blob: dd5268720b904f3b8e51c96c347fdb1237bb6818 (
plain)
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
|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i camlp4deps: "parsing/grammar.cma" i*)
(*i $Id$ i*)
open Ast
open Coqast
open Hipattern
open Names
open Libnames
open Pp
open Proof_type
open Tacticals
open Tacinterp
open Tactics
open Util
let is_empty ist =
if (is_empty_type (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let is_unit ist =
if (is_unit_type (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let is_conj ist =
let ind=(List.assoc 1 ist.lmatch) in
if (is_conjunction ind) && (is_nodep_ind ind) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let is_disj ist =
if (is_disjunction (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let not_dep_intros ist =
<:tactic<
Repeat
Match Context With
| [|- ?1 -> ?2 ] -> Intro
| [|- (Coq.Init.Logic.iff ? ?)] -> Unfold Coq.Init.Logic.iff
| [|- (Coq.Init.Logic.not ?)] -> Unfold Coq.Init.Logic.not
| [ H:(Coq.Init.Logic.iff ? ?)|- ?] -> Unfold Coq.Init.Logic.iff in H
| [ H:(Coq.Init.Logic.not ?)|-?] -> Unfold Coq.Init.Logic.not in H
| [ H:(Coq.Init.Logic.iff ? ?)->?|- ?] -> Unfold Coq.Init.Logic.iff in H
| [ H:(Coq.Init.Logic.not ?)->?|-?] -> Unfold Coq.Init.Logic.not in H >>
let axioms ist =
let t_is_unit = tacticIn is_unit
and t_is_empty = tacticIn is_empty in
<:tactic<
Match Reverse Context With
|[|- ?1] -> $t_is_unit;Constructor 1
|[_:?1 |- ?] -> $t_is_empty;ElimType ?1;Assumption
|[_:?1 |- ?1] -> Assumption>>
let simplif ist =
let t_is_unit = tacticIn is_unit
and t_is_conj = tacticIn is_conj
and t_is_disj = tacticIn is_disj
and t_not_dep_intros = tacticIn not_dep_intros in
<:tactic<
$t_not_dep_intros;
Repeat
((Match Reverse Context With
| [id: (?1 ? ?) |- ?] ->
$t_is_conj;Elim id;Do 2 Intro;Clear id
| [id: (?1 ? ?) |- ?] -> $t_is_disj;Elim id;Intro;Clear id
| [id0: ?1-> ?2; id1: ?1|- ?] -> Generalize (id0 id1);Intro;Clear id0
| [id: ?1 -> ?2|- ?] ->
$t_is_unit;Cut ?2;
[Intro;Clear id
| (* id : ?1 -> ?2 |- ?2 *)
Cut ?1;[Exact id|Constructor 1;Fail]
]
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_conj;Cut ?2-> ?3-> ?4;
[Intro;Clear id
| (* id: (?1 ?2 ?3) -> ?4 |- ?2 -> ?3 -> ?4 *)
Intro;Intro; Cut (?1 ?2 ?3);[Exact id|Split;Assumption]
]
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_disj;
Cut ?3-> ?4;
[Cut ?2-> ?4;
[Intro;Intro;Clear id
| (* id: (?1 ?2 ?3) -> ?4 |- ?2 -> ?4 *)
Intro; Cut (?1 ?2 ?3);[Exact id|Left;Assumption]
]
| (* id: (?1 ?2 ?3) -> ?4 |- ?3 -> ?4 *)
Intro; Cut (?1 ?2 ?3);[Exact id|Right;Assumption]
]
| [|- (?1 ? ?)] -> $t_is_conj;Split);
$t_not_dep_intros)>>
let rec tauto_intuit t_reduce solver ist =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn simplif
and t_is_disj = tacticIn is_disj
and t_tauto_intuit = tacticIn (tauto_intuit t_reduce solver) in
let t_solver = Tacexpr.TacArg (valueIn (VTactic (dummy_loc,solver))) in
<:tactic<
($t_simplif;$t_axioms
Orelse
(Match Reverse Context With
| [id:(?1-> ?2)-> ?3|- ?] ->
Cut ?3;
[ Intro;Clear id;$t_tauto_intuit
| Cut ?1 -> ?2;
[ Exact id
| Generalize [y:?2](id [x:?1]y);Intro;Clear id;
Solve [ $t_tauto_intuit ]]]
| [|- (?1 ? ?)] ->
$t_is_disj;Solve [Left;$t_tauto_intuit | Right;$t_tauto_intuit]
)
Orelse
(* NB: [|- ? -> ?] matches any product *)
(Match Context With |[ |- ? -> ? ] -> Intro;$t_tauto_intuit
|[|-?]->$t_reduce;$t_solver)
Orelse
$t_solver
) >>
let reduction_not_iff=interp
<:tactic<Repeat
(Match Context With
|[|- ?]->
Progress Unfold Coq.Init.Logic.not Coq.Init.Logic.iff
|[H:?|- ?]->
Progress Unfold Coq.Init.Logic.not Coq.Init.Logic.iff in H)>>
let t_reduction_not_iff =
Tacexpr.TacArg (valueIn (VTactic (dummy_loc,reduction_not_iff)))
let intuition_gen tac =
interp (tacticIn (tauto_intuit t_reduction_not_iff tac))
let simplif_gen = interp (tacticIn simplif)
let tauto g =
try intuition_gen (interp <:tactic<Fail>>) g
with
Refiner.FailError _ | UserError _ ->
errorlabstrm "tauto" [< str "Tauto failed" >]
let default_intuition_tac = interp <:tactic< Auto with * >>
let q_elim tac=
<:tactic<
Match Context With
[x:?1;H:?1->?|-?]->
Generalize (H x);Clear H;$tac>>
let rec lfo n gl=
if n=0 then (tclFAIL 0 "LinearIntuition failed" gl) else
let p=if n<0 then n else (n-1) in
let lfo_rec=q_elim (Tacexpr.TacArg (valueIn (VTactic(dummy_loc,lfo p)))) in
intuition_gen (interp lfo_rec) gl
let lfo_wrap n gl=
try lfo n gl
with
Refiner.FailError _ | UserError _ ->
errorlabstrm "LinearIntuition" [< str "LinearIntuition failed." >]
TACTIC EXTEND Tauto
| [ "Tauto" ] -> [ tauto ]
END
TACTIC EXTEND TSimplif
| [ "Simplif" ] -> [ simplif_gen ]
END
TACTIC EXTEND Intuition
| [ "Intuition" ] -> [ intuition_gen default_intuition_tac ]
| [ "Intuition" tactic(t) ] -> [ intuition_gen (snd t) ]
END
TACTIC EXTEND LinearIntuition
| [ "LinearIntuition" ] -> [ lfo_wrap (-1)]
| [ "LinearIntuition" integer(n)] -> [ lfo_wrap n]
END
|
