Commit 3bf252ed authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Make some proofs more robust by (among others) avoiding `=> //`.

parent 2e9d27eb
......@@ -15,7 +15,7 @@ From iris.prelude Require Import options.
with lists of values. *)
Definition array `{!heapG Σ} (l : loc) (dq : dfrac) (vs : list val) : iProp Σ :=
([ list] i v vs, (l + i) {dq} v)%I.
[ list] i v vs, (l + i) {dq} v.
(** FIXME: Refactor these notations using custom entries once Coq bug #13654
has been fixed. *)
......@@ -165,7 +165,8 @@ Lemma wp_load_offset s E l dq off vs v :
{{{ l ↦∗{dq} vs }}} ! #(l + off) @ s; E {{{ RET v; l ↦∗{dq} vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_load_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_load_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_load_offset_vec s E l dq sz (off : fin sz) (vs : vec val sz) :
......@@ -189,7 +190,8 @@ Lemma wp_store_offset s E l off vs v :
{{{ l ↦∗ vs }}} #(l + off) <- v @ s; E {{{ RET #(); l ↦∗ <[off:=v]> vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_store_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_store_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_store_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
......@@ -202,7 +204,8 @@ 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 }}}.
Proof.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_store_offset_vec with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_store_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_xchg_offset s E l off vs v v' :
......@@ -211,7 +214,7 @@ Lemma twp_xchg_offset s E l off vs v v' :
Proof.
iIntros (Hlookup Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_xchg with "Hl1") => //. iIntros "Hl1".
iApply (twp_xchg with "Hl1"). iIntros "Hl1".
iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
Lemma wp_xchg_offset s E l off vs v v' :
......@@ -219,20 +222,22 @@ Lemma wp_xchg_offset s E l off vs v v' :
{{{ l ↦∗ vs }}} Xchg #(l + off) v' @ s; E {{{ RET v; l ↦∗ <[off:=v']> vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_xchg_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_xchg_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_xchg_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
[[{ l ↦∗ vs }]] Xchg #(l + off) v @ s; E [[{ RET (vs !!! off); l ↦∗ vinsert off v vs }]].
Proof.
setoid_rewrite vec_to_list_insert. apply twp_xchg_offset => //.
setoid_rewrite vec_to_list_insert. apply twp_xchg_offset.
by apply vlookup_lookup.
Qed.
Lemma wp_xchg_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
{{{ l ↦∗ vs }}} Xchg #(l + off) v @ s; E {{{ RET (vs !!! off); l ↦∗ vinsert off v vs }}}.
Proof.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_xchg_offset_vec with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_xchg_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_cmpxchg_suc_offset s E l off vs v' v1 v2 :
......@@ -257,7 +262,8 @@ Lemma wp_cmpxchg_suc_offset s E l off vs v' v1 v2 :
{{{ RET (v', #true); l ↦∗ <[off:=v2]> vs }}}.
Proof.
iIntros (??? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_suc_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_cmpxchg_suc_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
......@@ -267,7 +273,8 @@ Lemma twp_cmpxchg_suc_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, #true); l ↦∗ vinsert off v2 vs }]].
Proof.
intros. setoid_rewrite vec_to_list_insert. eapply twp_cmpxchg_suc_offset=> //.
intros. setoid_rewrite vec_to_list_insert.
apply twp_cmpxchg_suc_offset; [|done..].
by apply vlookup_lookup.
Qed.
Lemma wp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
......@@ -278,7 +285,8 @@ Lemma wp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2
{{{ RET (vs !!! off, #true); l ↦∗ vinsert off v2 vs }}}.
Proof.
iIntros (?? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_suc_offset_vec with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_cmpxchg_suc_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_cmpxchg_fail_offset s E l dq off vs v0 v1 v2 :
......@@ -305,7 +313,8 @@ Lemma wp_cmpxchg_fail_offset s E l dq off vs v0 v1 v2 :
{{{ RET (v0, #false); l ↦∗{dq} vs }}}.
Proof.
iIntros (??? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_fail_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_cmpxchg_fail_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
Lemma twp_cmpxchg_fail_offset_vec s E l dq sz (off : fin sz) (vs : vec val sz) v1 v2 :
......@@ -314,14 +323,20 @@ Lemma twp_cmpxchg_fail_offset_vec s E l dq sz (off : fin sz) (vs : vec val sz) v
[[{ l ↦∗{dq} vs }]]
CmpXchg #(l + off) v1 v2 @ s; E
[[{ RET (vs !!! off, #false); l ↦∗{dq} vs }]].
Proof. intros. eapply twp_cmpxchg_fail_offset=> //. by apply vlookup_lookup. Qed.
Proof.
intros. apply twp_cmpxchg_fail_offset; [|done..].
by apply vlookup_lookup.
Qed.
Lemma wp_cmpxchg_fail_offset_vec s E l dq sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off v1
vals_compare_safe (vs !!! off) v1
{{{ l ↦∗{dq} vs }}}
CmpXchg #(l + off) v1 v2 @ s; E
{{{ RET (vs !!! off, #false); l ↦∗{dq} vs }}}.
Proof. intros. eapply wp_cmpxchg_fail_offset=> //. by apply vlookup_lookup. Qed.
Proof.
intros. eapply wp_cmpxchg_fail_offset; [|done..].
by apply vlookup_lookup.
Qed.
Lemma twp_faa_offset s E l off vs (i1 i2 : Z) :
vs !! off = Some #i1
......@@ -339,7 +354,7 @@ Lemma wp_faa_offset s E l off vs (i1 i2 : Z) :
{{{ RET LitV (LitInt i1); l ↦∗ <[off:=#(i1 + i2)]> vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_faa_offset with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_faa_offset with "H"); [by eauto..|]; iIntros "H HΦ". by iApply "HΦ".
Qed.
Lemma twp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
......@@ -347,7 +362,7 @@ Lemma twp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
[[{ 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=> //.
intros. setoid_rewrite vec_to_list_insert. apply twp_faa_offset.
by apply vlookup_lookup.
Qed.
Lemma wp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
......@@ -356,7 +371,8 @@ Lemma wp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
{{{ RET LitV (LitInt i1); l ↦∗ vinsert off #(i1 + i2) vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_faa_offset_vec with "H"); [eauto..|]; iIntros "H HΦ". by iApply "HΦ".
iApply (twp_faa_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
(** Derived prophecy laws *)
......@@ -368,7 +384,7 @@ Lemma wp_resolve_proph s E (p : proph_id) (pvs : list (val * val)) v :
{{{ pvs', RET (LitV LitUnit); pvs = (LitV LitUnit, v)::pvs' proph p pvs' }}}.
Proof.
iIntros (Φ) "Hp HΦ". iApply (wp_resolve with "Hp"); first done.
iApply lifting.wp_pure_step_later=> //=. iApply wp_value.
iApply lifting.wp_pure_step_later; first done. iApply wp_value.
iIntros "!>" (vs') "HEq Hp". iApply "HΦ". iFrame.
Qed.
......
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