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
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i camlp4deps: "grammar/grammar.cma" i*)
(* Syntax for rewriting with strategies *)
open Names
open Misctypes
open Locus
open Constrexpr
open Glob_term
open Geninterp
open Extraargs
open Tacmach
open Tacticals
open Rewrite
DECLARE PLUGIN "g_rewrite"
type constr_expr_with_bindings = constr_expr with_bindings
type glob_constr_with_bindings = Tacexpr.glob_constr_and_expr with_bindings
type glob_constr_with_bindings_sign = interp_sign * Tacexpr.glob_constr_and_expr with_bindings
let pr_glob_constr_with_bindings_sign _ _ _ (ge : glob_constr_with_bindings_sign) = Printer.pr_glob_constr (fst (fst (snd ge)))
let pr_glob_constr_with_bindings _ _ _ (ge : glob_constr_with_bindings) = Printer.pr_glob_constr (fst (fst ge))
let pr_constr_expr_with_bindings prc _ _ (ge : constr_expr_with_bindings) = prc (fst ge)
let interp_glob_constr_with_bindings ist gl c = Tacmach.project gl , (ist, c)
let glob_glob_constr_with_bindings ist l = Tacintern.intern_constr_with_bindings ist l
let subst_glob_constr_with_bindings s c =
Tacsubst.subst_glob_with_bindings s c
ARGUMENT EXTEND glob_constr_with_bindings
PRINTED BY pr_glob_constr_with_bindings_sign
INTERPRETED BY interp_glob_constr_with_bindings
GLOBALIZED BY glob_glob_constr_with_bindings
SUBSTITUTED BY subst_glob_constr_with_bindings
RAW_TYPED AS constr_expr_with_bindings
RAW_PRINTED BY pr_constr_expr_with_bindings
GLOB_TYPED AS glob_constr_with_bindings
GLOB_PRINTED BY pr_glob_constr_with_bindings
[ constr_with_bindings(bl) ] -> [ bl ]
END
type raw_strategy = (constr_expr, Tacexpr.raw_red_expr) strategy_ast
type glob_strategy = (Tacexpr.glob_constr_and_expr, Tacexpr.raw_red_expr) strategy_ast
let interp_strategy ist gl s =
let sigma = project gl in
sigma, strategy_of_ast s
let glob_strategy ist s = map_strategy (Tacintern.intern_constr ist) (fun c -> c) s
let subst_strategy s str = str
let pr_strategy _ _ _ (s : strategy) = Pp.str "<strategy>"
let pr_raw_strategy _ _ _ (s : raw_strategy) = Pp.str "<strategy>"
let pr_glob_strategy _ _ _ (s : glob_strategy) = Pp.str "<strategy>"
ARGUMENT EXTEND rewstrategy
PRINTED BY pr_strategy
INTERPRETED BY interp_strategy
GLOBALIZED BY glob_strategy
SUBSTITUTED BY subst_strategy
RAW_TYPED AS raw_strategy
RAW_PRINTED BY pr_raw_strategy
GLOB_TYPED AS glob_strategy
GLOB_PRINTED BY pr_glob_strategy
[ glob(c) ] -> [ StratConstr (c, true) ]
| [ "<-" constr(c) ] -> [ StratConstr (c, false) ]
| [ "subterms" rewstrategy(h) ] -> [ StratUnary (Subterms, h) ]
| [ "subterm" rewstrategy(h) ] -> [ StratUnary (Subterm, h) ]
| [ "innermost" rewstrategy(h) ] -> [ StratUnary(Innermost, h) ]
| [ "outermost" rewstrategy(h) ] -> [ StratUnary(Outermost, h) ]
| [ "bottomup" rewstrategy(h) ] -> [ StratUnary(Bottomup, h) ]
| [ "topdown" rewstrategy(h) ] -> [ StratUnary(Topdown, h) ]
| [ "id" ] -> [ StratId ]
| [ "fail" ] -> [ StratFail ]
| [ "refl" ] -> [ StratRefl ]
| [ "progress" rewstrategy(h) ] -> [ StratUnary (Progress, h) ]
| [ "try" rewstrategy(h) ] -> [ StratUnary (Try, h) ]
| [ "any" rewstrategy(h) ] -> [ StratUnary (Any, h) ]
| [ "repeat" rewstrategy(h) ] -> [ StratUnary (Repeat, h) ]
| [ rewstrategy(h) ";" rewstrategy(h') ] -> [ StratBinary (Compose, h, h') ]
| [ "(" rewstrategy(h) ")" ] -> [ h ]
| [ "choice" rewstrategy(h) rewstrategy(h') ] -> [ StratBinary (Choice, h, h') ]
| [ "old_hints" preident(h) ] -> [ StratHints (true, h) ]
| [ "hints" preident(h) ] -> [ StratHints (false, h) ]
| [ "terms" constr_list(h) ] -> [ StratTerms h ]
| [ "eval" red_expr(r) ] -> [ StratEval r ]
| [ "fold" constr(c) ] -> [ StratFold c ]
END
(* By default the strategy for "rewrite_db" is top-down *)
let db_strat db = StratUnary (Topdown, StratHints (false, db))
let cl_rewrite_clause_db db = cl_rewrite_clause_strat (strategy_of_ast (db_strat db))
let cl_rewrite_clause_db =
if Flags.profile then
let key = Profile.declare_profile "cl_rewrite_clause_db" in
Profile.profile3 key cl_rewrite_clause_db
else cl_rewrite_clause_db
TACTIC EXTEND rewrite_strat
| [ "rewrite_strat" rewstrategy(s) "in" hyp(id) ] -> [ Proofview.V82.tactic (cl_rewrite_clause_strat s (Some id)) ]
| [ "rewrite_strat" rewstrategy(s) ] -> [ Proofview.V82.tactic (cl_rewrite_clause_strat s None) ]
| [ "rewrite_db" preident(db) "in" hyp(id) ] -> [ Proofview.V82.tactic (cl_rewrite_clause_db db (Some id)) ]
| [ "rewrite_db" preident(db) ] -> [ Proofview.V82.tactic (cl_rewrite_clause_db db None) ]
END
let clsubstitute o c =
let is_tac id = match fst (fst (snd c)) with GVar (_, id') when Id.equal id' id -> true | _ -> false in
Tacticals.onAllHypsAndConcl
(fun cl ->
match cl with
| Some id when is_tac id -> tclIDTAC
| _ -> cl_rewrite_clause c o AllOccurrences cl)
TACTIC EXTEND substitute
| [ "substitute" orient(o) glob_constr_with_bindings(c) ] -> [ Proofview.V82.tactic (clsubstitute o c) ]
END
(* Compatibility with old Setoids *)
TACTIC EXTEND setoid_rewrite
[ "setoid_rewrite" orient(o) glob_constr_with_bindings(c) ]
-> [ Proofview.V82.tactic (cl_rewrite_clause c o AllOccurrences None) ]
| [ "setoid_rewrite" orient(o) glob_constr_with_bindings(c) "in" hyp(id) ] ->
[ Proofview.V82.tactic (cl_rewrite_clause c o AllOccurrences (Some id))]
| [ "setoid_rewrite" orient(o) glob_constr_with_bindings(c) "at" occurrences(occ) ] ->
[ Proofview.V82.tactic (cl_rewrite_clause c o (occurrences_of occ) None)]
| [ "setoid_rewrite" orient(o) glob_constr_with_bindings(c) "at" occurrences(occ) "in" hyp(id)] ->
[ Proofview.V82.tactic (cl_rewrite_clause c o (occurrences_of occ) (Some id))]
| [ "setoid_rewrite" orient(o) glob_constr_with_bindings(c) "in" hyp(id) "at" occurrences(occ)] ->
[ Proofview.V82.tactic (cl_rewrite_clause c o (occurrences_of occ) (Some id))]
END
VERNAC COMMAND EXTEND AddRelation CLASSIFIED AS SIDEFF
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) (Some lemma2) None ]
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) None None ]
| [ "Add" "Relation" constr(a) constr(aeq) "as" ident(n) ] ->
[ declare_relation a aeq n None None None ]
END
VERNAC COMMAND EXTEND AddRelation2 CLASSIFIED AS SIDEFF
[ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2)
"as" ident(n) ] ->
[ declare_relation a aeq n None (Some lemma2) None ]
| [ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation a aeq n None (Some lemma2) (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddRelation3 CLASSIFIED AS SIDEFF
[ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) None (Some lemma3) ]
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ]
| [ "Add" "Relation" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation a aeq n None None (Some lemma3) ]
END
type binders_argtype = local_binder list
let wit_binders =
(Genarg.create_arg None "binders" : binders_argtype Genarg.uniform_genarg_type)
let binders = Pcoq.create_generic_entry "binders" (Genarg.rawwit wit_binders)
open Pcoq
GEXTEND Gram
GLOBAL: binders;
binders:
[ [ b = Pcoq.Constr.binders -> b ] ];
END
VERNAC COMMAND EXTEND AddParametricRelation CLASSIFIED AS SIDEFF
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq)
"reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) None ]
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq)
"reflexivity" "proved" "by" constr(lemma1)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) None None ]
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None None None ]
END
VERNAC COMMAND EXTEND AddParametricRelation2 CLASSIFIED AS SIDEFF
[ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None (Some lemma2) None ]
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None (Some lemma2) (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddParametricRelation3 CLASSIFIED AS SIDEFF
[ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) None (Some lemma3) ]
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ]
| [ "Add" "Parametric" "Relation" binders(b) ":" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None None (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddSetoid1 CLASSIFIED AS SIDEFF
[ "Add" "Setoid" constr(a) constr(aeq) constr(t) "as" ident(n) ] ->
[ add_setoid (not (Locality.make_section_locality (Locality.LocalityFixme.consume ()))) [] a aeq t n ]
| [ "Add" "Parametric" "Setoid" binders(binders) ":" constr(a) constr(aeq) constr(t) "as" ident(n) ] ->
[ add_setoid (not (Locality.make_section_locality (Locality.LocalityFixme.consume ()))) binders a aeq t n ]
| [ "Add" "Morphism" constr(m) ":" ident(n) ]
(* This command may or may not open a goal *)
=> [ Vernacexpr.VtUnknown, Vernacexpr.VtNow ]
-> [ add_morphism_infer (not (Locality.make_section_locality (Locality.LocalityFixme.consume ()))) m n ]
| [ "Add" "Morphism" constr(m) "with" "signature" lconstr(s) "as" ident(n) ]
=> [ Vernacexpr.(VtStartProof("Classic",GuaranteesOpacity,[n]), VtLater) ]
-> [ add_morphism (not (Locality.make_section_locality (Locality.LocalityFixme.consume ()))) [] m s n ]
| [ "Add" "Parametric" "Morphism" binders(binders) ":" constr(m)
"with" "signature" lconstr(s) "as" ident(n) ]
=> [ Vernacexpr.(VtStartProof("Classic",GuaranteesOpacity,[n]), VtLater) ]
-> [ add_morphism (not (Locality.make_section_locality (Locality.LocalityFixme.consume ()))) binders m s n ]
END
TACTIC EXTEND setoid_symmetry
[ "setoid_symmetry" ] -> [ setoid_symmetry ]
| [ "setoid_symmetry" "in" hyp(n) ] -> [ setoid_symmetry_in n ]
END
TACTIC EXTEND setoid_reflexivity
[ "setoid_reflexivity" ] -> [ setoid_reflexivity ]
END
TACTIC EXTEND setoid_transitivity
[ "setoid_transitivity" constr(t) ] -> [ setoid_transitivity (Some t) ]
| [ "setoid_etransitivity" ] -> [ setoid_transitivity None ]
END
|
