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
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id: hipattern.mli 8652 2006-03-22 08:27:14Z herbelin $ i*)
(*i*)
open Util
open Names
open Term
open Sign
open Evd
open Pattern
open Proof_trees
(*i*)
(*s 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 *)
(*s 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 = constr -> 'a option
type testing_function = constr -> bool
val match_with_non_recursive_type : (constr * constr list) matching_function
val is_non_recursive_type : testing_function
val match_with_disjunction : (constr * constr list) matching_function
val is_disjunction : testing_function
val match_with_conjunction : (constr * constr list) matching_function
val is_conjunction : testing_function
val match_with_empty_type : constr matching_function
val is_empty_type : testing_function
val match_with_unit_type : constr matching_function
(* type with only one constructor and no arguments *)
val is_unit_type : testing_function
val match_with_equation : (constr * constr list) matching_function
val is_equation : testing_function
val match_with_nottype : (constr * constr) matching_function
val is_nottype : testing_function
val match_with_forall_term : (name * 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
(***** Destructing patterns bound to some theory *)
open Coqlib
(* Match terms [(eq A t u)] or [(identity A t u)] *)
(* Returns associated lemmas and [A,t,u] *)
val find_eq_data_decompose : constr ->
coq_leibniz_eq_data * (constr * constr * constr)
(* Match a term of the form [(existS A P t p)] or [(existT A P t p)] *)
(* Returns associated lemmas and [A,P,t,p] *)
val find_sigma_data_decompose : constr ->
coq_sigma_data * (constr * constr * constr * constr)
(* Match a term of the form [{x:A|P}], returns [A] and [P] *)
val match_sigma : constr -> constr * constr
val is_matching_sigma : 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 : constr -> bool * constr * constr * constr * constr
(* Match an equality up to conversion; returns [(eq,t1,t2)] in normal form *)
open Proof_type
open Tacmach
val dest_nf_eq : goal sigma -> constr -> (constr * constr * constr)
(* Match a negation *)
val is_matching_not : constr -> bool
val is_matching_imp_False : constr -> bool
|
