tactics.v 60.5 KB
Newer Older
1
2
From iris.proofmode Require Import coq_tactics.
From iris.proofmode Require Import intro_patterns spec_patterns sel_patterns.
3
From iris.base_logic Require Export base_logic.
Robbert Krebbers's avatar
Robbert Krebbers committed
4
From iris.proofmode Require Export classes notation.
5
From iris.proofmode Require Import class_instances.
6
From iris.prelude Require Import stringmap hlist.
7
From iris.proofmode Require Import strings.
8
Set Default Proof Using "Type".
Robbert Krebbers's avatar
Robbert Krebbers committed
9
10

Declare Reduction env_cbv := cbv [
11
  beq ascii_beq string_beq
12
13
  env_lookup env_lookup_delete env_delete env_app env_replace env_dom
  env_persistent env_spatial env_spatial_is_nil envs_dom
14
  envs_lookup envs_lookup_delete envs_delete envs_snoc envs_app
15
16
    envs_simple_replace envs_replace envs_split
    envs_clear_spatial envs_clear_persistent
17
    envs_split_go envs_split].
Robbert Krebbers's avatar
Robbert Krebbers committed
18
19
20
Ltac env_cbv :=
  match goal with |- ?u => let v := eval env_cbv in u in change v end.

21
(** * Misc *)
22
23
(* Tactic Notation tactics cannot return terms *)
Ltac iFresh' H :=
Robbert Krebbers's avatar
Robbert Krebbers committed
24
25
  lazymatch goal with
  |- of_envs ?Δ  _ =>
26
27
28
     (* [vm_compute fails] if any of the hypotheses in [Δ] contain evars, so
     first use [cbv] to compute the domain of [Δ] *)
     let Hs := eval cbv in (envs_dom Δ) in
29
30
     eval vm_compute in (fresh_string_of_set H (of_list Hs))
  | _ => H
Robbert Krebbers's avatar
Robbert Krebbers committed
31
  end.
32
Ltac iFresh := iFresh' "~".
Robbert Krebbers's avatar
Robbert Krebbers committed
33
34
35

Tactic Notation "iTypeOf" constr(H) tactic(tac):=
  let Δ := match goal with |- of_envs ?Δ  _ => Δ end in
36
  lazymatch eval env_cbv in (envs_lookup H Δ) with
Robbert Krebbers's avatar
Robbert Krebbers committed
37
38
39
  | Some (?p,?P) => tac p P
  end.

40
Tactic Notation "iMatchHyp" tactic1(tac) :=
41
42
43
44
  match goal with
  | |- context[ environments.Esnoc _ ?x ?P ] => tac x P
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
45
(** * Start a proof *)
46
Ltac iStartProof :=
Robbert Krebbers's avatar
Robbert Krebbers committed
47
  lazymatch goal with
48
  | |- of_envs _  _ => idtac
49
  | |- ?P =>
50
    lazymatch eval hnf in P with
51
    (* need to use the unfolded version of [uPred_valid] due to the hnf *)
52
53
54
55
    | True  _ => apply tac_adequate
    | _  _ => apply uPred.wand_entails, tac_adequate
    (* need to use the unfolded version of [⊣⊢] due to the hnf *)
    | uPred_equiv' _ _ => apply uPred.iff_equiv, tac_adequate
56
    | _ => fail "iStartProof: not a uPred"
57
    end
Robbert Krebbers's avatar
Robbert Krebbers committed
58
59
60
61
62
63
64
65
  end.

(** * Context manipulation *)
Tactic Notation "iRename" constr(H1) "into" constr(H2) :=
  eapply tac_rename with _ H1 H2 _ _; (* (i:=H1) (j:=H2) *)
    [env_cbv; reflexivity || fail "iRename:" H1 "not found"
    |env_cbv; reflexivity || fail "iRename:" H2 "not fresh"|].

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
Local Inductive esel_pat :=
  | ESelPure
  | ESelName : bool  string  esel_pat.

Ltac iElaborateSelPat pat tac :=
  let rec go pat Δ Hs :=
    lazymatch pat with
    | [] => let Hs' := eval cbv in Hs in tac Hs'
    | SelPure :: ?pat => go pat Δ (ESelPure :: Hs)
    | SelPersistent :: ?pat =>
       let Hs' := eval env_cbv in (env_dom (env_persistent Δ)) in
       let Δ' := eval env_cbv in (envs_clear_persistent Δ) in
       go pat Δ' ((ESelName true <$> Hs') ++ Hs)
    | SelSpatial :: ?pat =>
       let Hs' := eval env_cbv in (env_dom (env_spatial Δ)) in
       let Δ' := eval env_cbv in (envs_clear_spatial Δ) in
       go pat Δ' ((ESelName false <$> Hs') ++ Hs)
    | SelName ?H :: ?pat =>
       lazymatch eval env_cbv in (envs_lookup_delete H Δ) with
       | Some (?p,_,?Δ') => go pat Δ' (ESelName p H :: Hs)
       | None => fail "iElaborateSelPat:" H "not found"
       end
    end in
  lazymatch goal with
  | |- of_envs ?Δ  _ =>
    let pat := sel_pat.parse pat in go pat Δ (@nil esel_pat)
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
94
95
Tactic Notation "iClear" constr(Hs) :=
  let rec go Hs :=
96
    lazymatch Hs with
Robbert Krebbers's avatar
Robbert Krebbers committed
97
    | [] => idtac
98
99
    | ESelPure :: ?Hs => clear; go Hs
    | ESelName _ ?H :: ?Hs =>
Robbert Krebbers's avatar
Robbert Krebbers committed
100
101
102
       eapply tac_clear with _ H _ _; (* (i:=H) *)
         [env_cbv; reflexivity || fail "iClear:" H "not found"|go Hs]
    end in
103
104
  iElaborateSelPat Hs go.

105
106
Tactic Notation "iClear" "(" ident_list(xs) ")" constr(Hs) :=
  iClear Hs; clear xs.
Robbert Krebbers's avatar
Robbert Krebbers committed
107
108
109

(** * Assumptions *)
Tactic Notation "iExact" constr(H) :=
110
111
  eapply tac_assumption with H _ _; (* (i:=H) *)
    [env_cbv; reflexivity || fail "iExact:" H "not found"
112
    |let P := match goal with |- FromAssumption _ ?P _ => P end in
113
     apply _ || fail "iExact:" H ":" P "does not match goal"].
Robbert Krebbers's avatar
Robbert Krebbers committed
114
115
116
117
118
119
120
121
122
123
124
125

Tactic Notation "iAssumptionCore" :=
  let rec find Γ i P :=
    match Γ with
    | Esnoc ?Γ ?j ?Q => first [unify P Q; unify i j| find Γ i P]
    end in
  match goal with
  | |- envs_lookup ?i (Envs ?Γp ?Γs) = Some (_, ?P) =>
     first [is_evar i; fail 1 | env_cbv; reflexivity]
  | |- envs_lookup ?i (Envs ?Γp ?Γs) = Some (_, ?P) =>
     is_evar i; first [find Γp i P | find Γs i P]; env_cbv; reflexivity
  end.
126

Robbert Krebbers's avatar
Robbert Krebbers committed
127
Tactic Notation "iAssumption" :=
128
129
130
131
  let Hass := fresh in
  let rec find p Γ Q :=
    match Γ with
    | Esnoc ?Γ ?j ?P => first
132
       [pose proof (_ : FromAssumption p P Q) as Hass;
133
134
135
136
137
138
139
140
        apply (tac_assumption _ j p P); [env_cbv; reflexivity|apply Hass]
       |find p Γ Q]
    end in
  match goal with
  | |- of_envs (Envs ?Γp ?Γs)  ?Q =>
     first [find true Γp Q | find false Γs Q
           |fail "iAssumption:" Q "not found"]
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
141
142
143
144
145

(** * False *)
Tactic Notation "iExFalso" := apply tac_ex_falso.

(** * Making hypotheses persistent or pure *)
146
Local Tactic Notation "iPersistent" constr(H) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
147
148
  eapply tac_persistent with _ H _ _ _; (* (i:=H) *)
    [env_cbv; reflexivity || fail "iPersistent:" H "not found"
149
    |let Q := match goal with |- IntoPersistentP ?Q _ => Q end in
150
     apply _ || fail "iPersistent:" Q "not persistent"
Robbert Krebbers's avatar
Robbert Krebbers committed
151
152
    |env_cbv; reflexivity|].

153
Local Tactic Notation "iPure" constr(H) "as" simple_intropattern(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
154
155
  eapply tac_pure with _ H _ _ _; (* (i:=H1) *)
    [env_cbv; reflexivity || fail "iPure:" H "not found"
156
    |let P := match goal with |- IntoPure ?P _ => P end in
157
     apply _ || fail "iPure:" P "not pure"
Robbert Krebbers's avatar
Robbert Krebbers committed
158
159
    |intros pat].

160
161
Tactic Notation "iPureIntro" :=
  eapply tac_pure_intro;
162
    [let P := match goal with |- FromPure ?P _ => P end in
163
     apply _ || fail "iPureIntro:" P "not pure"|].
Robbert Krebbers's avatar
Robbert Krebbers committed
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
(** Framing *)
Local Ltac iFrameFinish :=
  lazy iota beta;
  try match goal with
  | |- _  True => exact (uPred.pure_intro _ _ I)
  end.

Local Ltac iFramePure t :=
  let φ := type of t in
  eapply (tac_frame_pure _ _ _ _ t);
    [apply _ || fail "iFrame: cannot frame" φ
    |iFrameFinish].

Local Ltac iFrameHyp H :=
  eapply tac_frame with _ H _ _ _;
    [env_cbv; reflexivity || fail "iFrame:" H "not found"
    |let R := match goal with |- Frame ?R _ _ => R end in
     apply _ || fail "iFrame: cannot frame" R
    |iFrameFinish].

Local Ltac iFrameAnyPure :=
  repeat match goal with H : _ |- _ => iFramePure H end.

Local Ltac iFrameAnyPersistent :=
  let rec go Hs :=
    match Hs with [] => idtac | ?H :: ?Hs => repeat iFrameHyp H; go Hs end in
  match goal with
  | |- of_envs ?Δ  _ =>
     let Hs := eval cbv in (env_dom (env_persistent Δ)) in go Hs
  end.

Local Ltac iFrameAnySpatial :=
  let rec go Hs :=
    match Hs with [] => idtac | ?H :: ?Hs => try iFrameHyp H; go Hs end in
  match goal with
  | |- of_envs ?Δ  _ =>
     let Hs := eval cbv in (env_dom (env_spatial Δ)) in go Hs
  end.

Tactic Notation "iFrame" := iFrameAnySpatial.

Tactic Notation "iFrame" "(" constr(t1) ")" :=
  iFramePure t1.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) ")" :=
  iFramePure t1; iFrame ( t2 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) ")" :=
  iFramePure t1; iFrame ( t2 t3 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4) ")" :=
  iFramePure t1; iFrame ( t2 t3 t4 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) ")" :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) ")" :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) constr(t7) ")" :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 ).
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) constr(t7) constr(t8)")" :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 t8 ).

Tactic Notation "iFrame" constr(Hs) :=
  let rec go Hs :=
    match Hs with
    | [] => idtac
231
232
233
234
    | SelPure :: ?Hs => iFrameAnyPure; go Hs
    | SelPersistent :: ?Hs => iFrameAnyPersistent; go Hs
    | SelSpatial :: ?Hs => iFrameAnySpatial; go Hs
    | SelName ?H :: ?Hs => iFrameHyp H; go Hs
235
    end
236
  in let Hs := sel_pat.parse Hs in go Hs.
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
Tactic Notation "iFrame" "(" constr(t1) ")" constr(Hs) :=
  iFramePure t1; iFrame Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) ")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) ")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4) ")"
    constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 t4 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) ")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) ")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) constr(t7) ")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 ) Hs.
Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
    constr(t5) constr(t6) constr(t7) constr(t8)")" constr(Hs) :=
  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 t8 ) Hs.

Robbert Krebbers's avatar
Robbert Krebbers committed
259
(** * Specialize *)
260
261
262
263
264
Record iTrm {X As} :=
  ITrm { itrm : X ; itrm_vars : hlist As ; itrm_hyps : string }.
Arguments ITrm {_ _} _ _ _.

Notation "( H $! x1 .. xn )" :=
265
  (ITrm H (hcons x1 .. (hcons xn hnil) ..) "") (at level 0, x1, xn at level 9).
266
Notation "( H $! x1 .. xn 'with' pat )" :=
267
  (ITrm H (hcons x1 .. (hcons xn hnil) ..) pat) (at level 0, x1, xn at level 9).
268
269
Notation "( H 'with' pat )" := (ITrm H hnil pat) (at level 0).

270
Local Tactic Notation "iSpecializeArgs" constr(H) open_constr(xs) :=
271
272
273
274
275
  match xs with
  | hnil => idtac
  | _ =>
    eapply tac_forall_specialize with _ H _ _ _ xs; (* (i:=H) (a:=x) *)
      [env_cbv; reflexivity || fail 1 "iSpecialize:" H "not found"
276
277
      |let P := match goal with |- ForallSpecialize _ ?P _ => P end in
       apply _ || fail 1 "iSpecialize:" P "not a forall of the right arity or type"
Robbert Krebbers's avatar
Robbert Krebbers committed
278
      |cbn [himpl hcurry]; reflexivity|]
279
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
280

281
Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
282
  let solve_to_wand H1 :=
283
    let P := match goal with |- IntoWand ?P _ _ => P end in
284
    apply _ || fail "iSpecialize:" P "not an implication/wand" in
Robbert Krebbers's avatar
Robbert Krebbers committed
285
286
287
  let rec go H1 pats :=
    lazymatch pats with
    | [] => idtac
288
    | SName ?H2 :: ?pats =>
Robbert Krebbers's avatar
Robbert Krebbers committed
289
290
291
       eapply tac_specialize with _ _ H2 _ H1 _ _ _ _; (* (j:=H1) (i:=H2) *)
         [env_cbv; reflexivity || fail "iSpecialize:" H2 "not found"
         |env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
292
293
         |let P := match goal with |- IntoWand ?P ?Q _ => P end in
          let Q := match goal with |- IntoWand ?P ?Q _ => Q end in
294
          apply _ || fail "iSpecialize: cannot instantiate" P "with" Q
Robbert Krebbers's avatar
Robbert Krebbers committed
295
         |env_cbv; reflexivity|go H1 pats]
296
    | SGoalPersistent :: ?pats =>
297
       eapply tac_specialize_assert_persistent with _ _ H1 _ _ _ _;
298
299
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
300
301
         |let Q := match goal with |- PersistentP ?Q => Q end in
          apply _ || fail "iSpecialize:" Q "not persistent"
302
303
304
305
         |env_cbv; reflexivity
         |(*goal*)
         |go H1 pats]
    | SGoalPure :: ?pats =>
306
       eapply tac_specialize_assert_pure with _ H1 _ _ _ _ _;
Robbert Krebbers's avatar
Robbert Krebbers committed
307
308
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
309
         |let Q := match goal with |- FromPure ?Q _ => Q end in
310
311
312
313
          apply _ || fail "iSpecialize:" Q "not pure"
         |env_cbv; reflexivity
         |(*goal*)
         |go H1 pats]
314
    | SGoal (SpecGoal ?m ?lr ?Hs_frame ?Hs) :: ?pats =>
315
       let Hs' := eval cbv in (if lr then Hs else Hs_frame ++ Hs) in
316
       eapply tac_specialize_assert with _ _ _ H1 _ lr Hs' _ _ _ _;
Robbert Krebbers's avatar
Robbert Krebbers committed
317
318
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
319
320
321
         |match m with
          | false => apply elim_modal_dummy
          | true => apply _ || fail "iSpecialize: goal not a modality"
322
          end
323
         |env_cbv; reflexivity || fail "iSpecialize:" Hs "not found"
324
         |iFrame Hs_frame (*goal*)
Robbert Krebbers's avatar
Robbert Krebbers committed
325
         |go H1 pats]
326
327
    end in let pats := spec_pat.parse pat in go H pats.

Robbert Krebbers's avatar
Robbert Krebbers committed
328
(* The argument [p] denotes whether the conclusion of the specialized term is
329
330
331
332
333
persistent. If so, one can use all spatial hypotheses for both proving the
premises and the remaning goal. The argument [p] can either be a Boolean or an
introduction pattern, which will be coerced into [true] when it solely contains
`#` or `%` patterns at the top-level. *)
Tactic Notation "iSpecializeCore" open_constr(t) "as" constr(p) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
334
  let p := intro_pat_persistent p in
335
336
  let t :=
    match type of t with string => constr:(ITrm t hnil "") | _ => t end in
337
338
  lazymatch t with
  | ITrm ?H ?xs ?pat =>
339
340
341
342
343
344
345
346
347
    lazymatch type of H with
    | string =>
      lazymatch p with
      | true =>
         eapply tac_specialize_persistent_helper with _ H _ _ _;
           [env_cbv; reflexivity || fail "iSpecialize:" H "not found"
           |iSpecializeArgs H xs; iSpecializePat H pat; last (iExact H)
           |let Q := match goal with |- PersistentP ?Q => Q end in
            apply _ || fail "iSpecialize:" Q "not persistent"
348
349
           |env_cbv; reflexivity|(* goal *)]
      | false => iSpecializeArgs H xs; iSpecializePat H pat
350
351
      end
    | _ => fail "iSpecialize:" H "should be a hypothesis, use iPoseProof instead"
352
    end
353
  | _ => fail "iSpecialize:" t "should be a proof mode term"
354
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
355

356
Tactic Notation "iSpecialize" open_constr(t) :=
357
358
359
  iSpecializeCore t as false.
Tactic Notation "iSpecialize" open_constr(t) "as" "#" :=
  iSpecializeCore t as true.
360

Robbert Krebbers's avatar
Robbert Krebbers committed
361
(** * Pose proof *)
362
363
(* The tactic [iIntoValid] tactic solves a goal [uPred_valid Q]. The
arguments [t] is a Coq term whose type is of the following shape:
364

365
- [∀ (x_1 : A_1) .. (x_n : A_n), uPred_valid Q]
366
- [∀ (x_1 : A_1) .. (x_n : A_n), P1 ⊢ P2], in which case [Q] becomes [P1 -∗ P2]
367
368
369
370
- [∀ (x_1 : A_1) .. (x_n : A_n), P1 ⊣⊢ P2], in which case [Q] becomes [P1 ↔ P2]

The tactic instantiates each dependent argument [x_i] with an evar and generates
a goal [P] for non-dependent arguments [x_i : P]. *)
371
Tactic Notation "iIntoValid" open_constr(t) :=
372
  let rec go t :=
373
374
    let tT := type of t in
    lazymatch eval hnf in tT with
375
376
    | True  _ => apply t
    | _  _ => apply (uPred.entails_wand _ _ t)
377
378
    (* need to use the unfolded version of [⊣⊢] due to the hnf *)
    | uPred_equiv' _ _ => apply (uPred.equiv_iff _ _ t)
379
    | ?P  ?Q => let H := fresh in assert P as H; [|go uconstr:(t H); clear H]
380
381
382
383
384
    |  _ : ?T, _ =>
       (* Put [T] inside an [id] to avoid TC inference from being invoked. *)
       (* This is a workarround for Coq bug #4969. *)
       let e := fresh in evar (e:id T);
       let e' := eval unfold e in e in clear e; go (t e')
385
386
    end in
  go t.
387

388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
(* The tactic [tac] is called with a temporary fresh name [H]. The argument
[lazy_tc] denotes whether type class inference on the premises of [lem] should
be performed before (if false) or after (if true) [tac H] is called. *)
Tactic Notation "iPoseProofCore" open_constr(lem)
    "as" constr(p) constr(lazy_tc) tactic(tac) :=
  try iStartProof;
  let Htmp := iFresh in
  let t :=
    lazymatch lem with ITrm ?t ?xs ?pat => t | _ => lem end in
  let spec_tac _ :=
    lazymatch lem with
    | ITrm ?t ?xs ?pat => iSpecializeCore (ITrm Htmp xs pat) as p
    | _ => idtac
    end in
  let go goal_tac :=
403
404
405
406
407
    lazymatch type of t with
    | string =>
       eapply tac_pose_proof_hyp with _ _ t _ Htmp _;
         [env_cbv; reflexivity || fail "iPoseProof:" t "not found"
         |env_cbv; reflexivity || fail "iPoseProof:" Htmp "not fresh"
408
         |goal_tac ()]
409
410
    | _ =>
       eapply tac_pose_proof with _ Htmp _; (* (j:=H) *)
411
         [iIntoValid t
412
         |env_cbv; reflexivity || fail "iPoseProof:" Htmp "not fresh"
413
         |goal_tac ()]
414
    end;
415
416
417
418
    try (apply _) in
  lazymatch eval compute in lazy_tc with
  | true => go ltac:(fun _ => spec_tac (); last (tac Htmp))
  | false => go spec_tac; last (tac Htmp)
Robbert Krebbers's avatar
Robbert Krebbers committed
419
420
  end.

421
Tactic Notation "iPoseProof" open_constr(lem) "as" constr(H) :=
422
  iPoseProofCore lem as false false (fun Htmp => iRename Htmp into H).
Robbert Krebbers's avatar
Robbert Krebbers committed
423
424

(** * Apply *)
425
Tactic Notation "iApply" open_constr(lem) :=
426
427
  let rec go H := first
    [eapply tac_apply with _ H _ _ _;
428
      [env_cbv; reflexivity
429
430
      |apply _
      |lazy beta (* reduce betas created by instantiation *)]
431
    |iSpecializePat H "[]"; last go H] in
432
433
  iPoseProofCore lem as false true (fun H =>
    first [iExact H|go H|iTypeOf H (fun Q => fail 1 "iApply: cannot apply" Q)]).
Robbert Krebbers's avatar
Robbert Krebbers committed
434
435

(** * Revert *)
436
Local Tactic Notation "iForallRevert" ident(x) :=
437
438
439
440
441
442
  let err x :=
    intros x;
    iMatchHyp (fun H P =>
      lazymatch P with
      | context [x] => fail 2 "iRevert:" x "is used in hypothesis" H
      end) in
443
444
  let A := type of x in
  lazymatch type of A with
445
446
447
  | Prop => revert x; first [apply tac_pure_revert|err x]
  | _ => revert x; first [apply tac_forall_revert|err x]
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
448
449

Tactic Notation "iRevert" constr(Hs) :=
450
451
  let rec go Hs :=
    lazymatch Hs with
452
    | [] => idtac
453
454
455
456
457
458
459
    | ESelPure :: ?Hs =>
       repeat match goal with x : _ |- _ => revert x end;
       go Hs
    | ESelName _ ?H :: ?Hs =>
       eapply tac_revert with _ H _ _; (* (i:=H2) *)
         [env_cbv; reflexivity || fail "iRevert:" H "not found"
         |env_cbv; go Hs]
460
    end in
461
  iElaborateSelPat Hs go.
Robbert Krebbers's avatar
Robbert Krebbers committed
462

463
Tactic Notation "iRevert" "(" ident(x1) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
464
  iForallRevert x1.
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ")" :=
  iForallRevert x2; iRevert ( x1 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ")" :=
  iForallRevert x3; iRevert ( x1 x2 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4) ")" :=
  iForallRevert x4; iRevert ( x1 x2 x3 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ")" :=
  iForallRevert x5; iRevert ( x1 x2 x3 x4 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ")" :=
  iForallRevert x6; iRevert ( x1 x2 x3 x4 x5 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ident(x7) ")" :=
  iForallRevert x7; iRevert ( x1 x2 x3 x4 x5 x6 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ident(x7) ident(x8) ")" :=
  iForallRevert x8; iRevert ( x1 x2 x3 x4 x5 x6 x7 ).

Tactic Notation "iRevert" "(" ident(x1) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 x3 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
491
    constr(Hs) :=
492
493
494
495
496
497
498
499
500
501
502
503
504
  iRevert Hs; iRevert ( x1 x2 x3 x4 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 x3 x4 x5 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 x3 x4 x5 x6 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ident(x7) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 x3 x4 x5 x6 x7 ).
Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
    ident(x5) ident(x6) ident(x7) ident(x8) ")" constr(Hs) :=
  iRevert Hs; iRevert ( x1 x2 x3 x4 x5 x6 x7 x8 ).
Robbert Krebbers's avatar
Robbert Krebbers committed
505
506
507

(** * Disjunction *)
Tactic Notation "iLeft" :=
508
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
509
  eapply tac_or_l;
510
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
511
512
     apply _ || fail "iLeft:" P "not a disjunction"|].
Tactic Notation "iRight" :=
513
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
514
  eapply tac_or_r;
515
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
516
517
     apply _ || fail "iRight:" P "not a disjunction"|].

518
Local Tactic Notation "iOrDestruct" constr(H) "as" constr(H1) constr(H2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
519
520
  eapply tac_or_destruct with _ _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
    [env_cbv; reflexivity || fail "iOrDestruct:" H "not found"
521
    |let P := match goal with |- IntoOr ?P _ _ => P end in
522
     apply _ || fail "iOrDestruct: cannot destruct" P
Robbert Krebbers's avatar
Robbert Krebbers committed
523
524
525
526
527
    |env_cbv; reflexivity || fail "iOrDestruct:" H1 "not fresh"
    |env_cbv; reflexivity || fail "iOrDestruct:" H2 "not fresh"| |].

(** * Conjunction and separating conjunction *)
Tactic Notation "iSplit" :=
528
  iStartProof;
529
530
531
  lazymatch goal with
  | |- _  _ =>
    eapply tac_and_split;
532
      [let P := match goal with |- FromAnd ?P _ _ => P end in
533
534
       apply _ || fail "iSplit:" P "not a conjunction"| |]
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
535
536

Tactic Notation "iSplitL" constr(Hs) :=
537
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
538
539
  let Hs := words Hs in
  eapply tac_sep_split with _ _ false Hs _ _; (* (js:=Hs) *)
540
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
541
     apply _ || fail "iSplitL:" P "not a separating conjunction"
542
    |env_cbv; reflexivity || fail "iSplitL: hypotheses" Hs
543
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
544
Tactic Notation "iSplitR" constr(Hs) :=
545
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
546
547
  let Hs := words Hs in
  eapply tac_sep_split with _ _ true Hs _ _; (* (js:=Hs) *)
548
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
549
     apply _ || fail "iSplitR:" P "not a separating conjunction"
550
    |env_cbv; reflexivity || fail "iSplitR: hypotheses" Hs
551
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
552
553
554
555

Tactic Notation "iSplitL" := iSplitR "".
Tactic Notation "iSplitR" := iSplitL "".

556
557
558
559
560
561
562
563
564
565
566
567
568
Local Tactic Notation "iAndDestruct" constr(H) "as" constr(H1) constr(H2) :=
  eapply tac_and_destruct with _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
    [env_cbv; reflexivity || fail "iAndDestruct:" H "not found"
    |let P := match goal with |- IntoAnd _ ?P _ _ => P end in
     apply _ || fail "iAndDestruct: cannot destruct" P
    |env_cbv; reflexivity || fail "iAndDestruct:" H1 "or" H2 " not fresh"|].

Local Tactic Notation "iAndDestructChoice" constr(H) "as" constr(lr) constr(H') :=
  eapply tac_and_destruct_choice with _ H _ lr H' _ _ _;
    [env_cbv; reflexivity || fail "iAndDestruct:" H "not found"
    |let P := match goal with |- IntoAnd _ ?P _ _ => P end in
     apply _ || fail "iAndDestruct: cannot destruct" P
    |env_cbv; reflexivity || fail "iAndDestruct:" H' " not fresh"|].
Robbert Krebbers's avatar
Robbert Krebbers committed
569
570
571
572
573

Tactic Notation "iCombine" constr(H1) constr(H2) "as" constr(H) :=
  eapply tac_combine with _ _ _ H1 _ _ H2 _ _ H _;
    [env_cbv; reflexivity || fail "iCombine:" H1 "not found"
    |env_cbv; reflexivity || fail "iCombine:" H2 "not found"
574
575
    |let P1 := match goal with |- FromSep _ ?P1 _ => P1 end in
     let P2 := match goal with |- FromSep _ _ ?P2 => P2 end in
576
     apply _ || fail "iCombine: cannot combine" P1 "and" P2
Robbert Krebbers's avatar
Robbert Krebbers committed
577
578
579
    |env_cbv; reflexivity || fail "iCombine:" H "not fresh"|].

(** * Existential *)
Robbert Krebbers's avatar
Robbert Krebbers committed
580
Tactic Notation "iExists" uconstr(x1) :=
581
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
582
  eapply tac_exist;
583
    [let P := match goal with |- FromExist ?P _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
584
     apply _ || fail "iExists:" P "not an existential"
Robbert Krebbers's avatar
Robbert Krebbers committed
585
    |cbv beta; eexists x1].
Robbert Krebbers's avatar
Robbert Krebbers committed
586

Robbert Krebbers's avatar
Robbert Krebbers committed
587
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
588
  iExists x1; iExists x2.
Robbert Krebbers's avatar
Robbert Krebbers committed
589
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
590
  iExists x1; iExists x2, x3.
Robbert Krebbers's avatar
Robbert Krebbers committed
591
592
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
593
  iExists x1; iExists x2, x3, x4.
Robbert Krebbers's avatar
Robbert Krebbers committed
594
595
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
596
  iExists x1; iExists x2, x3, x4, x5.
Robbert Krebbers's avatar
Robbert Krebbers committed
597
598
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
599
  iExists x1; iExists x2, x3, x4, x5, x6.
Robbert Krebbers's avatar
Robbert Krebbers committed
600
601
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) "," uconstr(x7) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
602
  iExists x1; iExists x2, x3, x4, x5, x6, x7.
Robbert Krebbers's avatar
Robbert Krebbers committed
603
604
605
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) "," uconstr(x7) ","
    uconstr(x8) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
606
607
  iExists x1; iExists x2, x3, x4, x5, x6, x7, x8.

608
609
Local Tactic Notation "iExistDestruct" constr(H)
    "as" simple_intropattern(x) constr(Hx) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
610
611
  eapply tac_exist_destruct with H _ Hx _ _; (* (i:=H) (j:=Hx) *)
    [env_cbv; reflexivity || fail "iExistDestruct:" H "not found"
612
    |let P := match goal with |- IntoExist ?P _ => P end in
613
     apply _ || fail "iExistDestruct: cannot destruct" P|];
614
615
616
617
  let y := fresh in
  intros y; eexists; split;
    [env_cbv; reflexivity || fail "iExistDestruct:" Hx "not fresh"
    |revert y; intros x].
Robbert Krebbers's avatar
Robbert Krebbers committed
618

Robbert Krebbers's avatar
Robbert Krebbers committed
619
620
(** * Always *)
Tactic Notation "iAlways":=
621
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
622
623
624
625
  apply tac_always_intro;
    [reflexivity || fail "iAlways: spatial context non-empty"|].

(** * Later *)
626
Tactic Notation "iNext" open_constr(n) :=
627
  iStartProof;
628
629
630
631
632
633
634
635
636
637
  let P := match goal with |- _  ?P => P end in
  try lazymatch n with 0 => fail 1 "iNext: cannot strip 0 laters" end;
  eapply (tac_next _ _ n);
    [apply _ || fail "iNext:" P "does not contain" n "laters"
    |lazymatch goal with
     | |- IntoLaterNEnvs 0 _ _ => fail "iNext:" P "does not contain laters"
     | _ => apply _
     end|].

Tactic Notation "iNext":= iNext _.
Robbert Krebbers's avatar
Robbert Krebbers committed
638

639
(** * Update modality *)
640
Tactic Notation "iModIntro" :=
641
  iStartProof;
642
  eapply tac_modal_intro;
643
    [let P := match goal with |- FromModal ?P _ => P end in
644
645
646
647
648
649
650
651
     apply _ || fail "iModIntro:" P "not a modality"|].

Tactic Notation "iModCore" constr(H) :=
  eapply tac_modal_elim with _ H _ _ _ _;
    [env_cbv; reflexivity || fail "iMod:" H "not found"
    |let P := match goal with |- ElimModal ?P _ _ _ => P end in
     let Q := match goal with |- ElimModal _ _ ?Q _ => Q end in
     apply _ || fail "iMod: cannot eliminate modality " P "in" Q
Robbert Krebbers's avatar
Robbert Krebbers committed
652
653
    |env_cbv; reflexivity|].

654
(** * Basic destruct tactic *)
655
Local Tactic Notation "iDestructHyp" constr(H) "as" constr(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
656
657
658
  let rec go Hz pat :=
    lazymatch pat with
    | IAnom => idtac
659
    | IDrop => iClear Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
660
    | IFrame => iFrame Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
661
    | IName ?y => iRename Hz into y
662
    | IList [[]] => iExFalso; iExact Hz
663
664
    | IList [[?pat1; IDrop]] => iAndDestructChoice Hz as true Hz; go Hz pat1
    | IList [[IDrop; ?pat2]] => iAndDestructChoice Hz as false Hz; go Hz pat2
Robbert Krebbers's avatar
Robbert Krebbers committed
665
    | IList [[?pat1; ?pat2]] =>
666
       let Hy := iFresh in iAndDestruct Hz as Hz Hy; go Hz pat1; go Hy pat2
Robbert Krebbers's avatar
Robbert Krebbers committed
667
    | IList [[?pat1];[?pat2]] => iOrDestruct Hz as Hz Hz; [go Hz pat1|go Hz pat2]
Robbert Krebbers's avatar
Robbert Krebbers committed
668
669
    | IPureElim => iPure Hz as ?
    | IAlwaysElim ?pat => iPersistent Hz; go Hz pat
670
    | IModalElim ?pat => iModCore Hz; go Hz pat
Robbert Krebbers's avatar
Robbert Krebbers committed
671
672
673
674
    | _ => fail "iDestruct:" pat "invalid"
    end
  in let pat := intro_pat.parse_one pat in go H pat.

675
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
676
677
    constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as @ pat.
678
679
680
681
682
683
684
685
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
    simple_intropattern(x2) ")" constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
    simple_intropattern(x2) simple_intropattern(x3) ")" constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
686
    constr(pat) :=
687
688
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 x4 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
Robbert Krebbers's avatar
Robbert Krebbers committed
689
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
690
691
692
    simple_intropattern(x5) ")" constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 x4 x5 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
Robbert Krebbers's avatar
Robbert Krebbers committed
693
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
694
695
696
    simple_intropattern(x5) simple_intropattern(x6) ")" constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 x4 x5 x6 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
Robbert Krebbers's avatar
Robbert Krebbers committed
697
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
698
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
699
    constr(pat) :=
700
701
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 x4 x5 x6 x7 ) pat.
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1)
Robbert Krebbers's avatar
Robbert Krebbers committed
702
703
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7)
704
705
    simple_intropattern(x8) ")" constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as ( x2 x3 x4 x5 x6 x7 x8 ) pat.
Robbert Krebbers's avatar
Robbert Krebbers committed
706
707

(** * Introduction tactic *)
708
Local Tactic Notation "iIntro" "(" simple_intropattern(x) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
709
  try iStartProof;
710
711
712
713
714
  try first
    [(* (∀ _, _) *) apply tac_forall_intro
    |(* (?P → _) *) eapply tac_impl_intro_pure;
      [let P := match goal with |- IntoPure ?P _ => P end in
       apply _ || fail "iIntro:" P "not pure"|]
715
    |(* (?P -∗ _) *) eapply tac_wand_intro_pure;
716
      [let P := match goal with |- IntoPure ?P _ => P end in
717
       apply _ || fail "iIntro:" P "not pure"|]
Robbert Krebbers's avatar
Robbert Krebbers committed
718
719
    |(* ⌜∀ _, _⌝ *) apply tac_pure_forall_intro
    |(* ⌜_ → _⌝ *) apply tac_pure_impl_intro];
720
  intros x.
721

Robbert Krebbers's avatar
Robbert Krebbers committed
722
723
724
Local Tactic Notation "iIntro" constr(H) :=
  iStartProof;
  first
725
  [ (* (?Q → _) *)
726
    eapply tac_impl_intro with _ H; (* (i:=H) *)
727
728
      [reflexivity || fail 1 "iIntro: introducing" H
                             "into non-empty spatial context"
729
      |env_cbv; reflexivity || fail "iIntro:" H "not fresh"|]
730
  | (* (_ -∗ _) *)
731
    eapply tac_wand_intro with _ H; (* (i:=H) *)
732
733
      [env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
734

Robbert Krebbers's avatar
Robbert Krebbers committed
735
736
737
Local Tactic Notation "iIntro" "#" constr(H) :=
  iStartProof;
  first
738
  [ (* (?P → _) *)
739
    eapply tac_impl_intro_persistent with _ H _; (* (i:=H) *)
740
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
741
742
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
743
  | (* (?P -∗ _) *)
744
    eapply tac_wand_intro_persistent with _ H _; (* (i:=H) *)
745
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
746
747
748
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
749

750
Local Tactic Notation "iIntroForall" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
751
  try iStartProof;
752
753
754
  lazymatch goal with
  | |-  _, ?P => fail
  | |-  _, _ => intro
755
  | |- _  ( x : _, _) => let x' := fresh x in iIntro (x')
756
757
  end.
Local Tactic Notation "iIntro" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
758
  try iStartProof;
759
760
  lazymatch goal with
  | |- _  ?P => intro
761
  | |- _  (_ - _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
762
  | |- _  (_  _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
763
764
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
765
766
767
768
Tactic Notation "iIntros" constr(pat) :=
  let rec go pats :=
    lazymatch pats with
    | [] => idtac
Robbert Krebbers's avatar
Robbert Krebbers committed
769
770
771
772
773
774
775
    | IPureElim :: ?pats => iIntro (?); go pats
    | IAlwaysElim IAnom :: ?pats => let H := iFresh in iIntro #H; go pats
    | IAnom :: ?pats => let H := iFresh in iIntro H; go pats
    | IAlwaysElim (IName ?H) :: ?pats => iIntro #H; go pats
    | IName ?H :: ?pats => iIntro H; go pats
    | IPureIntro :: ?pats => iPureIntro; go pats
    | IAlwaysIntro :: ?pats => iAlways; go pats
776
    | IModalIntro :: ?pats => iModIntro; go pats
Robbert Krebbers's avatar
Robbert Krebbers committed
777
    | ISimpl :: ?pats => simpl; go pats
778
779
    | IForall :: ?pats => repeat iIntroForall; go pats
    | IAll :: ?pats => repeat (iIntroForall || iIntro); go pats
780
781
782
783
784
785
786
    | IClear ?cpats :: ?pats =>
       let rec clr cpats :=
         match cpats with
         | [] => go pats
         | (false,?H) :: ?cpats => iClear H; clr cpats
         | (true,?H) :: ?cpats => iFrame H; clr cpats
         end in clr cpats
Robbert Krebbers's avatar
Robbert Krebbers committed
787
    | IAlwaysElim ?pat :: ?pats =>
Robbert Krebbers's avatar
Robbert Krebbers committed
788
789
790
791
       let H := iFresh in iIntro #H; iDestructHyp H as pat; go pats
    | ?pat :: ?pats =>
       let H := iFresh in iIntro H; iDestructHyp H as pat; go pats
    end
Robbert Krebbers's avatar
Robbert Krebbers committed
792
  in let pats := intro_pat.parse pat in go pats.
Robbert Krebbers's avatar
Robbert Krebbers committed
793
Tactic Notation "iIntros" := iIntros [IAll].
Robbert Krebbers's avatar
Robbert Krebbers committed
794

795
Tactic Notation "iIntros" "(" simple_intropattern(x1) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
796
  iIntro ( x1 ).
797
798
799
800
801
802
803
804
805
806
807
808
809
Tactic Notation "iIntros" "(" simple_intropattern(x1)
    simple_intropattern(x2) ")" :=
  iIntros ( x1 ); iIntro ( x2 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) ")" :=
  iIntros ( x1 x2 ); iIntro ( x3 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) simple_intropattern(x4) ")" :=
  iIntros ( x1 x2 x3 ); iIntro ( x4 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5) ")" :=
  iIntros ( x1 x2 x3 x4 ); iIntro ( x5 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
Robbert Krebbers's avatar
Robbert Krebbers committed
810
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
811
812
813
    simple_intropattern(x6) ")" :=
  iIntros ( x1 x2 x3 x4 x5 ); iIntro ( x6 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
Robbert Krebbers's avatar
Robbert Krebbers committed
814
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
815
816
817
    simple_intropattern(x6) simple_intropattern(x7) ")" :=
  iIntros ( x1 x2 x3 x4 x5 x6 ); iIntro ( x7 ).
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
Robbert Krebbers's avatar
Robbert Krebbers committed
818
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
819
820
    simple_intropattern(x6) simple_intropattern(x7) simple_intropattern(x8) ")" :=
  iIntros ( x1 x2 x3 x4 x5 x6 x7 ); iIntro ( x8 ).
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
    simple_intropattern(x6) simple_intropattern(x7) simple_intropattern(x8)
    simple_intropattern(x9) ")" :=
  iIntros ( x1 x2 x3 x4 x5 x6 x7