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
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <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 Names
open Evd
open EConstr
open Coqlib
(** High-order patterns *)
(** Given a term with second-order variables in it,
represented by Meta's, and possibly applied using SoApp
terms, this function will perform second-order, binding-preserving,
matching, in the case where the pattern is a pattern in the sense
of Dale Miller.
ALGORITHM:
Given a pattern, we decompose it, flattening casts and apply's,
recursing on all operators, and pushing the name of the binder each
time we descend a binder.
When we reach a first-order variable, we ask that the corresponding
term's free-rels all be higher than the depth of the current stack.
When we reach a second-order application, we ask that the
intersection of the free-rels of the term and the current stack be
contained in the arguments of the application *)
(** I implemented the following functions which test whether a term [t]
is an inductive but non-recursive type, a general conjuction, a
general disjunction, or a type with no constructors.
They are more general than matching with [or_term], [and_term], etc,
since they do not depend on the name of the type. Hence, they
also work on ad-hoc disjunctions introduced by the user.
(Eduardo, 6/8/97). *)
type 'a matching_function = evar_map -> constr -> 'a option
type testing_function = evar_map -> constr -> bool
val match_with_non_recursive_type : (constr * constr list) matching_function
val is_non_recursive_type : testing_function
(** Non recursive type with no indices and exactly one argument for each
constructor; canonical definition of n-ary disjunction if strict *)
val match_with_disjunction : ?strict:bool -> ?onlybinary:bool -> (constr * constr list) matching_function
val is_disjunction : ?strict:bool -> ?onlybinary:bool -> testing_function
(** Non recursive tuple (one constructor and no indices) with no inner
dependencies; canonical definition of n-ary conjunction if strict *)
val match_with_conjunction : ?strict:bool -> ?onlybinary:bool -> (constr * constr list) matching_function
val is_conjunction : ?strict:bool -> ?onlybinary:bool -> testing_function
(** Non recursive tuple, possibly with inner dependencies *)
val match_with_record : (constr * constr list) matching_function
val is_record : testing_function
(** Like record but supports and tells if recursive (e.g. Acc) *)
val match_with_tuple : (constr * constr list * bool) matching_function
val is_tuple : testing_function
(** No constructor, possibly with indices *)
val match_with_empty_type : constr matching_function
val is_empty_type : testing_function
(** type with only one constructor and no arguments, possibly with indices *)
val match_with_unit_or_eq_type : constr matching_function
val is_unit_or_eq_type : testing_function
(** type with only one constructor and no arguments, no indices *)
val is_unit_type : testing_function
(** type with only one constructor, no arguments and at least one dependency *)
val is_inductive_equality : inductive -> bool
val match_with_equality_type : (constr * constr list) matching_function
val is_equality_type : testing_function
val match_with_nottype : Environ.env -> (constr * constr) matching_function
val is_nottype : Environ.env -> testing_function
val match_with_forall_term : (Name.t * constr * constr) matching_function
val is_forall_term : testing_function
val match_with_imp_term : (constr * constr) matching_function
val is_imp_term : testing_function
(** I added these functions to test whether a type contains dependent
products or not, and if an inductive has constructors with dependent types
(excluding parameters). this is useful to check whether a conjunction is a
real conjunction and not a dependent tuple. (Pierre Corbineau, 13/5/2002) *)
val has_nodep_prod_after : int -> testing_function
val has_nodep_prod : testing_function
val match_with_nodep_ind : (constr * constr list * int) matching_function
val is_nodep_ind : testing_function
val match_with_sigma_type : (constr * constr list) matching_function
val is_sigma_type : testing_function
(** Recongnize inductive relation defined by reflexivity *)
type equation_kind =
| MonomorphicLeibnizEq of constr * constr
| PolymorphicLeibnizEq of constr * constr * constr
| HeterogenousEq of constr * constr * constr * constr
exception NoEquationFound
val match_with_equation:
Environ.env -> evar_map -> constr -> coq_eq_data option * constr * equation_kind
(***** Destructing patterns bound to some theory *)
(** Match terms [eq A t u], [identity A t u] or [JMeq A t A u]
Returns associated lemmas and [A,t,u] or fails PatternMatchingFailure *)
val find_eq_data_decompose : Proofview.Goal.t -> constr ->
coq_eq_data * EInstance.t * (types * constr * constr)
(** Idem but fails with an error message instead of PatternMatchingFailure *)
val find_this_eq_data_decompose : Proofview.Goal.t -> constr ->
coq_eq_data * EInstance.t * (types * constr * constr)
(** A variant that returns more informative structure on the equality found *)
val find_eq_data : evar_map -> constr -> coq_eq_data * EInstance.t * equation_kind
(** Match a term of the form [(existT A P t p)]
Returns associated lemmas and [A,P,t,p] *)
val find_sigma_data_decompose : Environ.env -> evar_map -> constr ->
coq_sigma_data * (EInstance.t * constr * constr * constr * constr)
(** Match a term of the form [{x:A|P}], returns [A] and [P] *)
val match_sigma : Environ.env -> evar_map -> constr -> constr * constr
val is_matching_sigma : Environ.env -> evar_map -> constr -> bool
(** Match a decidable equality judgement (e.g [{t=u:>T}+{~t=u}]), returns
[t,u,T] and a boolean telling if equality is on the left side *)
val match_eqdec : Environ.env -> evar_map -> constr -> bool * Globnames.global_reference * constr * constr * constr
(** Match a negation *)
val is_matching_not : Environ.env -> evar_map -> constr -> bool
val is_matching_imp_False : Environ.env -> evar_map -> constr -> bool
|
