tactics.v 56.3 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.
Robbert Krebbers's avatar
Robbert Krebbers committed
8
9

Declare Reduction env_cbv := cbv [
10
  beq ascii_beq string_beq
11
12
  env_lookup env_lookup_delete env_delete env_app env_replace env_dom
  env_persistent env_spatial env_spatial_is_nil envs_dom
13
  envs_lookup envs_lookup_delete envs_delete envs_snoc envs_app
14
15
    envs_simple_replace envs_replace envs_split
    envs_clear_spatial envs_clear_persistent
16
    envs_split_go envs_split].
Robbert Krebbers's avatar
Robbert Krebbers committed
17
18
19
Ltac env_cbv :=
  match goal with |- ?u => let v := eval env_cbv in u in change v end.

20
(** * Misc *)
21
22
(* Tactic Notation tactics cannot return terms *)
Ltac iFresh' H :=
Robbert Krebbers's avatar
Robbert Krebbers committed
23
24
  lazymatch goal with
  |- of_envs ?Δ  _ =>
25
26
27
     (* [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
28
29
     eval vm_compute in (fresh_string_of_set H (of_list Hs))
  | _ => H
Robbert Krebbers's avatar
Robbert Krebbers committed
30
  end.
31
Ltac iFresh := iFresh' "~".
Robbert Krebbers's avatar
Robbert Krebbers committed
32
33
34

Tactic Notation "iTypeOf" constr(H) tactic(tac):=
  let Δ := match goal with |- of_envs ?Δ  _ => Δ end in
35
  lazymatch eval env_cbv in (envs_lookup H Δ) with
Robbert Krebbers's avatar
Robbert Krebbers committed
36
37
38
  | Some (?p,?P) => tac p P
  end.

39
Tactic Notation "iMatchHyp" tactic1(tac) :=
40
41
42
43
  match goal with
  | |- context[ environments.Esnoc _ ?x ?P ] => tac x P
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
44
(** * Start a proof *)
45
Ltac iStartProof :=
Robbert Krebbers's avatar
Robbert Krebbers committed
46
  lazymatch goal with
47
  | |- of_envs _  _ => idtac
48
  | |- ?P =>
49
    lazymatch eval hnf in P with
50
    (* need to use the unfolded version of [uPred_valid] due to the hnf *)
51
52
53
54
    | 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
55
    | _ => fail "iStartProof: not a uPred"
56
    end
Robbert Krebbers's avatar
Robbert Krebbers committed
57
58
59
60
61
62
63
64
  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"|].

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
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
93
94
Tactic Notation "iClear" constr(Hs) :=
  let rec go Hs :=
95
    lazymatch Hs with
Robbert Krebbers's avatar
Robbert Krebbers committed
96
    | [] => idtac
97
98
    | ESelPure :: ?Hs => clear; go Hs
    | ESelName _ ?H :: ?Hs =>
Robbert Krebbers's avatar
Robbert Krebbers committed
99
100
101
       eapply tac_clear with _ H _ _; (* (i:=H) *)
         [env_cbv; reflexivity || fail "iClear:" H "not found"|go Hs]
    end in
102
103
  iElaborateSelPat Hs go.

104
105
Tactic Notation "iClear" "(" ident_list(xs) ")" constr(Hs) :=
  iClear Hs; clear xs.
Robbert Krebbers's avatar
Robbert Krebbers committed
106
107
108

(** * Assumptions *)
Tactic Notation "iExact" constr(H) :=
109
110
  eapply tac_assumption with H _ _; (* (i:=H) *)
    [env_cbv; reflexivity || fail "iExact:" H "not found"
111
    |let P := match goal with |- FromAssumption _ ?P _ => P end in
112
     apply _ || fail "iExact:" H ":" P "does not match goal"].
Robbert Krebbers's avatar
Robbert Krebbers committed
113
114
115
116
117
118
119
120
121
122
123
124

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.
125

Robbert Krebbers's avatar
Robbert Krebbers committed
126
Tactic Notation "iAssumption" :=
127
128
129
130
  let Hass := fresh in
  let rec find p Γ Q :=
    match Γ with
    | Esnoc ?Γ ?j ?P => first
131
       [pose proof (_ : FromAssumption p P Q) as Hass;
132
133
134
135
136
137
138
139
        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
140
141
142
143
144

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

(** * Making hypotheses persistent or pure *)
145
Local Tactic Notation "iPersistent" constr(H) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
146
147
  eapply tac_persistent with _ H _ _ _; (* (i:=H) *)
    [env_cbv; reflexivity || fail "iPersistent:" H "not found"
148
    |let Q := match goal with |- IntoPersistentP ?Q _ => Q end in
149
     apply _ || fail "iPersistent:" Q "not persistent"
Robbert Krebbers's avatar
Robbert Krebbers committed
150
151
    |env_cbv; reflexivity|].

152
Local Tactic Notation "iPure" constr(H) "as" simple_intropattern(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
153
154
  eapply tac_pure with _ H _ _ _; (* (i:=H1) *)
    [env_cbv; reflexivity || fail "iPure:" H "not found"
155
    |let P := match goal with |- IntoPure ?P _ => P end in
156
     apply _ || fail "iPure:" P "not pure"
Robbert Krebbers's avatar
Robbert Krebbers committed
157
158
    |intros pat].

159
160
Tactic Notation "iPureIntro" :=
  eapply tac_pure_intro;
161
    [let P := match goal with |- FromPure ?P _ => P end in
162
     apply _ || fail "iPureIntro:" P "not pure"|].
Robbert Krebbers's avatar
Robbert Krebbers committed
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
(** 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
230
231
232
233
    | SelPure :: ?Hs => iFrameAnyPure; go Hs
    | SelPersistent :: ?Hs => iFrameAnyPersistent; go Hs
    | SelSpatial :: ?Hs => iFrameAnySpatial; go Hs
    | SelName ?H :: ?Hs => iFrameHyp H; go Hs
234
    end
235
  in let Hs := sel_pat.parse Hs in go Hs.
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
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
258
(** * Specialize *)
259
260
261
262
263
Record iTrm {X As} :=
  ITrm { itrm : X ; itrm_vars : hlist As ; itrm_hyps : string }.
Arguments ITrm {_ _} _ _ _.

Notation "( H $! x1 .. xn )" :=
264
  (ITrm H (hcons x1 .. (hcons xn hnil) ..) "") (at level 0, x1, xn at level 9).
265
Notation "( H $! x1 .. xn 'with' pat )" :=
266
  (ITrm H (hcons x1 .. (hcons xn hnil) ..) pat) (at level 0, x1, xn at level 9).
267
268
Notation "( H 'with' pat )" := (ITrm H hnil pat) (at level 0).

269
Local Tactic Notation "iSpecializeArgs" constr(H) open_constr(xs) :=
270
271
272
273
274
  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"
275
276
      |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
277
      |cbn [himpl hcurry]; reflexivity|]
278
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
279

280
Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
281
  let solve_to_wand H1 :=
282
    let P := match goal with |- IntoWand ?P _ _ => P end in
283
    apply _ || fail "iSpecialize:" P "not an implication/wand" in
Robbert Krebbers's avatar
Robbert Krebbers committed
284
285
286
  let rec go H1 pats :=
    lazymatch pats with
    | [] => idtac
287
    | SForall :: ?pats => try (iSpecializeArgs H1 (hcons _ _)); go H1 pats
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
329
330
(* The argument [p] denotes whether the conclusion of the specialized term is
persistent. It can either be a Boolean or an introduction pattern, which will be
coerced into [true] when it only contains `#` or `%` patterns at the top-level. *)
331
Tactic Notation "iSpecializeCore" open_constr(t) "as" constr(p) tactic(tac) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
332
  let p := intro_pat_persistent p in
333
334
  lazymatch t with
  | ITrm ?H ?xs ?pat =>
335
336
337
338
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"
           |env_cbv; reflexivity|tac H]
      | false => iSpecializeArgs H xs; iSpecializePat H pat; last (tac H)
      end
    | _ => fail "iSpecialize:" H "should be a hypothesis, use iPoseProof instead"
348
    end
349
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
350

351
352
353
354
355
Tactic Notation "iSpecialize" open_constr(t) :=
  iSpecializeCore t as false (fun _ => idtac).
Tactic Notation "iSpecialize" open_constr(t) "#" :=
  iSpecializeCore t as true (fun _ => idtac).

Robbert Krebbers's avatar
Robbert Krebbers committed
356
(** * Pose proof *)
357
358
(* The tactic [iIntoValid] tactic solves a goal [uPred_valid Q]. The
arguments [t] is a Coq term whose type is of the following shape:
359

360
- [∀ (x_1 : A_1) .. (x_n : A_n), uPred_valid Q]
361
- [∀ (x_1 : A_1) .. (x_n : A_n), P1 ⊢ P2], in which case [Q] becomes [P1 -∗ P2]
362
363
364
365
- [∀ (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]. *)
366
Tactic Notation "iIntoValid" open_constr(t) :=
367
  let rec go t :=
368
369
    let tT := type of t in
    lazymatch eval hnf in tT with
370
371
    | True  _ => apply t
    | _  _ => apply (uPred.entails_wand _ _ t)
372
373
    (* need to use the unfolded version of [⊣⊢] due to the hnf *)
    | uPred_equiv' _ _ => apply (uPred.equiv_iff _ _ t)
374
    | ?P  ?Q => let H := fresh in assert P as H; [|go uconstr:(t H); clear H]
375
376
377
378
379
380
381
382
    |  _ : ?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')
    end
  in go t.

383
Tactic Notation "iPoseProofCore" open_constr(lem) "as" constr(p) tactic(tac) :=
384
385
  let pose_trm t tac :=
    let Htmp := iFresh in
386
    iStartProof;
387
388
389
390
391
392
393
394
    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"
         |tac Htmp]
    | _ =>
       eapply tac_pose_proof with _ Htmp _; (* (j:=H) *)
395
         [iIntoValid t
396
397
398
399
400
401
402
         |env_cbv; reflexivity || fail "iPoseProof:" Htmp "not fresh"
         |tac Htmp]
    end;
    try (apply _) (* solve TC constraints. It is essential that this happens
    after the continuation [tac] has been called. *)
  in lazymatch lem with
  | ITrm ?t ?xs ?pat =>
403
     pose_trm t ltac:(fun Htmp => iSpecializeCore (ITrm Htmp xs pat) as p tac)
404
  | _ => pose_trm lem tac
Robbert Krebbers's avatar
Robbert Krebbers committed
405
406
  end.

407
Tactic Notation "iPoseProof" open_constr(lem) "as" constr(H) :=
408
  iPoseProofCore lem as false (fun Htmp => iRename Htmp into H).
Robbert Krebbers's avatar
Robbert Krebbers committed
409
410

(** * Apply *)
411
Tactic Notation "iApply" open_constr(lem) :=
412
413
414
415
  let finish H := first
    [iExact H
    |eapply tac_apply with _ H _ _ _;
       [env_cbv; reflexivity || fail 1 "iApply:" H "not found"
416
       |let P := match goal with |- IntoWand ?P _ _ => P end in
417
        apply _ || fail 1 "iApply: cannot apply" P
418
       |lazy beta (* reduce betas created by instantiation *)]] in
419
420
  lazymatch lem with
  | ITrm ?t ?xs ?pat =>
421
     iPoseProofCore t as false (fun Htmp =>
422
423
       iSpecializeArgs Htmp xs;
       try (iSpecializeArgs Htmp (hcons _ _));
424
       iSpecializePat Htmp pat; last finish Htmp)
425
  | _ =>
426
     iPoseProofCore lem as false (fun Htmp =>
427
       try (iSpecializeArgs Htmp (hcons _ _));
428
       finish Htmp)
429
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
430
431

(** * Revert *)
432
Local Tactic Notation "iForallRevert" ident(x) :=
433
434
435
436
437
438
  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
439
440
  let A := type of x in
  lazymatch type of A with
441
442
443
  | 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
444
445

Tactic Notation "iRevert" constr(Hs) :=
446
447
  let rec go Hs :=
    lazymatch Hs with
448
    | [] => idtac
449
450
451
452
453
454
455
    | 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]
456
    end in
457
  iElaborateSelPat Hs go.
Robbert Krebbers's avatar
Robbert Krebbers committed
458

459
Tactic Notation "iRevert" "(" ident(x1) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
460
  iForallRevert x1.
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
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
487
    constr(Hs) :=
488
489
490
491
492
493
494
495
496
497
498
499
500
  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
501
502
503

(** * Disjunction *)
Tactic Notation "iLeft" :=
504
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
505
  eapply tac_or_l;
506
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
507
508
     apply _ || fail "iLeft:" P "not a disjunction"|].
Tactic Notation "iRight" :=
509
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
510
  eapply tac_or_r;
511
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
512
513
     apply _ || fail "iRight:" P "not a disjunction"|].

514
Local Tactic Notation "iOrDestruct" constr(H) "as" constr(H1) constr(H2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
515
516
  eapply tac_or_destruct with _ _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
    [env_cbv; reflexivity || fail "iOrDestruct:" H "not found"
517
    |let P := match goal with |- IntoOr ?P _ _ => P end in
518
     apply _ || fail "iOrDestruct: cannot destruct" P
Robbert Krebbers's avatar
Robbert Krebbers committed
519
520
521
522
523
    |env_cbv; reflexivity || fail "iOrDestruct:" H1 "not fresh"
    |env_cbv; reflexivity || fail "iOrDestruct:" H2 "not fresh"| |].

(** * Conjunction and separating conjunction *)
Tactic Notation "iSplit" :=
524
  iStartProof;
525
526
527
  lazymatch goal with
  | |- _  _ =>
    eapply tac_and_split;
528
      [let P := match goal with |- FromAnd ?P _ _ => P end in
529
530
       apply _ || fail "iSplit:" P "not a conjunction"| |]
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
531
532

Tactic Notation "iSplitL" constr(Hs) :=
533
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
534
535
  let Hs := words Hs in
  eapply tac_sep_split with _ _ false Hs _ _; (* (js:=Hs) *)
536
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
537
     apply _ || fail "iSplitL:" P "not a separating conjunction"
538
    |env_cbv; reflexivity || fail "iSplitL: hypotheses" Hs
539
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
540
Tactic Notation "iSplitR" constr(Hs) :=
541
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
542
543
  let Hs := words Hs in
  eapply tac_sep_split with _ _ true Hs _ _; (* (js:=Hs) *)
544
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
545
     apply _ || fail "iSplitR:" P "not a separating conjunction"
546
    |env_cbv; reflexivity || fail "iSplitR: hypotheses" Hs
547
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
548
549
550
551

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

552
553
554
555
556
557
558
559
560
561
562
563
564
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
565
566
567
568
569

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"
570
571
    |let P1 := match goal with |- FromSep _ ?P1 _ => P1 end in
     let P2 := match goal with |- FromSep _ _ ?P2 => P2 end in
572
     apply _ || fail "iCombine: cannot combine" P1 "and" P2
Robbert Krebbers's avatar
Robbert Krebbers committed
573
574
575
    |env_cbv; reflexivity || fail "iCombine:" H "not fresh"|].

(** * Existential *)
Robbert Krebbers's avatar
Robbert Krebbers committed
576
Tactic Notation "iExists" uconstr(x1) :=
577
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
578
  eapply tac_exist;
579
    [let P := match goal with |- FromExist ?P _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
580
     apply _ || fail "iExists:" P "not an existential"
Robbert Krebbers's avatar
Robbert Krebbers committed
581
    |cbv beta; eexists x1].
Robbert Krebbers's avatar
Robbert Krebbers committed
582

Robbert Krebbers's avatar
Robbert Krebbers committed
583
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
584
  iExists x1; iExists x2.
Robbert Krebbers's avatar
Robbert Krebbers committed
585
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
586
  iExists x1; iExists x2, x3.
Robbert Krebbers's avatar
Robbert Krebbers committed
587
588
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
589
  iExists x1; iExists x2, x3, x4.
Robbert Krebbers's avatar
Robbert Krebbers committed
590
591
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
592
  iExists x1; iExists x2, x3, x4, x5.
Robbert Krebbers's avatar
Robbert Krebbers committed
593
594
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
595
  iExists x1; iExists x2, x3, x4, x5, x6.
Robbert Krebbers's avatar
Robbert Krebbers committed
596
597
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) "," uconstr(x7) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
598
  iExists x1; iExists x2, x3, x4, x5, x6, x7.
Robbert Krebbers's avatar
Robbert Krebbers committed
599
600
601
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
602
603
  iExists x1; iExists x2, x3, x4, x5, x6, x7, x8.

604
605
Local Tactic Notation "iExistDestruct" constr(H)
    "as" simple_intropattern(x) constr(Hx) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
606
607
  eapply tac_exist_destruct with H _ Hx _ _; (* (i:=H) (j:=Hx) *)
    [env_cbv; reflexivity || fail "iExistDestruct:" H "not found"
608
    |let P := match goal with |- IntoExist ?P _ => P end in
609
     apply _ || fail "iExistDestruct: cannot destruct" P|];
610
611
612
613
  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
614

Robbert Krebbers's avatar
Robbert Krebbers committed
615
616
(** * Always *)
Tactic Notation "iAlways":=
617
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
618
619
620
621
  apply tac_always_intro;
    [reflexivity || fail "iAlways: spatial context non-empty"|].

(** * Later *)
622
Tactic Notation "iNext" open_constr(n) :=
623
  iStartProof;
624
625
626
627
628
629
630
631
632
633
  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
634

635
(** * Update modality *)
636
Tactic Notation "iModIntro" :=
637
  iStartProof;
638
639
640
641
642
643
644
645
646
647
  eapply tac_modal_intro;
    [let P := match goal with |- IntoModal _ ?P => P end in
     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
648
649
    |env_cbv; reflexivity|].

650
(** * Basic destruct tactic *)
651
Local Tactic Notation "iDestructHyp" constr(H) "as" constr(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
652
653
654
  let rec go Hz pat :=
    lazymatch pat with
    | IAnom => idtac
655
    | IDrop => iClear Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
656
    | IFrame => iFrame Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
657
    | IName ?y => iRename Hz into y
658
    | IList [[]] => iExFalso; iExact Hz
659
660
    | 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
661
    | IList [[?pat1; ?pat2]] =>
662
       let Hy := iFresh in iAndDestruct Hz as Hz Hy; go Hz pat1; go Hy pat2
Robbert Krebbers's avatar
Robbert Krebbers committed
663
    | IList [[?pat1];[?pat2]] => iOrDestruct Hz as Hz Hz; [go Hz pat1|go Hz pat2]
Robbert Krebbers's avatar
Robbert Krebbers committed
664
665
    | IPureElim => iPure Hz as ?
    | IAlwaysElim ?pat => iPersistent Hz; go Hz pat
666
    | IModalElim ?pat => iModCore Hz; go Hz pat
Robbert Krebbers's avatar
Robbert Krebbers committed
667
668
669
670
    | _ => fail "iDestruct:" pat "invalid"
    end
  in let pat := intro_pat.parse_one pat in go H pat.

671
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
672
673
    constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as @ pat.
674
675
676
677
678
679
680
681
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
682
    constr(pat) :=
683
684
  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
685
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
686
687
688
    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
689
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
690
691
692
    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
693
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
694
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
695
    constr(pat) :=
696
697
  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
698
699
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7)
700
701
    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
702
703

(** * Introduction tactic *)
704
Local Tactic Notation "iIntro" "(" simple_intropattern(x) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
705
  try iStartProof;
706
707
708
709
710
  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"|]
711
    |(* (?P -∗ _) *) eapply tac_wand_intro_pure;
712
      [let P := match goal with |- IntoPure ?P _ => P end in
713
       apply _ || fail "iIntro:" P "not pure"|]
Robbert Krebbers's avatar
Robbert Krebbers committed
714
715
    |(* ⌜∀ _, _⌝ *) apply tac_pure_forall_intro
    |(* ⌜_ → _⌝ *) apply tac_pure_impl_intro];
716
  intros x.
717

Robbert Krebbers's avatar
Robbert Krebbers committed
718
719
720
Local Tactic Notation "iIntro" constr(H) :=
  iStartProof;
  first
721
  [ (* (?Q → _) *)
722
    eapply tac_impl_intro with _ H; (* (i:=H) *)
723
724
      [reflexivity || fail 1 "iIntro: introducing" H
                             "into non-empty spatial context"
725
      |env_cbv; reflexivity || fail "iIntro:" H "not fresh"|]
726
  | (* (_ -∗ _) *)
727
    eapply tac_wand_intro with _ H; (* (i:=H) *)
728
729
      [env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
730

Robbert Krebbers's avatar
Robbert Krebbers committed
731
732
733
Local Tactic Notation "iIntro" "#" constr(H) :=
  iStartProof;
  first
734
  [ (* (?P → _) *)
735
    eapply tac_impl_intro_persistent with _ H _; (* (i:=H) *)
736
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
737
738
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
739
  | (* (?P -∗ _) *)
740
    eapply tac_wand_intro_persistent with _ H _; (* (i:=H) *)
741
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
742
743
744
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
745

746
Local Tactic Notation "iIntroForall" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
747
  try iStartProof;
748
749
750
  lazymatch goal with
  | |-  _, ?P => fail
  | |-  _, _ => intro
751
  | |- _  ( x : _, _) => let x' := fresh x in iIntro (x')
752
753
  end.
Local Tactic Notation "iIntro" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
754
  try iStartProof;
755
756
  lazymatch goal with
  | |- _  ?P => intro
757
  | |- _  (_ - _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
758
  | |- _  (_  _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
759
760
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
761
762
763
764
Tactic Notation "iIntros" constr(pat) :=
  let rec go pats :=
    lazymatch pats with
    | [] => idtac
Robbert Krebbers's avatar
Robbert Krebbers committed
765
766
767
768
769
770
771
    | 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
772
    | IModalIntro :: ?pats => iModIntro; go pats
Robbert Krebbers's avatar
Robbert Krebbers committed
773
    | ISimpl :: ?pats => simpl; go pats
774
775
    | IForall :: ?pats => repeat iIntroForall; go pats
    | IAll :: ?pats => repeat (iIntroForall || iIntro); go pats
776
777
778
779
780
781
782
    | 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
783
    | IAlwaysElim ?pat :: ?pats =>
Robbert Krebbers's avatar
Robbert Krebbers committed
784
785
786
787
       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
788
  in let pats := intro_pat.parse pat in go pats.
Robbert Krebbers's avatar
Robbert Krebbers committed
789
Tactic Notation "iIntros" := iIntros [IAll].
Robbert Krebbers's avatar
Robbert Krebbers committed
790

791
Tactic Notation "iIntros" "(" simple_intropattern(x1) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
792
  iIntro ( x1 ).
793
794
795
796
797
798
799
800
801
802
803
804
805
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
806
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
807
808
809
    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
810
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
811
812
813
    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
814
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
    simple_intropattern(x6) simple_intropattern(x7) simple_intropattern(x8) ")" :=
  iIntros ( x1 x2 x3 x4 x5 x6 x7 ); iIntro ( x8 ).

Tactic Notation "iIntros" "(" simple_intropattern(x1) ")" constr(p) :=
  iIntros ( x1 ); iIntros p.
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    ")" constr(p) :=
  iIntros ( x1 x2 ); iIntros p.
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) ")" constr(p) :=
  iIntros ( x1 x2 x3 ); iIntros p.
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
    simple_intropattern(x3) simple_intropattern(x4) ")" constr(p) :=
  iIntros ( x1 x2 x3 x4 ); iIntros p.
Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
Robbert Krebbers's avatar
Robbert Krebbers committed
830
    simple_intropattern(x3) simple_intropattern(x4) simple_intropattern(x5)
831
832
833
    ")" constr(p) :=
  iIn