))

let check_eq g u v =
  Universe.equal u v ||
  (not (Universe.is_sprop u || Universe.is_sprop v) &&
   (real_check_leq g u v && real_check_leq g v u))

let check_eq_level g u v =
  u == v ||
  (not (Level.is_sprop u || Level.is_sprop v) && G.check_eq g.graph u v)

let empty_universes = {graph=G.empty; sprop_cumulative=false}

let initial_universes =
  let big_rank = 1000000 in
  let g = G.empty in
  let g = G.add ~rank:big_rank Level.prop g in
  let g = G.add ~rank:big_rank Level.set g in
  {graph=G.enforce_lt Level.prop Level.set g; sprop_cumulative=false}

let enforce_constraint (u,d,v) g =
  match d with
  | Le -> G.enforce_leq u v g
  | Lt -> G.enforce_lt u v g
  | Eq -> G.enforce_eq u v g

let enforce_constraint (u,d,v as cst) g =
  match Level.is_sprop u, d, Level.is_sprop v with
  | false, _, false -> g_map (enforce_constraint cst) g
  | true, (Eq|Le), true -> g
  | true, Le, false when g.sprop_cumulative -> g
  | _ ->  raise (UniverseInconsistency (d,Universe.make u, Universe.make v, None))

let merge_constraints csts g = Constraint.fold enforce_constraint csts g

let check_constraint g (u,d,v) =
  match d with
  | Le -> G.check_leq g u v
  | Lt -> G.check_lt g u v
  | Eq -> G.check_eq g u v

let check_constraint g (u,d,v as cst) =
  match Level.is_sprop u, d, Level.is_sprop v with
  | false, _, false -> check_constraint g.graph cst
  | true, (Eq|Le), true -> true
  | true, Le, false -> g.sprop_cumulative
  | _ -> false

let check_constraints csts g = Constraint.for_all (check_constraint g) csts

let leq_expr (u,m) (v,n) =
  let d = match m - n with
    | 1 -> Lt
    | diff -> assert (diff <= 0); Le
  in
  (u,d,v)

let enforce_leq_alg u v g =
  let open Util in
  let enforce_one (u,v) = function
    | Inr _ as orig -> orig
    | Inl (cstrs,g) as orig ->
      if check_smaller_expr g u v then orig
      else
        (let c = leq_expr u v in
         match enforce_constraint c g with
         | g -> Inl (Constraint.add c cstrs,g)
         | exception (UniverseInconsistency _ as e) -> Inr e)
  in
  (* max(us) <= max(vs) <-> forall u in us, exists v in vs, u <= v *)
  let c = Universe.map (fun u -> Universe.map (fun v -> (u,v)) v) u in
  let c = List.cartesians enforce_one (Inl (Constraint.empty,g)) c in
  (* We pick a best constraint: smallest number of constraints, not an error if possible. *)
  let order x y = match x, y with
    | Inr _, Inr _ -> 0
    | Inl _, Inr _ -> -1
    | Inr _, Inl _ -> 1
    | Inl (c,_), Inl (c',_) ->
      Int.compare (Constraint.cardinal c) (Constraint.cardinal c')
  in
  match List.min order c with
  | Inl x -> x
  | Inr e -> raise e

(* sanity check wrapper *)
let enforce_leq_alg u v g =
  let _,g as cg = enforce_leq_alg u v g in
  assert (check_leq g u v);
  cg

exception AlreadyDeclared = G.AlreadyDeclared
let add_universe u ~lbound ~strict g =
  let graph = G.add u g.graph in
  let d = if strict then Lt else Le in
  enforce_constraint (lbound,d,u) {g with graph}

let add_universe_unconstrained u g = {g with graph=G.add u g.graph}

exception UndeclaredLevel = G.Undeclared
let check_declared_universes g l = G.check_declared g.graph (LSet.remove Level.sprop l)

let constraints_of_universes g = G.constraints_of g.graph
let constraints_for ~kept g = G.constraints_for ~kept:(LSet.remove Level.sprop kept) g.graph

(** Subtyping of polymorphic contexts *)

let check_subtype ~lbound univs ctxT ctx =
  if AUContext.size ctxT == AUContext.size ctx then
    let (inst, cst) = UContext.dest (AUContext.repr ctx) in
    let cstT = UContext.constraints (AUContext.repr ctxT) in
    let push accu v = add_universe v ~lbound ~strict:false accu in
    let univs = Array.fold_left push univs (Instance.to_array inst) in
    let univs = merge_constraints cstT univs in
    check_constraints cst univs
  else false

(** Instances *)

let check_eq_instances g t1 t2 =
  let t1 = Instance.to_array t1 in
  let t2 = Instance.to_array t2 in
  t1 == t2 ||
    (Int.equal (Array.length t1) (Array.length t2) &&
        let rec aux i =
          (Int.equal i (Array.length t1)) || (check_eq_level g t1.(i) t2.(i) && aux (i + 1))
        in aux 0)

let domain g = LSet.add Level.sprop (G.domain g.graph)
let choose p g u = if Level.is_sprop u
  then if p u then Some u else None
  else G.choose p g.graph u

let dump_universes f g = G.dump f g.graph

let check_universes_invariants g = G.check_invariants ~required_canonical:Level.is_small g.graph

let pr_universes prl g = G.pr prl g.graph

let dummy_mp = Names.DirPath.make [Names.Id.of_string "Type"]
let make_dummy i = Level.(make (UGlobal.make dummy_mp i))
let sort_universes g = g_map (G.sort make_dummy [Level.prop;Level.set]) g

(** Profiling *)

let merge_constraints =
  if Flags.profile then
    let key = CProfile.declare_profile "merge_constraints" in
      CProfile.profile2 key merge_constraints
  else merge_constraints
let check_constraints =
  if Flags.profile then
    let key = CProfile.declare_profile "check_constraints" in
      CProfile.profile2 key check_constraints
  else check_constraints

let check_eq =
  if Flags.profile then
    let check_eq_key = CProfile.declare_profile "check_eq" in
      CProfile.profile3 check_eq_key check_eq
  else check_eq

let check_leq =
  if Flags.profile then
    let check_leq_key = CProfile.declare_profile "check_leq" in
      CProfile.profile3 check_leq_key check_leq
  else check_leq