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
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
|
(************************************************************************)
(* 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: tacexpr.ml,v 1.33.2.3 2005/05/15 12:47:04 herbelin Exp $ i*)
open Names
open Topconstr
open Libnames
open Nametab
open Rawterm
open Util
open Genarg
open Pattern
type 'a or_metaid = AI of 'a | MetaId of loc * string
type direction_flag = bool (* true = Left-to-right false = right-to-right *)
type raw_red_flag =
| FBeta
| FIota
| FZeta
| FConst of reference list
| FDeltaBut of reference list
let make_red_flag =
let rec add_flag red = function
| [] -> red
| FBeta :: lf -> add_flag { red with rBeta = true } lf
| FIota :: lf -> add_flag { red with rIota = true } lf
| FZeta :: lf -> add_flag { red with rZeta = true } lf
| FConst l :: lf ->
if red.rDelta then
error
"Cannot set both constants to unfold and constants not to unfold";
add_flag { red with rConst = list_union red.rConst l } lf
| FDeltaBut l :: lf ->
if red.rConst <> [] & not red.rDelta then
error
"Cannot set both constants to unfold and constants not to unfold";
add_flag
{ red with rConst = list_union red.rConst l; rDelta = true }
lf
in
add_flag
{rBeta = false; rIota = false; rZeta = false; rDelta = false; rConst = []}
type hyp_location_flag = (* To distinguish body and type of local defs *)
| InHyp
| InHypTypeOnly
| InHypValueOnly
type 'a raw_hyp_location =
'a * int list * (hyp_location_flag * hyp_location_flag option ref)
type 'a induction_arg =
| ElimOnConstr of 'a
| ElimOnIdent of identifier located
| ElimOnAnonHyp of int
type inversion_kind =
| SimpleInversion
| FullInversion
| FullInversionClear
type ('c,'id) inversion_strength =
| NonDepInversion of inversion_kind * 'id list * intro_pattern_expr option
| DepInversion of inversion_kind * 'c option * intro_pattern_expr option
| InversionUsing of 'c * 'id list
type ('a,'b) location = HypLocation of 'a | ConclLocation of 'b
type 'id gsimple_clause = ('id raw_hyp_location) option
(* onhyps:
[None] means *on every hypothesis*
[Some l] means on hypothesis belonging to l *)
type 'id gclause =
{ onhyps : 'id raw_hyp_location list option;
onconcl : bool;
concl_occs :int list }
let simple_clause_of = function
{ onhyps = Some[scl]; onconcl = false } -> Some scl
| { onhyps = Some []; onconcl = true; concl_occs=[] } -> None
| _ -> error "not a simple clause (one hypothesis or conclusion)"
type pattern_expr = constr_expr
(* Type of patterns *)
type 'a match_pattern =
| Term of 'a
| Subterm of identifier option * 'a
(* Type of hypotheses for a Match Context rule *)
type 'a match_context_hyps =
| Hyp of name located * 'a match_pattern
(* Type of a Match rule for Match Context and Match *)
type ('a,'t) match_rule =
| Pat of 'a match_context_hyps list * 'a match_pattern * 't
| All of 't
type ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_atomic_tactic_expr =
(* Basic tactics *)
| TacIntroPattern of intro_pattern_expr list
| TacIntrosUntil of quantified_hypothesis
| TacIntroMove of identifier option * identifier located option
| TacAssumption
| TacExact of 'constr
| TacApply of 'constr with_bindings
| TacElim of 'constr with_bindings * 'constr with_bindings option
| TacElimType of 'constr
| TacCase of 'constr with_bindings
| TacCaseType of 'constr
| TacFix of identifier option * int
| TacMutualFix of identifier * int * (identifier * int * 'constr) list
| TacCofix of identifier option
| TacMutualCofix of identifier * (identifier * 'constr) list
| TacCut of 'constr
| TacTrueCut of name * 'constr
| TacForward of bool * name * 'constr
| TacGeneralize of 'constr list
| TacGeneralizeDep of 'constr
| TacLetTac of name * 'constr * 'id gclause
| TacInstantiate of int * 'constr * 'id gclause
(* Derived basic tactics *)
| TacSimpleInduction of (quantified_hypothesis * (bool ref * intro_pattern_expr list ref list) list ref)
| TacNewInduction of 'constr induction_arg * 'constr with_bindings option
* (intro_pattern_expr option * (bool ref * intro_pattern_expr list ref list) list ref)
| TacSimpleDestruct of quantified_hypothesis
| TacNewDestruct of 'constr induction_arg * 'constr with_bindings option
* (intro_pattern_expr option * (bool ref * intro_pattern_expr list ref list) list ref)
| TacDoubleInduction of quantified_hypothesis * quantified_hypothesis
| TacDecomposeAnd of 'constr
| TacDecomposeOr of 'constr
| TacDecompose of 'ind list * 'constr
| TacSpecialize of int option * 'constr with_bindings
| TacLApply of 'constr
(* Automation tactics *)
| TacTrivial of string list option
| TacAuto of int or_var option * string list option
| TacAutoTDB of int option
| TacDestructHyp of (bool * identifier located)
| TacDestructConcl
| TacSuperAuto of (int option * reference list * bool * bool)
| TacDAuto of int or_var option * int option
(* Context management *)
| TacClear of 'id list
| TacClearBody of 'id list
| TacMove of bool * 'id * 'id
| TacRename of 'id * 'id
(* Constructors *)
| TacLeft of 'constr bindings
| TacRight of 'constr bindings
| TacSplit of bool * 'constr bindings
| TacAnyConstructor of 'tac option
| TacConstructor of int or_metaid * 'constr bindings
(* Conversion *)
| TacReduce of ('constr,'cst) red_expr_gen * 'id gclause
| TacChange of
'constr occurrences option * 'constr * 'id gclause
(* Equivalence relations *)
| TacReflexivity
| TacSymmetry of 'id gclause
| TacTransitivity of 'constr
(* Equality and inversion *)
| TacInversion of ('constr,'id) inversion_strength * quantified_hypothesis
(* For ML extensions *)
| TacExtend of loc * string * ('constr,'tac) generic_argument list
(* For syntax extensions *)
| TacAlias of loc * string *
(identifier * ('constr,'tac) generic_argument) list
* (dir_path * 'tac)
and ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr =
| TacAtom of loc * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_atomic_tactic_expr
| TacThen of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacThens of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr list
| TacFirst of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr list
| TacSolve of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr list
| TacTry of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacOrelse of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacDo of int or_var * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacRepeat of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacProgress of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacAbstract of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * identifier option
| TacId of string
| TacFail of int or_var * string
| TacInfo of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacLetRecIn of (identifier located * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_fun_ast) list * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacLetIn of (identifier located * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr option * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg) list * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
| TacMatch of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * ('pat,('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr) match_rule list
| TacMatchContext of direction_flag * ('pat,('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr) match_rule list
| TacFun of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_fun_ast
| TacArg of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg
and ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_fun_ast =
identifier option list * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
(* These are possible arguments of a tactic definition *)
and ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg =
| TacDynamic of loc * Dyn.t
| TacVoid
| MetaIdArg of loc * string
| ConstrMayEval of ('constr,'cst) may_eval
| IntroPattern of intro_pattern_expr
| Reference of 'ref
| Integer of int
| TacCall of loc *
'ref * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg list
| TacFreshId of string option
| Tacexp of 'tac
type raw_tactic_expr =
(constr_expr,
pattern_expr,
reference,
reference,
reference,
identifier located or_metaid,
raw_tactic_expr) gen_tactic_expr
type raw_atomic_tactic_expr =
(constr_expr, (* constr *)
pattern_expr, (* pattern *)
reference, (* evaluable reference *)
reference, (* inductive *)
reference, (* ltac reference *)
identifier located or_metaid, (* identifier *)
raw_tactic_expr) gen_atomic_tactic_expr
type raw_tactic_arg =
(constr_expr,
pattern_expr,
reference,
reference,
reference,
identifier located or_metaid,
raw_tactic_expr) gen_tactic_arg
type raw_generic_argument =
(constr_expr,raw_tactic_expr) generic_argument
type raw_red_expr = (constr_expr, reference) red_expr_gen
(* Globalized tactics *)
type glob_tactic_expr =
(rawconstr_and_expr,
constr_pattern,
evaluable_global_reference and_short_name or_var,
inductive or_var,
ltac_constant located or_var,
identifier located,
glob_tactic_expr) gen_tactic_expr
type glob_atomic_tactic_expr =
(rawconstr_and_expr,
constr_pattern,
evaluable_global_reference and_short_name or_var,
inductive or_var,
ltac_constant located or_var,
identifier located,
glob_tactic_expr) gen_atomic_tactic_expr
type glob_tactic_arg =
(rawconstr_and_expr,
constr_pattern,
evaluable_global_reference and_short_name or_var,
inductive or_var,
ltac_constant located,
identifier located or_var,
glob_tactic_expr) gen_tactic_arg
type glob_generic_argument =
(rawconstr_and_expr,glob_tactic_expr) generic_argument
type glob_red_expr =
(rawconstr_and_expr, evaluable_global_reference or_var) red_expr_gen
type closed_raw_generic_argument =
(constr_expr,raw_tactic_expr) generic_argument
type 'a raw_abstract_argument_type =
('a,constr_expr,raw_tactic_expr) abstract_argument_type
type 'a glob_abstract_argument_type =
('a,rawconstr_and_expr,glob_tactic_expr) abstract_argument_type
type open_generic_argument =
(Term.constr,glob_tactic_expr) generic_argument
type closed_generic_argument =
(Term.constr,glob_tactic_expr) generic_argument
type 'a closed_abstract_argument_type =
('a,Term.constr,glob_tactic_expr) abstract_argument_type
type declaration_hook = Decl_kinds.strength -> global_reference -> unit
|