automation.v 14.5 KB
Newer Older
Michael Sammler's avatar
Michael Sammler committed
1
2
3
From iris.proofmode Require Import coq_tactics reduction.
From refinedc.typing Require Export type.
From refinedc.lithium Require Export tactics.
4
From refinedc.typing.automation Require Export normalize solvers simplification proof_state loc_eq.
5
From refinedc.typing Require Import programs function singleton own struct bytes int.
Michael Sammler's avatar
Michael Sammler committed
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Set Default Proof Using "Type".

(** * Registering extensions *)
(** We use autorewrite for the moment. *)
Ltac normalize_tac ::= normalize_autorewrite.
(* Goal ∀ l i (x : Z), *)
(*     0 < length (<[i:=x]> $ <[i:=x]> (<[length (<[i:=x]>l) :=x]> l ++ <[length (<[i:=x]>l) :=x]> l)). *)
(*   move => ???. normalize_goal. *)
(* Abort. *)

Ltac li_pm_reduce_tac H ::= eval cbv [t2mt mt_type mt_movable] in H.

Ltac custom_exist_tac A protect ::=
    lazymatch A with
    | mtype =>
      lazymatch protect with
      | true => fail 1000 "cannot protect mtype"
      | false =>
      (* it is important that we don't trigger typeclass search here
      as we want to keep Movable as an evar, thus we use notypeclasses
      refine. *)
        notypeclasses refine (ex_intro _ (t2mt _) _)
      end
    | Movable _ => eexists _
    end.

Michael Sammler's avatar
Michael Sammler committed
32
Global Hint Transparent ly_size : solve_protected_eq_db.
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Ltac solve_protected_eq_unfold_tac ::=
  lazymatch goal with
  (* unfold constants for function types *)
  | |- @eq (_  fn_params) ?a (λ x, _) =>
    lazymatch a with
    | (λ x, _) => idtac
    | _ =>
      let h := get_head a in
      unfold h;
      (* necessary to reduce after unfolding because of the strict
      opaqueness settings for unification *)
      liSimpl
    end
  (* don't fail if nothing matches *)
  | |- _ => idtac
  end.

Michael Sammler's avatar
Michael Sammler committed
50
51
52
53
54
55
56
57
58
Ltac can_solve_tac ::= solve_goal.

Ltac record_destruct_hint hint info ::= add_case_distinction_info hint info.

Ltac convert_to_i2p_tac P ::=
  lazymatch P with
  | typed_value ?v ?T => uconstr:(((_ : TypedValue _) _).(i2p_proof))
  | typed_bin_op ?v1 ?ty1 ?v2 ?ty2 ?o ?ot1 ?ot2 ?T => uconstr:(((_ : TypedBinOp _ _ _ _ _ _ _) _).(i2p_proof))
  | typed_un_op ?v ?ty ?o ?ot ?T => uconstr:(((_ : TypedUnOp _ _ _ _) _).(i2p_proof))
59
  | typed_call ?v ?P ?vl ?tys ?T => uconstr:(((_ : TypedCall _ _ _ _) _).(i2p_proof))
60
  | typed_copy_alloc_id ?v1 ?ty1 ?v2 ?ty2 ?ot ?T => uconstr:(((_ : TypedCopyAllocId _ _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
61
  | typed_place ?P ?l1 ?β1 ?ty1 ?T => uconstr:(((_ : TypedPlace _ _ _ _) _).(i2p_proof))
62
  | typed_if ?ot ?v ?P ?T1 ?T2 => uconstr:(((_ : TypedIf _ _ _) _ _).(i2p_proof))
63
  | typed_switch ?v ?ty ?it ?m ?ss ?def ?fn ?ls ?fr ?Q => uconstr:(((_ : TypedSwitch _ _ _) _ _ _ _ _ _ _).(i2p_proof))
64
  | typed_assert ?ot ?v ?ty ?s ?fn ?ls ?fr ?Q => uconstr:(((_ : TypedAssert _ _ _) _ _ _ _ _).(i2p_proof))
65
66
  | typed_read_end ?a ?E ?l ?β ?ty ?ly ?T => uconstr:(((_ : TypedReadEnd _ _ _ _ _ _) _).(i2p_proof))
  | typed_write_end ?a ?E ?ot ?v1 ?ty1 ?l2 ?β2 ?ty2 ?T => uconstr:(((_ : TypedWriteEnd _ _ _ _ _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
67
  | typed_addr_of_end ?l ?β ?ty ?T => uconstr:(((_ : TypedAddrOfEnd _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
68
  | typed_cas ?ot ?v1 ?P1 ?v2 ?P2 ?v3 ?P3 ?T => uconstr:(((_ : TypedCas _ _ _ _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
69
70
  | typed_annot_expr ?n ?a ?v ?P ?T => uconstr:(((_ : TypedAnnotExpr _ _ _ _) _) .(i2p_proof))
  | typed_annot_stmt ?a ?l ?P ?T => uconstr:(((_ : TypedAnnotStmt _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
71
  | typed_macro_expr ?m ?es ?T => uconstr:(((_ : TypedMacroExpr _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
72
73
74
75
76
77
  end.

(** * Main automation tactics *)
Section automation.
  Context `{!typeG Σ}.

78
79
80
  Lemma tac_simpl_subst xs s fn ls Q R:
    typed_stmt (W.to_stmt (W.subst_stmt xs s)) fn ls R Q -
    typed_stmt (subst_stmt xs (W.to_stmt s)) fn ls R Q.
Michael Sammler's avatar
Michael Sammler committed
81
82
  Proof. by rewrite W.to_stmt_subst. Qed.

83
  Lemma tac_typed_single_block_rec P b Q fn ls R s:
Michael Sammler's avatar
Michael Sammler committed
84
    Q !! b = Some s 
85
86
    (P  accu (λ A, typed_block (P  A) b fn ls R Q - P - A - typed_stmt s fn ls R Q)) -
    typed_stmt (Goto b) fn ls R Q.
Michael Sammler's avatar
Michael Sammler committed
87
88
89
90
91
92
93
94
95
96
97
98
99
100
  Proof.
    iIntros (HQ) "[HP Hs]". iIntros (Hls). unfold accu, typed_block.
    iDestruct "Hs" as (A) "[HA #Hs]". iLöb as "Hl".
    iApply wps_goto =>//. iModIntro. iApply ("Hs" with "[] HP HA") => //.
    iIntros "!# [HP HA]". by iApply ("Hl" with "HP HA").
  Qed.
End automation.

Ltac liRIntroduceLetInGoal :=
  lazymatch goal with
  | |- @envs_entails ?PROP ?Δ ?P =>
    let H := fresh "GOAL" in
    lazymatch P with
    | @bi_wand ?PROP ?Q ?T =>
101
      pose H := (LET_ID T); change_no_check (@envs_entails PROP Δ (@bi_wand PROP Q H))
Michael Sammler's avatar
Michael Sammler committed
102
    | @typed_val_expr ?Σ ?tG ?e ?T =>
103
      pose (H := LET_ID T); change_no_check (@envs_entails PROP Δ (@typed_val_expr Σ tG e H))
Michael Sammler's avatar
Michael Sammler committed
104
105
    | @typed_write ?Σ ?tG ?b ?e ?ot ?v ?ty ?Mov ?T =>
      pose (H := LET_ID T); change_no_check (@envs_entails PROP Δ (@typed_write Σ tG b e ot v ty Mov H))
Michael Sammler's avatar
Michael Sammler committed
106
    | @typed_place ?Σ ?tG ?P ?l1 ?β1 ?ty1 ?T =>
107
      pose (H := LET_ID T); change_no_check (@envs_entails PROP Δ (@typed_place Σ tG P l1 β1 ty1 H))
Michael Sammler's avatar
Michael Sammler committed
108
    | @typed_bin_op ?Σ ?tG ?v1 ?P1 ?v2 ?P2 ?op ?ot1 ?ot2 ?T =>
109
      pose (H := LET_ID T); change_no_check (@envs_entails PROP Δ (@typed_bin_op Σ tG v1 P1 v2 P2 op ot1 ot2 H))
Michael Sammler's avatar
Michael Sammler committed
110
111
112
    end
  end.

Michael Sammler's avatar
Michael Sammler committed
113
Ltac liRInstantiateEvars_hook := idtac.
Michael Sammler's avatar
Michael Sammler committed
114
Ltac liRInstantiateEvars :=
Michael Sammler's avatar
Michael Sammler committed
115
  liRInstantiateEvars_hook;
Michael Sammler's avatar
Michael Sammler committed
116
  lazymatch goal with
Michael Sammler's avatar
Michael Sammler committed
117
118
119
120
121
  | |- (_ < protected ?H)%nat  _ =>
    (* We would like to use [liInst H (S (protected (EVAR_ID _)))],
      but this causes a Error: No such section variable or assumption
      at Qed. time. Maybe this is related to https://github.com/coq/coq/issues/9937 *)
    instantiate_protected (protected H) ltac:(fun H => instantiate (1:=((S (protected (EVAR_ID _))))) in (Value of H))
Michael Sammler's avatar
Michael Sammler committed
122
123
124
125
  (* This is very hard to figure out for unification because of the
  dependent types in with refinement. Unificaiton likes to unfold the
  definition of ty without this. This is the reason why do_instantiate
  evars must come before do_side_cond *)
Michael Sammler's avatar
Michael Sammler committed
126
127
128
129
  | |- protected ?H = ( _ @ ?ty)%I  _ =>
    instantiate_protected (protected H) ltac:(fun H => instantiate (1:=((protected (EVAR_ID _)) @ ty)%I) in (Value of H))
  | |- protected ?H = ty_of_rty (frac_ptr ?β _)%I  _ =>
    instantiate_protected (protected H) ltac:(fun H => instantiate (1:=((frac_ptr β (protected (EVAR_ID _)))%I)) in (Value of H))
Michael Sammler's avatar
Michael Sammler committed
130
131
132
133
134
135
136
137
138
139
  | |- envs_entails _ (subsume (?x ◁ₗ{?β} ?ty) (_ ◁ₗ{_} (protected ?H)) _) => liInst H ty
  | |- envs_entails _ (subsume (?x ◁ₗ{?β} ?ty) (_ ◁ₗ{protected ?H} _) _) => liInst H β
  end.

Ltac liRStmt :=
  lazymatch goal with
  | |- envs_entails ?Δ (typed_stmt ?s ?fn ?ls ?fr ?Q) =>
    lazymatch s with
    | LocInfo ?info ?s2 =>
      update_loc_info (Some info);
140
      change_no_check (envs_entails Δ (typed_stmt s2 fn ls fr Q))
Michael Sammler's avatar
Michael Sammler committed
141
142
143
144
145
146
    | _ => update_loc_info (None : option location_info)
    end
  end;
  lazymatch goal with
  | |- envs_entails ?Δ (typed_stmt ?s ?fn ?ls ?fr ?Q) =>
    lazymatch s with
Michael Sammler's avatar
Michael Sammler committed
147
    | subst_stmt ?xs ?s =>
Michael Sammler's avatar
Michael Sammler committed
148
      let s' := W.of_stmt s in
Michael Sammler's avatar
Michael Sammler committed
149
150
      change (subst_stmt xs s) with (subst_stmt xs (W.to_stmt s'));
      refine (tac_fast_apply (tac_simpl_subst _ _ _ _ _ _) _); simpl; unfold W.to_stmt, W.to_expr
Michael Sammler's avatar
Michael Sammler committed
151
152
153
154
155
    | _ =>
      let s' := W.of_stmt s in
      lazymatch s' with
      | W.Assign _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_assign _ _ _ _ _ _ _ _ _) _)
      | W.Return _ => notypeclasses refine (tac_fast_apply (type_return _ _ _ _ _) _)
156
      | W.IfS _ _ _ _ => notypeclasses refine (tac_fast_apply (type_if _ _ _ _ _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
157
      | W.Switch _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_switch _ _ _ _ _ _ _ _ _) _)
158
      | W.Assert _ _ _ => notypeclasses refine (tac_fast_apply (type_assert _ _ _ _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
159
      | W.Goto ?bid => first [
160
         notypeclasses refine (tac_fast_apply (type_goto_precond _ _ _ _ _ _) _); progress liFindHyp FICSyntactic
Michael Sammler's avatar
Michael Sammler committed
161
162
       | lazymatch goal with
         | H : BLOCK_PRECOND bid ?P |- _ =>
163
           notypeclasses refine (tac_fast_apply (tac_typed_single_block_rec P _ _ _ _ _ _ _) _);[unfold_code_marker_and_compute_map_lookup|]
Michael Sammler's avatar
Michael Sammler committed
164
         end
165
       | notypeclasses refine (tac_fast_apply (type_goto _ _ _ _ _ _ _) _); [unfold_code_marker_and_compute_map_lookup|]
Michael Sammler's avatar
Michael Sammler committed
166
167
168
169
170
171
172
173
174
                     ]
      | W.ExprS _ _ => notypeclasses refine (tac_fast_apply (type_exprs _ _ _ _ _ _) _)
      | W.SkipS _ => notypeclasses refine (tac_fast_apply (type_skips' _ _ _ _ _) _)
      | W.AnnotStmt _ ?a _ => notypeclasses refine (tac_fast_apply (type_annot_stmt _ _ _ _ _ _ _) _)
      | _ => fail "do_stmt: unknown stmt" s
      end
    end
  end.

175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
Ltac liRIntroduceTypedStmt :=
  lazymatch goal with
  | |- @envs_entails ?PROP ?Δ (introduce_typed_stmt ?fn ?ls ?R) =>
    iEval (rewrite /introduce_typed_stmt !fmap_insert fmap_empty; simpl_subst);
      lazymatch goal with
      | |- @envs_entails ?PROP ?Δ (@typed_stmt ?Σ ?tG ?s ?fn ?ls ?R ?Q) =>
        let HQ := fresh "Q" in
        let HR := fresh "R" in
        pose (HQ := (CODE_MARKER Q));
        pose (HR := (RETURN_MARKER R));
        change_no_check (@envs_entails PROP Δ (@typed_stmt Σ tG s fn ls HR HQ));
        iEval (simpl) (* To simplify f_init *)
      end
  end.

Michael Sammler's avatar
Michael Sammler committed
190
191
192
193
194
Ltac liRPopLocationInfo :=
  lazymatch goal with
  (* TODO: don't hardcode this for two arguments *)
  | |- envs_entails ?Δ (pop_location_info ?info ?T ?a1 ?a2) =>
    update_loc_info [info; info];
195
    change_no_check (envs_entails Δ (T a1 a2))
Michael Sammler's avatar
Michael Sammler committed
196
197
198
199
200
201
202
203
  end.

Ltac liRExpr :=
  lazymatch goal with
  | |- envs_entails ?Δ (typed_val_expr ?e ?T) =>
    lazymatch e with
    | LocInfo ?info ?e2 =>
      update_loc_info [info];
204
      change_no_check (envs_entails Δ (typed_val_expr e2 (pop_location_info info T)))
Michael Sammler's avatar
Michael Sammler committed
205
206
207
208
209
210
211
212
213
    | _ => idtac
    end
  end;
  lazymatch goal with
  | |- envs_entails ?Δ (typed_val_expr ?e ?T) =>
    let e' := W.of_expr e in
    lazymatch e' with
    | W.Val _ => notypeclasses refine (tac_fast_apply (type_val _ _) _)
    | W.Loc _ => notypeclasses refine (tac_fast_apply (type_val _ _) _)
214
    | W.Use _ _ _ => notypeclasses refine (tac_fast_apply (type_use _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
215
216
    | W.AddrOf _ => notypeclasses refine (tac_fast_apply (type_addr_of _ _) _)
    | W.BinOp _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_bin_op _ _ _ _ _ _) _)
217
    | W.CopyAllocId _ _ _ => notypeclasses refine (tac_fast_apply (type_copy_alloc_id _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
218
219
    | W.UnOp _ _ _ => notypeclasses refine (tac_fast_apply (type_un_op _ _ _ _) _)
    | W.CAS _ _ _ _ => notypeclasses refine (tac_fast_apply (type_cas _ _ _ _ _) _)
220
    | W.Call _ _ => notypeclasses refine (tac_fast_apply (type_call _ _ _) _)
221
    | W.OffsetOf _ _ => notypeclasses refine (tac_fast_apply (type_offset_of _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
222
223
    | W.AnnotExpr _ ?a _ => notypeclasses refine (tac_fast_apply (type_annot_expr _ _ _ _) _)
    | W.StructInit _ _ => notypeclasses refine (tac_fast_apply (type_struct_init _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
224
    | W.IfE _ _ _ _ => notypeclasses refine (tac_fast_apply (type_ife _ _ _ _ _) _)
225
226
    | W.LogicalAnd _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_logical_and _ _ _ _ _) _)
    | W.LogicalOr _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_logical_or _ _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
227
    | W.SkipE _ => notypeclasses refine (tac_fast_apply (type_skipe' _ _) _)
Michael Sammler's avatar
Michael Sammler committed
228
    | W.MacroE _ _ _ => notypeclasses refine (tac_fast_apply (type_macro_expr _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
229
230
231
232
233
234
    | _ => fail "do_expr: unknown expr" e
    end
  end.

Ltac liRJudgement :=
  lazymatch goal with
235
    | |- envs_entails _ (typed_write _ _ _ _ _ _) => notypeclasses refine (tac_fast_apply (type_write _ _ _ _ _ _ _ _) _); [ solve [refine _ ] |]
236
    | |- envs_entails _ (typed_read _ _ _ _) => notypeclasses refine (tac_fast_apply (type_read _ _ _ _ _ _) _); [ solve [refine _ ] |]
Michael Sammler's avatar
Michael Sammler committed
237
238
239
240
241
    | |- envs_entails _ (typed_addr_of _ _) => notypeclasses refine (tac_fast_apply (type_addr_of_place _ _ _ _) _); [solve [refine _] |]
  end.

(* This does everything *)
Ltac liRStep :=
242
 liEnforceInvariantAndUnfoldInstantiatedEvars;
Michael Sammler's avatar
Michael Sammler committed
243
244
245
246
247
 try liRIntroduceLetInGoal;
 first [
   liRInstantiateEvars (* must be before do_side_cond and do_extensible_judgement *)
 | liRPopLocationInfo
 | liRStmt
248
 | liRIntroduceTypedStmt
Michael Sammler's avatar
Michael Sammler committed
249
250
251
252
253
 | liRExpr
 | liRJudgement
 | liStep
]; liSimpl.

Michael Sammler's avatar
Michael Sammler committed
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
Tactic Notation "liRStepUntil" open_constr(id) :=
  repeat lazymatch goal with
         | |- @environments.envs_entails _ _ ?P =>
           lazymatch P with
           | id _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ _ => fail
           | id _ _ _ _ _ _ => fail
           | id _ _ _ _ _ => fail
           | id _ _ _ _ => fail
           | id _ _ => fail
           | id _ => fail
           | id => fail
           | _  => liRStep
           end
         | _ => liRStep
  end; liShow.


Michael Sammler's avatar
Michael Sammler committed
280
281
282
283
284
(** * Tactics for starting a function *)
(* IMPORTANT: We need to make sure to never call simpl while the code
(Q) is part of the goal, because simpl seems to take exponential time
in the number of blocks! *)
(* TODO: don't use i... tactics here *)
Michael Sammler's avatar
Michael Sammler committed
285
Tactic Notation "start_function" constr(fnname) "(" simple_intropattern(x) ")" :=
Michael Sammler's avatar
Michael Sammler committed
286
287
288
289
  intros;
  repeat iIntros "#?";
  rewrite /typed_function;
  iIntros ( x );
Michael Sammler's avatar
Michael Sammler committed
290
  iSplit; [iPureIntro; simpl; by [repeat constructor] || fail "in" fnname "argument types don't match layout of arguments" |];
Michael Sammler's avatar
Michael Sammler committed
291
  let lsa := fresh "lsa" in let lsv := fresh "lsv" in
292
293
294
295
  iIntros "!#" (lsa lsv); inv_vec lsv; inv_vec lsa.

Tactic Notation "prepare_parameters" "(" ident_list(i) ")" :=
  revert i; repeat liForall.
Michael Sammler's avatar
Michael Sammler committed
296
297
298

Ltac liRSplitBlocksIntro :=
  repeat (
299
      liEnforceInvariantAndUnfoldInstantiatedEvars;
Michael Sammler's avatar
Michael Sammler committed
300
301
302
303
304
305
306
307
308
309
310
311
312
      first [
          liSep
        | liWand
        | liImpl
        | liForall
        | liExist true
        | liUnfoldLetGoal]; liSimpl);
  liShow.

(* TODO: don't use i... tactics here *)
Ltac split_blocks Pfull Ps :=
  (* cbn in * is important here to simplify the types of local
  variables, otherwise unification gets confused later *)
313
  cbn -[union] in *;
Michael Sammler's avatar
Michael Sammler committed
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
  let rec pose_Ps Ps :=
      lazymatch Ps with
      | <[?bid:=?P]>?m =>
        let Hblock := fresh "Hblock" in
        have Hblock: (BLOCK_PRECOND bid P) by exact: tt;
        pose_Ps m
      | _ => idtac
      end
  in
  pose_Ps Ps;
  let Hfull := fresh "Hfull" in
  (* We must do this pose first since do_split_block_intro might call
  subst and we want to subst in Ps as well. *)
  pose (Hfull := Pfull);
  liRSplitBlocksIntro;
329
  liRIntroduceTypedStmt;
Michael Sammler's avatar
Michael Sammler committed
330
331
  iApply (typed_block_rec Hfull); unfold Hfull; clear Hfull; last first; [|
  repeat (iApply big_sepM_insert; [reflexivity|]; iSplitL); last by [iApply big_sepM_empty];
332
  iExists _; (iSplitR; [iPureIntro; unfold_code_marker_and_compute_map_lookup|]); iModIntro ];
Michael Sammler's avatar
Michael Sammler committed
333
  repeat (iApply tac_split_big_sepM; [reflexivity|]; iIntros "?"); iIntros "_".