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
224
|
(***********************************************************************)
(* 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 *)
(***********************************************************************)
(* $Id$ *)
open Pp
open Util
open Names
open Term
open Termops
open Environ
open Reduction
open Inductiveops
open Proof_type
open Clenv
open Hipattern
open Tacmach
open Tacticals
open Tactics
open Hiddentac
let introElimAssumsThen tac ba =
let nassums =
List.fold_left
(fun acc b -> if b then acc+2 else acc+1)
0 ba.branchsign
in
let introElimAssums = tclDO nassums intro in
(tclTHEN introElimAssums (elim_on_ba tac ba))
let introCaseAssumsThen tac ba =
let case_thin_sign =
List.flatten
(List.map
(function b -> if b then [false;true] else [false])
ba.branchsign)
in
let introCaseAssums = intros_clearing case_thin_sign in
(tclTHEN introCaseAssums (case_on_ba tac ba))
(* The following tactic Decompose repeatedly applies the
elimination(s) rule(s) of the types satisfying the predicate
``recognizer'' onto a certain hypothesis. For example :
Require Elim.
Require Le.
Goal (y:nat){x:nat | (le O x)/\(le x y)}->{x:nat | (le O x)}.
Intros y H.
Decompose [sig and] H;EAuto.
Qed.
Another example :
Goal (A,B,C:Prop)(A/\B/\C \/ B/\C \/ C/\A) -> C.
Intros A B C H; Decompose [and or] H; Assumption.
Qed.
*)
let elimHypThen tac id gl =
elimination_then tac ([],[]) (mkVar id) gl
let rec general_decompose_on_hyp recognizer =
ifOnHyp recognizer (general_decompose recognizer) (fun _ -> tclIDTAC)
and general_decompose recognizer id =
elimHypThen
(introElimAssumsThen
(fun bas ->
tclTHEN (clear_one id)
(tclMAP (general_decompose_on_hyp recognizer) bas.assums)))
id
(* Faudrait ajouter un COMPLETE pour que l'hypothèse créée ne reste
pas si aucune élimination n'est possible *)
(* Meilleures stratégies mais perte de compatibilité *)
let tmphyp_name = id_of_string "_TmpHyp"
let up_to_delta = ref false (* true *)
let general_decompose recognizer c gl =
let typc = pf_type_of gl c in
(tclTHENS (cut typc)
[(tclTHEN (intro_using tmphyp_name)
(onLastHyp
(ifOnHyp recognizer (general_decompose recognizer) clear_one)));
(exact_no_check c)]) gl
let head_in gls indl t =
try
let ity,_ =
if !up_to_delta
then find_mrectype (pf_env gls) (project gls) t
else extract_mrectype t
in List.mem ity indl
with Induc -> false
let inductive_of_qualid gls qid =
let c =
try Declare.construct_qualified_reference qid
with Not_found -> Nametab.error_global_not_found qid
in
match kind_of_term c with
| Ind ity -> ity
| _ ->
errorlabstrm "Decompose"
(Nametab.pr_qualid qid ++ str " is not an inductive type")
let decompose_these c l gls =
let indl = List.map (inductive_of_qualid gls) l in
general_decompose (fun (_,t) -> head_in gls indl t) c gls
let decompose_nonrec c gls =
general_decompose
(fun (_,t) -> is_non_recursive_type t)
c gls
let decompose_and c gls =
general_decompose
(fun (_,t) -> is_conjunction t)
c gls
let decompose_or c gls =
general_decompose
(fun (_,t) -> is_disjunction t)
c gls
let dyn_decompose args gl =
let out_qualid = function
| Qualid qid -> qid
| l -> bad_tactic_args "DecomposeThese" [l] gl in
match args with
| Command c :: ids ->
decompose_these (pf_interp_constr gl c) (List.map out_qualid ids) gl
| Constr c :: ids ->
decompose_these c (List.map out_qualid ids) gl
| l -> bad_tactic_args "DecomposeThese" l gl
let h_decompose =
let v_decompose = hide_tactic "DecomposeThese" dyn_decompose in
fun ids c ->
v_decompose
(Constr c :: List.map (fun x -> Qualid (Nametab.qualid_of_sp x)) ids)
let vernac_decompose_and =
hide_constr_tactic "DecomposeAnd" decompose_and
let vernac_decompose_or =
hide_constr_tactic "DecomposeOr" decompose_or
(* The tactic Double performs a double induction *)
let simple_elimination c gls =
simple_elimination_then (fun _ -> tclIDTAC) c gls
let induction_trailer abs_i abs_j bargs =
tclTHEN
(tclDO (abs_j - abs_i) intro)
(onLastHyp
(fun id gls ->
let idty = pf_type_of gls (mkVar id) in
let fvty = global_vars (pf_env gls) idty in
let possible_bring_ids =
(List.tl (nLastHyps (abs_j - abs_i) gls))
@bargs.assums in
let (ids,_) = List.fold_left
(fun (bring_ids,leave_ids) cid ->
let cidty = pf_type_of gls (mkVar cid) in
if not (List.mem cid leave_ids)
then (cid::bring_ids,leave_ids)
else (bring_ids,cid::leave_ids))
([],fvty) possible_bring_ids
in
(tclTHEN (tclTHEN (bring_hyps ids) (clear_clauses (List.rev ids)))
(simple_elimination (mkVar id))) gls))
let double_ind abs_i abs_j gls =
let cl = pf_concl gls in
(tclTHEN (tclDO abs_i intro)
(onLastHyp
(fun id ->
elimination_then
(introElimAssumsThen (induction_trailer abs_i abs_j))
([],[]) (mkVar id)))) gls
let dyn_double_ind = function
| [Integer i; Integer j] -> double_ind i j
| _ -> assert false
let _ = add_tactic "DoubleInd" dyn_double_ind
(*****************************)
(* Decomposing introductions *)
(*****************************)
let rec intro_pattern p =
let clear_last = (tclLAST_HYP (fun c -> (clear_one (destVar c))))
and case_last = (tclLAST_HYP h_simplest_case) in
match p with
| WildPat -> (tclTHEN intro clear_last)
| IdPat id -> intro_mustbe id
| DisjPat l -> (tclTHEN introf
(tclTHENS
(tclTHEN case_last clear_last)
(List.map intro_pattern l)))
| ConjPat l -> (tclTHEN introf
(tclTHEN (tclTHEN case_last clear_last)
(intros_pattern l)))
| ListPat l -> intros_pattern l
and intros_pattern l = tclMAP intro_pattern l
let dyn_intro_pattern = function
| [] -> intros
| [Intropattern p] -> intro_pattern p
| l -> bad_tactic_args "Elim.dyn_intro_pattern" l
let v_intro_pattern = hide_tactic "Intros" dyn_intro_pattern
let h_intro_pattern p = v_intro_pattern [Intropattern p]
|
