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
|
(************************************************************************)
(* * 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 EConstr
open Evd
open Environ
type alias
val of_alias : alias -> EConstr.t
module AllowedEvars : sig
type t
(** Represents the set of evars that can be defined by the pretyper *)
val all : t
(** All evars can be defined *)
val mem : t -> Evar.t -> bool
(** [mem allowed evk] is true iff evk can be defined *)
val from_pred : (Evar.t -> bool) -> t
(** [from_pred p] means evars satisfying p can be defined *)
val except : Evar.Set.t -> t
(** [except evars] means all evars can be defined except the ones in [evars] *)
val remove : Evar.t -> t -> t
(** [remove evk allowed] removes [evk] from the set of evars allowed by [allowed] *)
end
type unify_flags = {
modulo_betaiota : bool;
(* Enable beta-iota reductions during unification *)
open_ts : TransparentState.t;
(* Enable delta reduction according to open_ts for open terms *)
closed_ts : TransparentState.t;
(* Enable delta reduction according to closed_ts for closed terms (when calling conversion) *)
subterm_ts : TransparentState.t;
(* Enable delta reduction according to subterm_ts for selection of subterms during higher-order
unifications. *)
allowed_evars : AllowedEvars.t;
(* Disallowed evars are treated like rigid variables during unification: they can not be instantiated. *)
allow_K_at_toplevel : bool;
(* During higher-order unifications, allow to produce K-redexes: i.e. to produce
an abstraction for an unused argument *)
with_cs : bool
(* Enable canonical structure resolution during unification *)
}
type unification_result =
| Success of evar_map
| UnifFailure of evar_map * Pretype_errors.unification_error
val is_success : unification_result -> bool
val is_evar_allowed : unify_flags -> Evar.t -> bool
(** Replace the vars and rels that are aliases to other vars and rels by
their representative that is most ancient in the context *)
val expand_vars_in_term : env -> evar_map -> constr -> constr
(** One might want to use different conversion strategies for types and terms:
e.g. preventing delta reductions when doing term unifications but allowing
arbitrary delta conversion when checking the types of evar instances. *)
type unification_kind =
| TypeUnification
| TermUnification
(** A unification function parameterized by:
- unification flags
- the kind of unification
- environment
- sigma
- conversion problem
- the two terms to unify. *)
type unifier = unify_flags -> unification_kind ->
env -> evar_map -> conv_pb -> constr -> constr -> unification_result
(** A conversion function: parameterized by the kind of unification,
environment, sigma, conversion problem and the two terms to convert.
Conversion is not allowed to instantiate evars contrary to unification. *)
type conversion_check = unify_flags -> unification_kind ->
env -> evar_map -> conv_pb -> constr -> constr -> bool
(** [instantiate_evar unify flags env sigma ev c] defines the evar [ev] with [c],
checking that the type of [c] is unifiable with [ev]'s declared type first.
Preconditions:
- [ev] does not occur in [c].
- [c] does not contain any Meta(_)
If [ev] and [c] have non inferably convertible types, an exception
[IllTypedInstance] is raised *)
val instantiate_evar : unifier -> unify_flags -> env -> evar_map ->
Evar.t -> constr -> evar_map
(** [evar_define choose env ev c] try to instantiate [ev] with [c] (typed in [env]),
possibly solving related unification problems, possibly leaving open
some problems that cannot be solved in a unique way (except if choose is
true); fails if the instance is not valid for the given [ev];
If [ev] and [c] have non inferably convertible types, an exception
[IllTypedInstance] is raised *)
val evar_define : unifier -> unify_flags -> ?choose:bool -> ?imitate_defs:bool ->
env -> evar_map -> bool option -> existential -> constr -> evar_map
val refresh_universes :
?status:Evd.rigid ->
?onlyalg:bool (* Only algebraic universes *) ->
?refreshset:bool ->
(* Also refresh Prop and Set universes, so that the returned type can be any supertype
of the original type *)
bool option (* direction: true for levels lower than the existing levels *) ->
env -> evar_map -> types -> evar_map * types
val solve_refl : ?can_drop:bool -> conversion_check -> unify_flags -> env -> evar_map ->
bool option -> Evar.t -> constr list -> constr list -> evar_map
val solve_evar_evar : ?force:bool ->
(env -> evar_map -> bool option -> existential -> constr -> evar_map) ->
unifier -> unify_flags ->
env -> evar_map -> bool option -> existential -> existential -> evar_map
(** The two evars are expected to be in inferably convertible types;
if not, an exception IllTypedInstance is raised *)
(* [solve_simple_eqn unifier flags env evd (direction,?ev[inst],t)]
makes progresses on problems of the form [?ev[inst] := t] (or
[?ev[inst] :<= t], or [?ev[inst] :>= t]). It uses imitation and a
limited form of projection. At the time of writing this comment,
only rels/vars (possibly indirectly via a chain of evars) and
constructors are used for projection. For instance
[?e[x,S 0] := x + S 0] will be solved by imitating [+] and
projecting [x] and [S 0] (so that [?e[a,b]:=a+b]) but in
[?e[0+0] := 0+0], the possible imitation will not be seen.
[choose] tells to make an irreversible choice when two valid
projections are competing. It is to be used when no more reversible
progress can be done. It is [false] by default.
[imitate_defs] tells to expand local definitions if they cannot be
projected. It is [true] by default.
*)
val solve_simple_eqn : unifier -> unify_flags -> ?choose:bool -> ?imitate_defs:bool -> env -> evar_map ->
bool option * existential * constr -> unification_result
val reconsider_unif_constraints : unifier -> unify_flags -> evar_map -> unification_result
val is_unification_pattern_evar : env -> evar_map -> existential -> constr list ->
constr -> alias list option
val is_unification_pattern : env * int -> evar_map -> constr -> constr list ->
constr -> alias list option
val solve_pattern_eqn : env -> evar_map -> alias list -> constr -> constr
val noccur_evar : env -> evar_map -> Evar.t -> constr -> bool
exception IllTypedInstance of env * types * types
val check_evar_instance : unifier -> unify_flags ->
env -> evar_map -> Evar.t -> constr -> evar_map
(** May raise IllTypedInstance if types are not convertible *)
val remove_instance_local_defs :
evar_map -> Evar.t -> 'a list -> 'a list
val get_type_of_refresh :
?polyprop:bool -> ?lax:bool -> env -> evar_map -> constr -> evar_map * types
|
