automation.v 13 KB
Newer Older
Michael Sammler's avatar
Michael Sammler committed
1
2
3
4
From iris.proofmode Require Import coq_tactics reduction.
From refinedc.typing Require Export type.
From refinedc.lithium Require Export tactics.
From refinedc.typing.automation Require Export normalize solvers simplification proof_state.
5
From refinedc.typing Require Import programs function singleton own struct uninit 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
32
33
34
35
36
37
38
39
40
41
42
43
Set Default Proof Using "Type".

(** * Registering extensions *)
(** More automation for modular arithmetics. *)
Ltac Zify.zify_post_hook ::= Z.to_euclidean_division_equations.

(** 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.

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))
44
  | typed_copy_alloc_id ?v1 ?ty1 ?v2 ?ty2 ?T => uconstr:(((_ : TypedCopyAllocId _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
45
  | typed_place ?P ?l1 ?β1 ?ty1 ?T => uconstr:(((_ : TypedPlace _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
46
  | typed_if ?ot ?v ?ty ?T1 ?T2 => uconstr:(((_ : TypedIf _ _ _) _ _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
47
48
  | typed_switch ?v ?ty ?it ?m ?ss ?def ?fn ?ls ?fr ?Q => uconstr:(((_ : TypedSwitch _ _ _) _ _ _ _ _ _ _ _).(i2p_proof))
  | typed_assert ?v ?ty ?s ?fn ?ls ?fr ?Q => uconstr:(((_ : TypedAssert _ _) _ _ _ _ _ _).(i2p_proof))
49
  | typed_read_end ?a ?l ?β ?ty ?ly ?T => uconstr:(((_ : TypedReadEnd _ _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
50
51
  | typed_write_end ?a ?v1 ?ty1 ?l2 ?β2 ?ty2 ?T => uconstr:(((_ : TypedWriteEnd _ _ _ _ _ _) _).(i2p_proof))
  | typed_addr_of_end ?l ?β ?ty ?T => uconstr:(((_ : TypedAddrOfEnd _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
52
  | typed_cas ?ot ?v1 ?P1 ?v2 ?P2 ?v3 ?P3 ?T => uconstr:(((_ : TypedCas _ _ _ _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
53
54
  | typed_annot_expr ?n ?a ?v ?ty ?T => uconstr:(((_ : TypedAnnotExpr _ _ _ _) _) .(i2p_proof))
  | typed_annot_stmt ?a ?l ?β ?ty ?T => uconstr:(((_ : TypedAnnotStmt _ _ _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
55
  | typed_macro_expr ?m ?es ?T => uconstr:(((_ : TypedMacroExpr _ _) _).(i2p_proof))
Michael Sammler's avatar
Michael Sammler committed
56
57
58
59
60
61
  end.

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

Michael Sammler's avatar
Michael Sammler committed
62
63
64
  Lemma tac_simpl_subst {B} xs s fn ls Q (fr : B  _):
    typed_stmt (W.to_stmt (W.subst_stmt xs s)) fn ls fr Q -
    typed_stmt (subst_stmt xs (W.to_stmt s)) fn ls fr Q.
Michael Sammler's avatar
Michael Sammler committed
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
  Proof. by rewrite W.to_stmt_subst. Qed.

  Lemma tac_typed_single_block_rec {B} P b Q fn ls (fr : B  _) s:
    Q !! b = Some s 
    (P  accu (λ A, typed_block (P  A) b fn ls fr Q - P - A - typed_stmt s fn ls fr Q)) -
    typed_stmt (Goto b) fn ls fr Q.
  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 =>
85
      pose H := (LET_ID T); change_no_check (@envs_entails PROP Δ (@bi_wand PROP Q H))
Michael Sammler's avatar
Michael Sammler committed
86
    | @typed_val_expr ?Σ ?tG ?e ?T =>
87
      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
88
    | @typed_write ?Σ ?tG ?b ?e ?v ?ty ?Mov ?T =>
89
      pose (H := LET_ID T); change_no_check (@envs_entails PROP Δ (@typed_write Σ tG b e v ty Mov H))
Michael Sammler's avatar
Michael Sammler committed
90
    | @typed_place ?Σ ?tG ?P ?l1 ?β1 ?ty1 ?T =>
91
      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
92
    | @typed_bin_op ?Σ ?tG ?v1 ?P1 ?v2 ?P2 ?op ?ot1 ?ot2 ?T =>
93
      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
94
95
96
    end
  end.

Michael Sammler's avatar
Michael Sammler committed
97
Ltac liRInstantiateEvars_hook := idtac.
Michael Sammler's avatar
Michael Sammler committed
98
Ltac liRInstantiateEvars :=
Michael Sammler's avatar
Michael Sammler committed
99
  liRInstantiateEvars_hook;
Michael Sammler's avatar
Michael Sammler committed
100
101
102
103
104
105
106
  lazymatch goal with
  | |- (_ < protected ?H)%nat  _ => liInst H (S (protected (EVAR_ID _)))
  (* 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 *)
  | |- protected ?H = ( _ @ ?ty)%I  _ => liInst H ((protected (EVAR_ID _)) @ ty)%I
Michael Sammler's avatar
Michael Sammler committed
107
  | |- protected ?H = ty_of_rty (frac_ptr ?β _)%I  _ => liInst H (frac_ptr β (protected (EVAR_ID _)))%I
Michael Sammler's avatar
Michael Sammler committed
108
109
110
111
112
113
114
115
116
117
118
  | |- 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);
119
      change_no_check (envs_entails Δ (typed_stmt s2 fn ls fr Q))
Michael Sammler's avatar
Michael Sammler committed
120
121
122
123
124
125
    | _ => 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
126
    | subst_stmt ?xs ?s =>
Michael Sammler's avatar
Michael Sammler committed
127
      let s' := W.of_stmt s in
Michael Sammler's avatar
Michael Sammler committed
128
129
      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
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
    | _ =>
      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 _ _ _ _ _) _)
      | W.If _ _ _ => notypeclasses refine (tac_fast_apply (type_if _ _ _ _ _ _ _) _)
      | W.Switch _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_switch _ _ _ _ _ _ _ _ _) _)
      | W.Assert _ _ => notypeclasses refine (tac_fast_apply (type_assert _ _ _ _ _ _) _)
      | W.Goto ?bid => first [
         notypeclasses refine (tac_fast_apply (type_goto_precond _ _ _ _ _ _) _); progress liFindHyp
       | lazymatch goal with
         | H : BLOCK_PRECOND bid ?P |- _ =>
           notypeclasses refine (tac_fast_apply (tac_typed_single_block_rec P _ _ _ _ _ _ _) _);[compute_map_lookup|]
         end
       | notypeclasses refine (tac_fast_apply (type_goto _ _ _ _ _ _ _) _); [compute_map_lookup|]
                     ]
      | 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.

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];
159
    change_no_check (envs_entails Δ (T a1 a2))
Michael Sammler's avatar
Michael Sammler committed
160
161
162
163
164
165
166
167
  end.

Ltac liRExpr :=
  lazymatch goal with
  | |- envs_entails ?Δ (typed_val_expr ?e ?T) =>
    lazymatch e with
    | LocInfo ?info ?e2 =>
      update_loc_info [info];
168
      change_no_check (envs_entails Δ (typed_val_expr e2 (pop_location_info info T)))
Michael Sammler's avatar
Michael Sammler committed
169
170
171
172
173
174
175
176
177
    | _ => 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 _ _) _)
178
    | W.Use _ _ _ => notypeclasses refine (tac_fast_apply (type_use _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
179
180
    | W.AddrOf _ => notypeclasses refine (tac_fast_apply (type_addr_of _ _) _)
    | W.BinOp _ _ _ _ _ => notypeclasses refine (tac_fast_apply (type_bin_op _ _ _ _ _ _) _)
181
    | W.CopyAllocId _ _ => notypeclasses refine (tac_fast_apply (type_copy_alloc_id _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
182
183
    | W.UnOp _ _ _ => notypeclasses refine (tac_fast_apply (type_un_op _ _ _ _) _)
    | W.CAS _ _ _ _ => notypeclasses refine (tac_fast_apply (type_cas _ _ _ _ _) _)
184
    | W.Call _ _ => notypeclasses refine (tac_fast_apply (type_call _ _ _) _)
185
    | W.OffsetOf _ _ => notypeclasses refine (tac_fast_apply (type_offset_of _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
186
187
    | 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
188
    | W.IfE _ _ _ _ => notypeclasses refine (tac_fast_apply (type_ife _ _ _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
189
    | W.SkipE _ => notypeclasses refine (tac_fast_apply (type_skipe' _ _) _)
Michael Sammler's avatar
Michael Sammler committed
190
    | W.MacroE _ _ _ => notypeclasses refine (tac_fast_apply (type_macro_expr _ _ _) _)
Michael Sammler's avatar
Michael Sammler committed
191
192
193
194
195
196
197
    | _ => fail "do_expr: unknown expr" e
    end
  end.

Ltac liRJudgement :=
  lazymatch goal with
    | |- envs_entails _ (typed_write _ _ _ _ _) => notypeclasses refine (tac_fast_apply (type_write _ _ _ _ _ _ _) _); [ solve [refine _ ] |]
198
    | |- envs_entails _ (typed_read _ _ _ _) => notypeclasses refine (tac_fast_apply (type_read _ _ _ _ _ _) _); [ solve [refine _ ] |]
Michael Sammler's avatar
Michael Sammler committed
199
200
201
202
203
204
    | |- envs_entails _ (typed_callable _ _ _) => notypeclasses refine (tac_fast_apply (type_callable _ _ _ _) _)
    | |- envs_entails _ (typed_addr_of _ _) => notypeclasses refine (tac_fast_apply (type_addr_of_place _ _ _ _) _); [solve [refine _] |]
  end.

(* This does everything *)
Ltac liRStep :=
205
 liEnforceInvariantAndUnfoldInstantiatedEvars;
Michael Sammler's avatar
Michael Sammler committed
206
207
208
209
210
211
212
213
214
215
216
 try liRIntroduceLetInGoal;
 first [
   liRInstantiateEvars (* must be before do_side_cond and do_extensible_judgement *)
 | liRPopLocationInfo
 | liRStmt
 | liRExpr
 | liRJudgement
 | liStep
]; liSimpl.

(** * Tactics for starting a function *)
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
(* Recursively destruct a product in hypothesis H, using the given name as template. *)
Ltac destruct_product_hypothesis name H :=
  match goal with
  | H : _ * _ |- _ => let tmp1 := fresh "tmp" in
                      let tmp2 := fresh "tmp" in
                      destruct H as [tmp1 tmp2];
                      destruct_product_hypothesis name tmp1;
                      destruct_product_hypothesis name tmp2
  |           |- _ => let id := fresh name in
                      rename H into id
  end.

Ltac prepare_initial_coq_context :=
  (* The automation assumes that all products in the context are destructed, see liForall *)
  repeat lazymatch goal with
  | H : _ * _ |- _ => destruct_product_hypothesis H H
  | H : unit |- _ => destruct H
  end.

Michael Sammler's avatar
Michael Sammler committed
236
237
238
239
(* 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
240
Tactic Notation "start_function" constr(fnname) "(" simple_intropattern(x) ")" :=
Michael Sammler's avatar
Michael Sammler committed
241
242
243
244
  intros;
  repeat iIntros "#?";
  rewrite /typed_function;
  iIntros ( x );
Michael Sammler's avatar
Michael Sammler committed
245
  iSplit; [iPureIntro; simpl; by [repeat constructor] || fail "in" fnname "argument types don't match layout of arguments" |];
Michael Sammler's avatar
Michael Sammler committed
246
  let lsa := fresh "lsa" in let lsv := fresh "lsv" in
247
  iIntros "!#" (lsa lsv); inv_vec lsv; inv_vec lsa; prepare_initial_coq_context.
Michael Sammler's avatar
Michael Sammler committed
248
249
250

Ltac liRSplitBlocksIntro :=
  repeat (
251
      liEnforceInvariantAndUnfoldInstantiatedEvars;
Michael Sammler's avatar
Michael Sammler committed
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
      first [
          liSep
        | liWand
        | liImpl
        | liForall
        | liExist true
        | liUnfoldLetGoal]; liSimpl);
  liShow.


(* TODO: don't use i... tactics here *)
Ltac split_blocks Pfull Ps :=
  (* simpl can be very slow if Q is large. The rewrites distribute the
  subst_stmt. *)
  (* cbn in * is important here to simplify the types of local
  variables, otherwise unification gets confused later *)
  cbn -[union] in *; rewrite !fmap_insert fmap_empty;
269
  simpl_subst;
Michael Sammler's avatar
Michael Sammler committed
270
271
272
  let Q := fresh "Q" in
  lazymatch goal with
  | |- @envs_entails ?PROP ?Δ (@bi_wand _ ?P (@typed_stmt ?Σ ?tG ?B ?s ?fn ?ls ?fr ?Q')) =>
273
    pose (Q := (Q')); change_no_check (@envs_entails PROP Δ (@bi_wand PROP P (@typed_stmt Σ tG B s fn ls fr Q)))
Michael Sammler's avatar
Michael Sammler committed
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
  end;
  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;
  iApply (typed_block_rec Hfull); unfold Hfull; clear Hfull; last first; [|
  repeat (iApply big_sepM_insert; [reflexivity|]; iSplitL); last by [iApply big_sepM_empty];
  iExists _; (iSplitR; [iPureIntro; compute_map_lookup|]); iModIntro ];
  repeat (iApply tac_split_big_sepM; [reflexivity|]; iIntros "?"); iIntros "_".