Commit d5b9382b authored by Ralf Jung's avatar Ralf Jung

avoid use of heap_lang notation in proofmode.v

parent f3f5c57f
...@@ -182,8 +182,8 @@ Lemma tac_wp_allocN Δ Δ' s E j K v n Φ : ...@@ -182,8 +182,8 @@ Lemma tac_wp_allocN Δ Δ' s E j K v n Φ :
MaybeIntoLaterNEnvs 1 Δ Δ' MaybeIntoLaterNEnvs 1 Δ Δ'
( l, Δ'', ( l, Δ'',
envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ' = Some Δ'' envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ' = Some Δ''
envs_entails Δ'' (WP fill K (Val $ LitV l) @ s; E {{ Φ }})) envs_entails Δ'' (WP fill K (Val $ LitV $ LitLoc l) @ s; E {{ Φ }}))
envs_entails Δ (WP fill K (AllocN #n v) @ s; E {{ Φ }}). envs_entails Δ (WP fill K (AllocN (Val $ LitV $ LitInt n) (Val v)) @ s; E {{ Φ }}).
Proof. Proof.
rewrite envs_entails_eq=> ? ? HΔ. rewrite envs_entails_eq=> ? ? HΔ.
rewrite -wp_bind. eapply wand_apply; first exact: wp_allocN. rewrite -wp_bind. eapply wand_apply; first exact: wp_allocN.
...@@ -196,8 +196,8 @@ Lemma tac_twp_allocN Δ s E j K v n Φ : ...@@ -196,8 +196,8 @@ Lemma tac_twp_allocN Δ s E j K v n Φ :
( l, Δ', ( l, Δ',
envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ
= Some Δ' = Some Δ'
envs_entails Δ' (WP fill K (Val $ LitV l) @ s; E [{ Φ }])) envs_entails Δ' (WP fill K (Val $ LitV $ LitLoc l) @ s; E [{ Φ }]))
envs_entails Δ (WP fill K (AllocN #n v) @ s; E [{ Φ }]). envs_entails Δ (WP fill K (AllocN (Val $ LitV $ LitInt n) (Val v)) @ s; E [{ Φ }]).
Proof. Proof.
rewrite envs_entails_eq=> ? HΔ. rewrite envs_entails_eq=> ? HΔ.
rewrite -twp_bind. eapply wand_apply; first exact: twp_allocN. rewrite -twp_bind. eapply wand_apply; first exact: twp_allocN.
...@@ -211,7 +211,7 @@ Lemma tac_wp_alloc Δ Δ' s E j K v Φ : ...@@ -211,7 +211,7 @@ Lemma tac_wp_alloc Δ Δ' s E j K v Φ :
( l, Δ'', ( l, Δ'',
envs_app false (Esnoc Enil j (l v)) Δ' = Some Δ'' envs_app false (Esnoc Enil j (l v)) Δ' = Some Δ''
envs_entails Δ'' (WP fill K (Val $ LitV l) @ s; E {{ Φ }})) envs_entails Δ'' (WP fill K (Val $ LitV l) @ s; E {{ Φ }}))
envs_entails Δ (WP fill K (Alloc v) @ s; E {{ Φ }}). envs_entails Δ (WP fill K (Alloc (Val v)) @ s; E {{ Φ }}).
Proof. Proof.
rewrite envs_entails_eq=> ? HΔ. rewrite envs_entails_eq=> ? HΔ.
rewrite -wp_bind. eapply wand_apply; first exact: wp_alloc. rewrite -wp_bind. eapply wand_apply; first exact: wp_alloc.
...@@ -222,8 +222,8 @@ Qed. ...@@ -222,8 +222,8 @@ Qed.
Lemma tac_twp_alloc Δ s E j K v Φ : Lemma tac_twp_alloc Δ s E j K v Φ :
( l, Δ', ( l, Δ',
envs_app false (Esnoc Enil j (l v)) Δ = Some Δ' envs_app false (Esnoc Enil j (l v)) Δ = Some Δ'
envs_entails Δ' (WP fill K (Val $ LitV l) @ s; E [{ Φ }])) envs_entails Δ' (WP fill K (Val $ LitV $ LitLoc l) @ s; E [{ Φ }]))
envs_entails Δ (WP fill K (Alloc v) @ s; E [{ Φ }]). envs_entails Δ (WP fill K (Alloc (Val v)) @ s; E [{ Φ }]).
Proof. Proof.
rewrite envs_entails_eq=> HΔ. rewrite envs_entails_eq=> HΔ.
rewrite -twp_bind. eapply wand_apply; first exact: twp_alloc. rewrite -twp_bind. eapply wand_apply; first exact: twp_alloc.
...@@ -284,9 +284,9 @@ Lemma tac_wp_cmpxchg Δ Δ' Δ'' s E i K l v v1 v2 Φ : ...@@ -284,9 +284,9 @@ Lemma tac_wp_cmpxchg Δ Δ' Δ'' s E i K l v v1 v2 Φ :
envs_simple_replace i false (Esnoc Enil i (l v2)) Δ' = Some Δ'' envs_simple_replace i false (Esnoc Enil i (l v2)) Δ' = Some Δ''
vals_cmpxchg_compare_safe v v1 vals_cmpxchg_compare_safe v v1
(val_for_compare v = val_for_compare v1 (val_for_compare v = val_for_compare v1
envs_entails Δ'' (WP fill K (Val (v, #true)) @ s; E {{ Φ }})) envs_entails Δ'' (WP fill K (Val $ PairV v (LitV $ LitBool true)) @ s; E {{ Φ }}))
(val_for_compare v val_for_compare v1 (val_for_compare v val_for_compare v1
envs_entails Δ' (WP fill K (Val (v, #false)) @ s; E {{ Φ }})) envs_entails Δ' (WP fill K (Val $ PairV v (LitV $ LitBool false)) @ s; E {{ Φ }}))
envs_entails Δ (WP fill K (CmpXchg (LitV l) (Val v1) (Val v2)) @ s; E {{ Φ }}). envs_entails Δ (WP fill K (CmpXchg (LitV l) (Val v1) (Val v2)) @ s; E {{ Φ }}).
Proof. Proof.
rewrite envs_entails_eq=> ???? Hsuc Hfail. rewrite envs_entails_eq=> ???? Hsuc Hfail.
...@@ -305,9 +305,9 @@ Lemma tac_twp_cmpxchg Δ Δ' s E i K l v v1 v2 Φ : ...@@ -305,9 +305,9 @@ Lemma tac_twp_cmpxchg Δ Δ' s E i K l v v1 v2 Φ :
envs_simple_replace i false (Esnoc Enil i (l v2)) Δ = Some Δ' envs_simple_replace i false (Esnoc Enil i (l v2)) Δ = Some Δ'
vals_cmpxchg_compare_safe v v1 vals_cmpxchg_compare_safe v v1
(val_for_compare v = val_for_compare v1 (val_for_compare v = val_for_compare v1
envs_entails Δ' (WP fill K (Val (v, #true)) @ s; E [{ Φ }])) envs_entails Δ' (WP fill K (Val $ PairV v (LitV $ LitBool true)) @ s; E [{ Φ }]))
(val_for_compare v val_for_compare v1 (val_for_compare v val_for_compare v1
envs_entails Δ (WP fill K (Val (v, #false)) @ s; E [{ Φ }])) envs_entails Δ (WP fill K (Val $ PairV v (LitV $ LitBool false)) @ s; E [{ Φ }]))
envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]). envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]).
Proof. Proof.
rewrite envs_entails_eq=> ??? Hsuc Hfail. rewrite envs_entails_eq=> ??? Hsuc Hfail.
...@@ -326,7 +326,7 @@ Lemma tac_wp_cmpxchg_fail Δ Δ' s E i K l q v v1 v2 Φ : ...@@ -326,7 +326,7 @@ Lemma tac_wp_cmpxchg_fail Δ Δ' s E i K l q v v1 v2 Φ :
MaybeIntoLaterNEnvs 1 Δ Δ' MaybeIntoLaterNEnvs 1 Δ Δ'
envs_lookup i Δ' = Some (false, l {q} v)%I envs_lookup i Δ' = Some (false, l {q} v)%I
val_for_compare v val_for_compare v1 vals_cmpxchg_compare_safe v v1 val_for_compare v val_for_compare v1 vals_cmpxchg_compare_safe v v1
envs_entails Δ' (WP fill K (Val (v, #false)) @ s; E {{ Φ }}) envs_entails Δ' (WP fill K (Val $ PairV v (LitV $ LitBool false)) @ s; E {{ Φ }})
envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E {{ Φ }}). envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E {{ Φ }}).
Proof. Proof.
rewrite envs_entails_eq=> ?????. rewrite envs_entails_eq=> ?????.
...@@ -337,7 +337,7 @@ Qed. ...@@ -337,7 +337,7 @@ Qed.
Lemma tac_twp_cmpxchg_fail Δ s E i K l q v v1 v2 Φ : Lemma tac_twp_cmpxchg_fail Δ s E i K l q v v1 v2 Φ :
envs_lookup i Δ = Some (false, l {q} v)%I envs_lookup i Δ = Some (false, l {q} v)%I
val_for_compare v val_for_compare v1 vals_cmpxchg_compare_safe v v1 val_for_compare v val_for_compare v1 vals_cmpxchg_compare_safe v v1
envs_entails Δ (WP fill K (Val (v, #false)) @ s; E [{ Φ }]) envs_entails Δ (WP fill K (Val $ PairV v (LitV $ LitBool false)) @ s; E [{ Φ }])
envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]). envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]).
Proof. Proof.
rewrite envs_entails_eq. intros. rewrite -twp_bind. rewrite envs_entails_eq. intros. rewrite -twp_bind.
...@@ -350,7 +350,7 @@ Lemma tac_wp_cmpxchg_suc Δ Δ' Δ'' s E i K l v v1 v2 Φ : ...@@ -350,7 +350,7 @@ Lemma tac_wp_cmpxchg_suc Δ Δ' Δ'' s E i K l v v1 v2 Φ :
envs_lookup i Δ' = Some (false, l v)%I envs_lookup i Δ' = Some (false, l v)%I
envs_simple_replace i false (Esnoc Enil i (l v2)) Δ' = Some Δ'' envs_simple_replace i false (Esnoc Enil i (l v2)) Δ' = Some Δ''
val_for_compare v = val_for_compare v1 vals_cmpxchg_compare_safe v v1 val_for_compare v = val_for_compare v1 vals_cmpxchg_compare_safe v v1
envs_entails Δ'' (WP fill K (Val (v, #true)) @ s; E {{ Φ }}) envs_entails Δ'' (WP fill K (Val $ PairV v (LitV $ LitBool true)) @ s; E {{ Φ }})
envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E {{ Φ }}). envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E {{ Φ }}).
Proof. Proof.
rewrite envs_entails_eq=> ??????; subst. rewrite envs_entails_eq=> ??????; subst.
...@@ -363,7 +363,7 @@ Lemma tac_twp_cmpxchg_suc Δ Δ' s E i K l v v1 v2 Φ : ...@@ -363,7 +363,7 @@ Lemma tac_twp_cmpxchg_suc Δ Δ' s E i K l v v1 v2 Φ :
envs_lookup i Δ = Some (false, l v)%I envs_lookup i Δ = Some (false, l v)%I
envs_simple_replace i false (Esnoc Enil i (l v2)) Δ = Some Δ' envs_simple_replace i false (Esnoc Enil i (l v2)) Δ = Some Δ'
val_for_compare v = val_for_compare v1 vals_cmpxchg_compare_safe v v1 val_for_compare v = val_for_compare v1 vals_cmpxchg_compare_safe v v1
envs_entails Δ' (WP fill K (Val (v, #true)) @ s; E [{ Φ }]) envs_entails Δ' (WP fill K (Val $ PairV v (LitV $ LitBool true)) @ s; E [{ Φ }])
envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]). envs_entails Δ (WP fill K (CmpXchg (LitV l) v1 v2) @ s; E [{ Φ }]).
Proof. Proof.
rewrite envs_entails_eq=>?????; subst. rewrite envs_entails_eq=>?????; subst.
......
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