Commit 0f2be668 authored by Robbert's avatar Robbert

Merge branch 'twp_array' into 'master'

Add twp_ lemmas for the arrays.

See merge request !374
parents 511ed69b cc67112b
Pipeline #23927 passed with stage
in 14 minutes and 18 seconds
......@@ -139,10 +139,25 @@ Proof.
iDestruct ("Hl2" $! v) as "Hl2". rewrite list_insert_id; last done.
iApply "Hl2". iApply "Hl1".
Qed.
Lemma twp_load_offset s E l off vs v :
vs !! off = Some v
[[{ l ↦∗ vs }]] ! #(l + off) @ s; E [[{ RET v; l ↦∗ vs }]].
Proof.
iIntros (Hlookup Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_load with "Hl1"). iIntros "Hl1". iApply "HΦ".
iDestruct ("Hl2" $! v) as "Hl2". rewrite list_insert_id; last done.
iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_load_offset_vec s E l sz (off : fin sz) (vs : vec val sz) :
{{{ l ↦∗ vs }}} ! #(l + off) @ s; E {{{ RET vs !!! off; l ↦∗ vs }}}.
Proof. apply wp_load_offset. by apply vlookup_lookup. Qed.
Lemma twp_load_offset_vec s E l sz (off : fin sz) (vs : vec val sz) :
[[{ l ↦∗ vs }]] ! #(l + off) @ s; E [[{ RET vs !!! off; l ↦∗ vs }]].
Proof. apply twp_load_offset. by apply vlookup_lookup. Qed.
Lemma wp_store_offset s E l off vs v :
is_Some (vs !! off)
......@@ -153,6 +168,15 @@ Proof.
iApply (wp_store with "Hl1"). iNext. iIntros "Hl1".
iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma twp_store_offset s E l off vs v :
is_Some (vs !! off)
[[{ l ↦∗ vs }]] #(l + off) <- v @ s; E [[{ RET #(); l ↦∗ <[off:=v]> vs }]].
Proof.
iIntros ([w Hlookup] Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_store with "Hl1"). iIntros "Hl1".
iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_store_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
{{{ l ↦∗ vs }}} #(l + off) <- v @ s; E {{{ RET #(); l ↦∗ vinsert off v vs }}}.
......@@ -160,6 +184,12 @@ Proof.
setoid_rewrite vec_to_list_insert. apply wp_store_offset.
eexists. by apply vlookup_lookup.
Qed.
Lemma twp_store_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
[[{ l ↦∗ vs }]] #(l + off) <- v @ s; E [[{ RET #(); l ↦∗ vinsert off v vs }]].
Proof.
setoid_rewrite vec_to_list_insert. apply twp_store_offset.
eexists. by apply vlookup_lookup.
Qed.
Lemma wp_cmpxchg_suc_offset s E l off vs v' v1 v2 :
vs !! off = Some v'
......@@ -174,6 +204,19 @@ Proof.
iApply (wp_cmpxchg_suc with "Hl1"); [done..|].
iNext. iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma twp_cmpxchg_suc_offset s E l off vs v' v1 v2 :
vs !! off = Some v'
v' = v1
vals_compare_safe v' v1
[[{ l ↦∗ vs }]]
CmpXchg #(l + off) v1 v2 @ s; E
[[{ RET (v', #true); l ↦∗ <[off:=v2]> vs }]].
Proof.
iIntros (Hlookup ?? Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_cmpxchg_suc with "Hl1"); [done..|].
iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off = v1
......@@ -185,6 +228,16 @@ Proof.
intros. setoid_rewrite vec_to_list_insert. eapply wp_cmpxchg_suc_offset=> //.
by apply vlookup_lookup.
Qed.
Lemma twp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off = v1
vals_compare_safe (vs !!! off) v1
[[{ l ↦∗ vs }]]
CmpXchg #(l + off) v1 v2 @ s; E
[[{ RET (vs !!! off, #true); l ↦∗ vinsert off v2 vs }]].
Proof.
intros. setoid_rewrite vec_to_list_insert. eapply twp_cmpxchg_suc_offset=> //.
by apply vlookup_lookup.
Qed.
Lemma wp_cmpxchg_fail_offset s E l off vs v0 v1 v2 :
vs !! off = Some v0
......@@ -201,6 +254,21 @@ Proof.
iIntros "!> Hl1". iApply "HΦ". iDestruct ("Hl2" $! v0) as "Hl2".
rewrite list_insert_id; last done. iApply "Hl2". iApply "Hl1".
Qed.
Lemma twp_cmpxchg_fail_offset s E l off vs v0 v1 v2 :
vs !! off = Some v0
v0 v1
vals_compare_safe v0 v1
[[{ l ↦∗ vs }]]
CmpXchg #(l + off) v1 v2 @ s; E
[[{ RET (v0, #false); l ↦∗ vs }]].
Proof.
iIntros (Hlookup HNEq Hcmp Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_cmpxchg_fail with "Hl1"); first done.
{ destruct Hcmp; by [ left | right ]. }
iIntros "Hl1". iApply "HΦ". iDestruct ("Hl2" $! v0) as "Hl2".
rewrite list_insert_id; last done. iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_cmpxchg_fail_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off v1
......@@ -209,6 +277,13 @@ Lemma wp_cmpxchg_fail_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2
CmpXchg #(l + off) v1 v2 @ s; E
{{{ RET (vs !!! off, #false); l ↦∗ vs }}}.
Proof. intros. eapply wp_cmpxchg_fail_offset=> //. by apply vlookup_lookup. Qed.
Lemma twp_cmpxchg_fail_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off v1
vals_compare_safe (vs !!! off) v1
[[{ l ↦∗ vs }]]
CmpXchg #(l + off) v1 v2 @ s; E
[[{ RET (vs !!! off, #false); l ↦∗ vs }]].
Proof. intros. eapply twp_cmpxchg_fail_offset=> //. by apply vlookup_lookup. Qed.
Lemma wp_faa_offset s E l off vs (i1 i2 : Z) :
vs !! off = Some #i1
......@@ -220,6 +295,16 @@ Proof.
iApply (wp_faa with "Hl1").
iNext. iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma twp_faa_offset s E l off vs (i1 i2 : Z) :
vs !! off = Some #i1
[[{ l ↦∗ vs }]] FAA #(l + off) #i2 @ s; E
[[{ RET LitV (LitInt i1); l ↦∗ <[off:=#(i1 + i2)]> vs }]].
Proof.
iIntros (Hlookup Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_faa with "Hl1").
iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
vs !!! off = #i1
......@@ -229,6 +314,14 @@ Proof.
intros. setoid_rewrite vec_to_list_insert. apply wp_faa_offset=> //.
by apply vlookup_lookup.
Qed.
Lemma twp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
vs !!! off = #i1
[[{ l ↦∗ vs }]] FAA #(l + off) #i2 @ s; E
[[{ RET LitV (LitInt i1); l ↦∗ vinsert off #(i1 + i2) vs }]].
Proof.
intros. setoid_rewrite vec_to_list_insert. apply twp_faa_offset=> //.
by apply vlookup_lookup.
Qed.
End lifting.
......
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