tactics.v 56.4 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
    | SForall :: ?pats => try (iSpecializeArgs H1 (hcons _ _)); go H1 pats
289
    | SName ?H2 :: ?pats =>
Robbert Krebbers's avatar
Robbert Krebbers committed
290
291
292
       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"
293
294
         |let P := match goal with |- IntoWand ?P ?Q _ => P end in
          let Q := match goal with |- IntoWand ?P ?Q _ => Q end in
295
          apply _ || fail "iSpecialize: cannot instantiate" P "with" Q
Robbert Krebbers's avatar
Robbert Krebbers committed
296
         |env_cbv; reflexivity|go H1 pats]
297
    | SGoalPersistent :: ?pats =>
298
       eapply tac_specialize_assert_persistent with _ _ H1 _ _ _ _;
299
300
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
301
302
         |let Q := match goal with |- PersistentP ?Q => Q end in
          apply _ || fail "iSpecialize:" Q "not persistent"
303
304
305
306
         |env_cbv; reflexivity
         |(*goal*)
         |go H1 pats]
    | SGoalPure :: ?pats =>
307
       eapply tac_specialize_assert_pure with _ H1 _ _ _ _ _;
Robbert Krebbers's avatar
Robbert Krebbers committed
308
309
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
310
         |let Q := match goal with |- FromPure ?Q _ => Q end in
311
312
313
314
          apply _ || fail "iSpecialize:" Q "not pure"
         |env_cbv; reflexivity
         |(*goal*)
         |go H1 pats]
315
    | SGoal (SpecGoal ?m ?lr ?Hs_frame ?Hs) :: ?pats =>
316
       let Hs' := eval cbv in (if lr then Hs else Hs_frame ++ Hs) in
317
       eapply tac_specialize_assert with _ _ _ H1 _ lr Hs' _ _ _ _;
Robbert Krebbers's avatar
Robbert Krebbers committed
318
319
         [env_cbv; reflexivity || fail "iSpecialize:" H1 "not found"
         |solve_to_wand H1
320
321
322
         |match m with
          | false => apply elim_modal_dummy
          | true => apply _ || fail "iSpecialize: goal not a modality"
323
          end
324
         |env_cbv; reflexivity || fail "iSpecialize:" Hs "not found"
325
         |iFrame Hs_frame (*goal*)
Robbert Krebbers's avatar
Robbert Krebbers committed
326
         |go H1 pats]
327
328
    end in let pats := spec_pat.parse pat in go H pats.

Robbert Krebbers's avatar
Robbert Krebbers committed
329
(* The argument [p] denotes whether the conclusion of the specialized term is
330
331
332
333
334
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
335
  let p := intro_pat_persistent p in
336
337
  lazymatch t with
  | ITrm ?H ?xs ?pat =>
338
339
340
341
342
343
344
345
346
    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"
347
348
           |env_cbv; reflexivity|(* goal *)]
      | false => iSpecializeArgs H xs; iSpecializePat H pat
349
350
      end
    | _ => fail "iSpecialize:" H "should be a hypothesis, use iPoseProof instead"
351
    end
352
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
353

354
Tactic Notation "iSpecialize" open_constr(t) :=
355
356
357
  iSpecializeCore t as false.
Tactic Notation "iSpecialize" open_constr(t) "as" "#" :=
  iSpecializeCore t as true.
358

Robbert Krebbers's avatar
Robbert Krebbers committed
359
(** * Pose proof *)
360
361
(* The tactic [iIntoValid] tactic solves a goal [uPred_valid Q]. The
arguments [t] is a Coq term whose type is of the following shape:
362

363
- [∀ (x_1 : A_1) .. (x_n : A_n), uPred_valid Q]
364
- [∀ (x_1 : A_1) .. (x_n : A_n), P1 ⊢ P2], in which case [Q] becomes [P1 -∗ P2]
365
366
367
368
- [∀ (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]. *)
369
Tactic Notation "iIntoValid" open_constr(t) :=
370
  let rec go t :=
371
372
    let tT := type of t in
    lazymatch eval hnf in tT with
373
374
    | True  _ => apply t
    | _  _ => apply (uPred.entails_wand _ _ t)
375
376
    (* need to use the unfolded version of [⊣⊢] due to the hnf *)
    | uPred_equiv' _ _ => apply (uPred.equiv_iff _ _ t)
377
    | ?P  ?Q => let H := fresh in assert P as H; [|go uconstr:(t H); clear H]
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')
383
384
    end in
  go t.
385

386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
(* 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 :=
401
402
403
404
405
    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"
406
         |goal_tac ()]
407
408
    | _ =>
       eapply tac_pose_proof with _ Htmp _; (* (j:=H) *)
409
         [iIntoValid t
410
         |env_cbv; reflexivity || fail "iPoseProof:" Htmp "not fresh"
411
         |goal_tac ()]
412
    end;
413
414
415
416
    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
417
418
  end.

419
Tactic Notation "iPoseProof" open_constr(lem) "as" constr(H) :=
420
  iPoseProofCore lem as false false (fun Htmp => iRename Htmp into H).
Robbert Krebbers's avatar
Robbert Krebbers committed
421
422

(** * Apply *)
423
Tactic Notation "iApply" open_constr(lem) :=
424
425
426
427
428
429
  let lem := (* add a `*` to specialize all top-level foralls *)
    lazymatch lem with
    | ITrm ?t ?xs ?pat => constr:(ITrm t xs ("*" +:+ pat))
    | _ => constr:(ITrm lem hnil "*")
    end in
  iPoseProofCore lem as false true (fun H => first
430
431
    [iExact H
    |eapply tac_apply with _ H _ _ _;
432
433
434
      [env_cbv; reflexivity
      |apply _
      |lazy beta (* reduce betas created by instantiation *)]]).
Robbert Krebbers's avatar
Robbert Krebbers committed
435
436

(** * Revert *)
437
Local Tactic Notation "iForallRevert" ident(x) :=
438
439
440
441
442
443
  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
444
445
  let A := type of x in
  lazymatch type of A with
446
447
448
  | 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
449
450

Tactic Notation "iRevert" constr(Hs) :=
451
452
  let rec go Hs :=
    lazymatch Hs with
453
    | [] => idtac
454
455
456
457
458
459
460
    | 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]
461
    end in
462
  iElaborateSelPat Hs go.
Robbert Krebbers's avatar
Robbert Krebbers committed
463

464
Tactic Notation "iRevert" "(" ident(x1) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
465
  iForallRevert x1.
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
491
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
492
    constr(Hs) :=
493
494
495
496
497
498
499
500
501
502
503
504
505
  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
506
507
508

(** * Disjunction *)
Tactic Notation "iLeft" :=
509
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
510
  eapply tac_or_l;
511
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
512
513
     apply _ || fail "iLeft:" P "not a disjunction"|].
Tactic Notation "iRight" :=
514
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
515
  eapply tac_or_r;
516
    [let P := match goal with |- FromOr ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
517
518
     apply _ || fail "iRight:" P "not a disjunction"|].

519
Local Tactic Notation "iOrDestruct" constr(H) "as" constr(H1) constr(H2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
520
521
  eapply tac_or_destruct with _ _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
    [env_cbv; reflexivity || fail "iOrDestruct:" H "not found"
522
    |let P := match goal with |- IntoOr ?P _ _ => P end in
523
     apply _ || fail "iOrDestruct: cannot destruct" P
Robbert Krebbers's avatar
Robbert Krebbers committed
524
525
526
527
528
    |env_cbv; reflexivity || fail "iOrDestruct:" H1 "not fresh"
    |env_cbv; reflexivity || fail "iOrDestruct:" H2 "not fresh"| |].

(** * Conjunction and separating conjunction *)
Tactic Notation "iSplit" :=
529
  iStartProof;
530
531
532
  lazymatch goal with
  | |- _  _ =>
    eapply tac_and_split;
533
      [let P := match goal with |- FromAnd ?P _ _ => P end in
534
535
       apply _ || fail "iSplit:" P "not a conjunction"| |]
  end.
Robbert Krebbers's avatar
Robbert Krebbers committed
536
537

Tactic Notation "iSplitL" constr(Hs) :=
538
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
539
540
  let Hs := words Hs in
  eapply tac_sep_split with _ _ false Hs _ _; (* (js:=Hs) *)
541
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
542
     apply _ || fail "iSplitL:" P "not a separating conjunction"
543
    |env_cbv; reflexivity || fail "iSplitL: hypotheses" Hs
544
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
545
Tactic Notation "iSplitR" constr(Hs) :=
546
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
547
548
  let Hs := words Hs in
  eapply tac_sep_split with _ _ true Hs _ _; (* (js:=Hs) *)
549
    [let P := match goal with |- FromSep ?P _ _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
550
     apply _ || fail "iSplitR:" P "not a separating conjunction"
551
    |env_cbv; reflexivity || fail "iSplitR: hypotheses" Hs
552
                                  "not found in the context"| |].
Robbert Krebbers's avatar
Robbert Krebbers committed
553
554
555
556

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

557
558
559
560
561
562
563
564
565
566
567
568
569
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
570
571
572
573
574

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"
575
576
    |let P1 := match goal with |- FromSep _ ?P1 _ => P1 end in
     let P2 := match goal with |- FromSep _ _ ?P2 => P2 end in
577
     apply _ || fail "iCombine: cannot combine" P1 "and" P2
Robbert Krebbers's avatar
Robbert Krebbers committed
578
579
580
    |env_cbv; reflexivity || fail "iCombine:" H "not fresh"|].

(** * Existential *)
Robbert Krebbers's avatar
Robbert Krebbers committed
581
Tactic Notation "iExists" uconstr(x1) :=
582
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
583
  eapply tac_exist;
584
    [let P := match goal with |- FromExist ?P _ => P end in
Robbert Krebbers's avatar
Robbert Krebbers committed
585
     apply _ || fail "iExists:" P "not an existential"
Robbert Krebbers's avatar
Robbert Krebbers committed
586
    |cbv beta; eexists x1].
Robbert Krebbers's avatar
Robbert Krebbers committed
587

Robbert Krebbers's avatar
Robbert Krebbers committed
588
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
589
  iExists x1; iExists x2.
Robbert Krebbers's avatar
Robbert Krebbers committed
590
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
591
  iExists x1; iExists x2, x3.
Robbert Krebbers's avatar
Robbert Krebbers committed
592
593
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
594
  iExists x1; iExists x2, x3, x4.
Robbert Krebbers's avatar
Robbert Krebbers committed
595
596
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
597
  iExists x1; iExists x2, x3, x4, x5.
Robbert Krebbers's avatar
Robbert Krebbers committed
598
599
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
600
  iExists x1; iExists x2, x3, x4, x5, x6.
Robbert Krebbers's avatar
Robbert Krebbers committed
601
602
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
    uconstr(x4) "," uconstr(x5) "," uconstr(x6) "," uconstr(x7) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
603
  iExists x1; iExists x2, x3, x4, x5, x6, x7.
Robbert Krebbers's avatar
Robbert Krebbers committed
604
605
606
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
607
608
  iExists x1; iExists x2, x3, x4, x5, x6, x7, x8.

609
610
Local Tactic Notation "iExistDestruct" constr(H)
    "as" simple_intropattern(x) constr(Hx) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
611
612
  eapply tac_exist_destruct with H _ Hx _ _; (* (i:=H) (j:=Hx) *)
    [env_cbv; reflexivity || fail "iExistDestruct:" H "not found"
613
    |let P := match goal with |- IntoExist ?P _ => P end in
614
     apply _ || fail "iExistDestruct: cannot destruct" P|];
615
616
617
618
  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
619

Robbert Krebbers's avatar
Robbert Krebbers committed
620
621
(** * Always *)
Tactic Notation "iAlways":=
622
  iStartProof;
Robbert Krebbers's avatar
Robbert Krebbers committed
623
624
625
626
  apply tac_always_intro;
    [reflexivity || fail "iAlways: spatial context non-empty"|].

(** * Later *)
627
Tactic Notation "iNext" open_constr(n) :=
628
  iStartProof;
629
630
631
632
633
634
635
636
637
638
  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
639

640
(** * Update modality *)
641
Tactic Notation "iModIntro" :=
642
  iStartProof;
643
644
645
646
647
648
649
650
651
652
  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
653
654
    |env_cbv; reflexivity|].

655
(** * Basic destruct tactic *)
656
Local Tactic Notation "iDestructHyp" constr(H) "as" constr(pat) :=
Robbert Krebbers's avatar
Robbert Krebbers committed
657
658
659
  let rec go Hz pat :=
    lazymatch pat with
    | IAnom => idtac
660
    | IDrop => iClear Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
661
    | IFrame => iFrame Hz
Robbert Krebbers's avatar
Robbert Krebbers committed
662
    | IName ?y => iRename Hz into y
663
    | IList [[]] => iExFalso; iExact Hz
664
665
    | 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
666
    | IList [[?pat1; ?pat2]] =>
667
       let Hy := iFresh in iAndDestruct Hz as Hz Hy; go Hz pat1; go Hy pat2
Robbert Krebbers's avatar
Robbert Krebbers committed
668
    | IList [[?pat1];[?pat2]] => iOrDestruct Hz as Hz Hz; [go Hz pat1|go Hz pat2]
Robbert Krebbers's avatar
Robbert Krebbers committed
669
670
    | IPureElim => iPure Hz as ?
    | IAlwaysElim ?pat => iPersistent Hz; go Hz pat
671
    | IModalElim ?pat => iModCore Hz; go Hz pat
Robbert Krebbers's avatar
Robbert Krebbers committed
672
673
674
675
    | _ => fail "iDestruct:" pat "invalid"
    end
  in let pat := intro_pat.parse_one pat in go H pat.

676
Local Tactic Notation "iDestructHyp" constr(H) "as" "(" simple_intropattern(x1) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
677
678
    constr(pat) :=
  iExistDestruct H as x1 H; iDestructHyp H as @ pat.
679
680
681
682
683
684
685
686
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
687
    constr(pat) :=
688
689
  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
690
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
691
692
693
    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
694
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
695
696
697
    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
698
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
699
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7) ")"
Robbert Krebbers's avatar
Robbert Krebbers committed
700
    constr(pat) :=
701
702
  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
703
704
    simple_intropattern(x2) simple_intropattern(x3) simple_intropattern(x4)
    simple_intropattern(x5) simple_intropattern(x6) simple_intropattern(x7)
705
706
    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
707
708

(** * Introduction tactic *)
709
Local Tactic Notation "iIntro" "(" simple_intropattern(x) ")" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
710
  try iStartProof;
711
712
713
714
715
  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"|]
716
    |(* (?P -∗ _) *) eapply tac_wand_intro_pure;
717
      [let P := match goal with |- IntoPure ?P _ => P end in
718
       apply _ || fail "iIntro:" P "not pure"|]
Robbert Krebbers's avatar
Robbert Krebbers committed
719
720
    |(* ⌜∀ _, _⌝ *) apply tac_pure_forall_intro
    |(* ⌜_ → _⌝ *) apply tac_pure_impl_intro];
721
  intros x.
722

Robbert Krebbers's avatar
Robbert Krebbers committed
723
724
725
Local Tactic Notation "iIntro" constr(H) :=
  iStartProof;
  first
726
  [ (* (?Q → _) *)
727
    eapply tac_impl_intro with _ H; (* (i:=H) *)
728
729
      [reflexivity || fail 1 "iIntro: introducing" H
                             "into non-empty spatial context"
730
      |env_cbv; reflexivity || fail "iIntro:" H "not fresh"|]
731
  | (* (_ -∗ _) *)
732
    eapply tac_wand_intro with _ H; (* (i:=H) *)
733
734
      [env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
735

Robbert Krebbers's avatar
Robbert Krebbers committed
736
737
738
Local Tactic Notation "iIntro" "#" constr(H) :=
  iStartProof;
  first
739
  [ (* (?P → _) *)
740
    eapply tac_impl_intro_persistent with _ H _; (* (i:=H) *)
741
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
742
743
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
744
  | (* (?P -∗ _) *)
745
    eapply tac_wand_intro_persistent with _ H _; (* (i:=H) *)
746
      [let P := match goal with |- IntoPersistentP ?P _ => P end in
747
748
749
       apply _ || fail 1 "iIntro: " P " not persistent"
      |env_cbv; reflexivity || fail 1 "iIntro:" H "not fresh"|]
  | fail 1 "iIntro: nothing to introduce" ].
750

751
Local Tactic Notation "iIntroForall" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
752
  try iStartProof;
753
754
755
  lazymatch goal with
  | |-  _, ?P => fail
  | |-  _, _ => intro
756
  | |- _  ( x : _, _) => let x' := fresh x in iIntro (x')
757
758
  end.
Local Tactic Notation "iIntro" :=
Robbert Krebbers's avatar
Robbert Krebbers committed
759
  try iStartProof;
760
761
  lazymatch goal with
  | |- _  ?P => intro
762
  | |- _  (_ - _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
763
  | |- _  (_  _) => iIntro (?) || let H := iFresh in iIntro #H || iIntro H
764
765
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
766
767
768
769
Tactic Notation "iIntros" constr(pat) :=
  let rec go pats :=
    lazymatch pats with
    | [] => idtac
Robbert Krebbers's avatar
Robbert Krebbers committed
770
771
772
773
774
775
776
    | 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
777
    | IModalIntro :: ?pats => iModIntro; go pats
Robbert Krebbers's avatar
Robbert Krebbers committed
778
    | ISimpl :: ?pats => simpl; go pats
779
780
    | IForall :: ?pats => repeat iIntroForall; go pats
    | IAll :: ?pats => repeat (iIntroForall || iIntro); go pats
781
782
783
784
785
786
787
    | 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
788
    | IAlwaysElim ?pat :: ?pats =>
Robbert Krebbers's avatar
Robbert Krebbers committed
789
790
791
792
       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
793
  in let pats := intro_pat.parse pat in go pats.
Robbert Krebbers's avatar
Robbert Krebbers committed
794
Tactic Notation "iIntros" := iIntros [IAll].
Robbert Krebbers's avatar
Robbert Krebbers committed
795

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