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
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Util
open Names
open Constr
open Environ
open Univ
val set_minimization : bool ref
val is_set_minimization : unit -> bool
(** Universes *)
val pr_with_global_universes : Level.t -> Pp.t
val reference_of_level : Level.t -> Libnames.reference
(** Global universe information outside the kernel, to handle
polymorphic universes in sections that have to be discharged. *)
val add_global_universe : Level.t -> Decl_kinds.polymorphic -> unit
val is_polymorphic : Level.t -> bool
(** Local universe name <-> level mapping *)
type universe_binders = Univ.Level.t Names.Id.Map.t
val empty_binders : universe_binders
val register_universe_binders : Globnames.global_reference -> universe_binders -> unit
val universe_binders_of_global : Globnames.global_reference -> universe_binders
type univ_name_list = Misctypes.lname list
(** [universe_binders_with_opt_names ref u l]
If [l] is [Some univs] return the universe binders naming the levels of [u] by [univs] (skipping Anonymous).
May error if the lengths mismatch.
Otherwise return [universe_binders_of_global ref]. *)
val universe_binders_with_opt_names : Globnames.global_reference ->
Univ.Level.t list -> univ_name_list option -> universe_binders
(** The global universe counter *)
type universe_id = DirPath.t * int
val set_remote_new_univ_id : universe_id RemoteCounter.installer
(** Side-effecting functions creating new universe levels. *)
val new_univ_id : unit -> universe_id
val new_univ_level : unit -> Level.t
val new_univ : unit -> Universe.t
val new_Type : unit -> types
val new_Type_sort : unit -> Sorts.t
val new_global_univ : unit -> Universe.t in_universe_context_set
val new_sort_in_family : Sorts.family -> Sorts.t
(** {6 Constraints for type inference}
When doing conversion of universes, not only do we have =/<= constraints but
also Lub constraints which correspond to unification of two levels which might
not be necessary if unfolding is performed.
*)
type universe_constraint_type = ULe | UEq | ULub
type universe_constraint = Universe.t * universe_constraint_type * Universe.t
module Constraints : sig
include Set.S with type elt = universe_constraint
val pr : t -> Pp.t
end
type universe_constraints = Constraints.t
[@@ocaml.deprecated "Use Constraints.t"]
type 'a constraint_accumulator = Constraints.t -> 'a -> 'a option
type 'a universe_constrained = 'a * Constraints.t
type 'a universe_constraint_function = 'a -> 'a -> Constraints.t -> Constraints.t
val subst_univs_universe_constraints : universe_subst_fn ->
Constraints.t -> Constraints.t
val enforce_eq_instances_univs : bool -> Instance.t universe_constraint_function
val to_constraints : UGraph.t -> Constraints.t -> Constraint.t
(** [eq_constr_univs_infer_With kind1 kind2 univs m n] is a variant of
{!eq_constr_univs_infer} taking kind-of-term functions, to expose
subterms of [m] and [n], arguments. *)
val eq_constr_univs_infer_with :
(constr -> (constr, types, Sorts.t, Univ.Instance.t) kind_of_term) ->
(constr -> (constr, types, Sorts.t, Univ.Instance.t) kind_of_term) ->
UGraph.t -> 'a constraint_accumulator -> constr -> constr -> 'a -> 'a option
(** [eq_constr_universes a b] [true, c] if [a] equals [b] modulo alpha, casts,
application grouping and the universe constraints in [c]. *)
val eq_constr_universes_proj : env -> constr -> constr -> bool universe_constrained
(** Build a fresh instance for a given context, its associated substitution and
the instantiated constraints. *)
val fresh_instance_from_context : AUContext.t ->
Instance.t constrained
val fresh_instance_from : AUContext.t -> Instance.t option ->
Instance.t in_universe_context_set
val fresh_sort_in_family : env -> Sorts.family ->
Sorts.t in_universe_context_set
val fresh_constant_instance : env -> Constant.t ->
pconstant in_universe_context_set
val fresh_inductive_instance : env -> inductive ->
pinductive in_universe_context_set
val fresh_constructor_instance : env -> constructor ->
pconstructor in_universe_context_set
val fresh_global_instance : ?names:Univ.Instance.t -> env -> Globnames.global_reference ->
constr in_universe_context_set
val fresh_global_or_constr_instance : env -> Globnames.global_reference_or_constr ->
constr in_universe_context_set
(** Get fresh variables for the universe context.
Useful to make tactics that manipulate constrs in universe contexts polymorphic. *)
val fresh_universe_context_set_instance : ContextSet.t ->
universe_level_subst * ContextSet.t
(** Raises [Not_found] if not a global reference. *)
val global_of_constr : constr -> Globnames.global_reference puniverses
val constr_of_global_univ : Globnames.global_reference puniverses -> constr
val extend_context : 'a in_universe_context_set -> ContextSet.t ->
'a in_universe_context_set
(** Simplification and pruning of constraints:
[normalize_context_set ctx us]
- Instantiate the variables in [us] with their most precise
universe levels respecting the constraints.
- Normalizes the context [ctx] w.r.t. equality constraints,
choosing a canonical universe in each equivalence class
(a global one if there is one) and transitively saturate
the constraints w.r.t to the equalities. *)
module UF : Unionfind.PartitionSig with type elt = Level.t
val level_subst_of : universe_subst_fn -> universe_level_subst_fn
val subst_univs_constraints : universe_subst_fn -> Constraint.t -> Constraint.t
val subst_univs_constr : universe_subst -> constr -> constr
type universe_opt_subst = Universe.t option universe_map
val make_opt_subst : universe_opt_subst -> universe_subst_fn
val subst_opt_univs_constr : universe_opt_subst -> constr -> constr
val normalize_context_set : ContextSet.t ->
universe_opt_subst (* The defined and undefined variables *) ->
LSet.t (* univ variables that can be substituted by algebraics *) ->
(universe_opt_subst * LSet.t) in_universe_context_set
val normalize_univ_variables : universe_opt_subst ->
universe_opt_subst * LSet.t * LSet.t * universe_subst
val normalize_univ_variable :
find:(Level.t -> Universe.t) ->
update:(Level.t -> Universe.t -> Universe.t) ->
Level.t -> Universe.t
val normalize_univ_variable_opt_subst : universe_opt_subst ref ->
(Level.t -> Universe.t)
val normalize_univ_variable_subst : universe_subst ref ->
(Level.t -> Universe.t)
val normalize_universe_opt_subst : universe_opt_subst ref ->
(Universe.t -> Universe.t)
val normalize_universe_subst : universe_subst ref ->
(Universe.t -> Universe.t)
(** Create a fresh global in the global environment, without side effects.
BEWARE: this raises an ANOMALY on polymorphic constants/inductives:
the constraints should be properly added to an evd.
See Evd.fresh_global, Evarutil.new_global, and pf_constr_of_global for
the proper way to get a fresh copy of a global reference. *)
val constr_of_global : Globnames.global_reference -> constr
(** ** DEPRECATED ** synonym of [constr_of_global] *)
val constr_of_reference : Globnames.global_reference -> constr
[@@ocaml.deprecated "synonym of [constr_of_global]"]
(** Returns the type of the global reference, by creating a fresh instance of polymorphic
references and computing their instantiated universe context. (side-effect on the
universe counter, use with care). *)
val type_of_global : Globnames.global_reference -> types in_universe_context_set
(** Full universes substitutions into terms *)
val nf_evars_and_universes_opt_subst : (existential -> constr option) ->
universe_opt_subst -> constr -> constr
val refresh_constraints : UGraph.t -> ContextSet.t -> ContextSet.t * UGraph.t
(** Pretty-printing *)
val pr_universe_opt_subst : universe_opt_subst -> Pp.t
(** {6 Support for template polymorphism } *)
val solve_constraints_system : Universe.t option array -> Universe.t array -> Universe.t array ->
Universe.t array
|
