Remove old files.

theories/examples/branching_proofs.v

-From iris.heap_lang Require Import proofmode notation.
-From osiris.channel Require Import branching.
-
-Definition branch_example b : expr :=
-  (let: "c" := new_chan #() in
-   select "c" #Left #b;;
-   Fork(branch: "c" @ #Right
-    left  send "c" #Right #5
-    right #());;
-   (if: #b then recv "c" #Left else #()))%E.
-
-Section BranchingExampleProofs.
-  Context `{!heapG Σ, !logrelG val Σ}.
-
-  Lemma branch_proof b :
-    {{{ True }}}
-      branch_example b
-    {{{ v, RET v; match b with
-                  | Left => ⌜v = #5⌝
-                  | Right => ⌜v = #()⌝
-                  end }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /branch_example.
-    wp_apply (new_chan_st_spec nroot ((<?> v @ ⌜v = 5⌝, TEnd) <+> TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]".
-    wp_apply (select_st_spec with "Hstl"); iIntros "Hstl".
-    wp_pures.
-    wp_apply (wp_fork with "[Hstr]").
-    - iNext.
-      simpl.
-      wp_apply (branch_st_spec with "Hstr")=> //;
-      iIntros (v) "[[-> Hstr]|[-> Hstr]]".
-      + wp_pures.
-        wp_apply (send_st_spec (A:=Z) with "[$Hstr //]"); auto.
-      + by wp_pures.
-    - destruct b.
-      + wp_apply (recv_st_spec (A:=Z) with "Hstl");
-        iIntros (v) "[Hstl ->]".
-        by iApply "HΦ".
-      + wp_pures. by iApply "HΦ".
-  Qed.
-End BranchingExampleProofs.
\ No newline at end of file

theories/examples/proofs_enc.v

-From iris.heap_lang Require Import proofmode notation.
-From osiris.channel Require Import proto_channel.
-
-Definition seq_example : expr :=
-  (let: "c" := new_chan #() in
-   send "c" #Left #5;;
-   recv "c" #Right)%E.
-
-Definition par_example : expr :=
-  (let: "c" := new_chan #() in
-   Fork(send "c" #Left #5);;
-   recv "c" #Right)%E.
-
-Definition par_2_example : expr :=
-  (let: "c" := new_chan #() in
-   Fork(let: "v" := recv "c" #Right in send "c" #Right ("v"+#2));;
-   send "c" #Left #5;;recv "c" #Left)%E.
-
-Definition heaplet_example : expr :=
-  (let: "c" := new_chan #() in
-   Fork(send "c" #Left (ref #5));;
-   !(recv "c" #Right))%E.
-
-Definition channel_example : expr :=
-  (let: "c" := new_chan #() in
-   Fork(
-       let: "c'" := new_chan #() in
-       send "c" #Left ("c'");; send "c'" #Left #5);;
-   let: "c'" := recv "c" #Right in
-   recv "c'" #Right
-  )%E.
-
-Definition bad_seq_example : expr :=
-  (let: "c" := new_chan #() in
-   let: "v" := recv "c" #Right in
-   send "c" #Left #5;; "v")%E.
-
-Definition bad_par_example : expr :=
-  (let: "c" := new_chan #() in
-   Fork(#());;
-   recv "c" #Right)%E.
-
-Definition bad_interleave_example : expr :=
-  (let: "c" := new_chan #() in
-   let: "c'" := new_chan #() in
-   Fork(recv "c" #Right;; send "c'" #Right #5);;
-   recv "c'" #Left;; send "c" #Left #5)%E.
-
-Section ExampleProofsEnc.
-  Context `{!heapG Σ, !logrelG val Σ}.
-
-  Lemma seq_proof :
-    {{{ True }}} seq_example {{{ v, RET v; ⌜v = #5⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /seq_example.
-    wp_apply (new_chan_st_spec nroot (<!> v @ ⌜v = 5⌝, TEnd))=> //;
-      iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (send_st_spec (A:=Z) with "[$Hstl //]"); iIntros "Hstl".
-    wp_apply (recv_st_spec (A:=Z) with "Hstr").
-    iIntros (v) "[Hstr ->]".
-    iApply "HΦ".
-    eauto.
-  Qed.
-
-  Lemma par_2_proof :
-    {{{ True }}}
-      par_2_example
-    {{{ (v:Z), RET #v; ⌜7 ≤ v⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /par_2_example.
-    wp_apply (new_chan_st_spec nroot
-      (<!> v @ ⌜5 ≤ v⌝, <?> v' @ ⌜v+2 ≤ v'⌝, TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (wp_fork with "[Hstr]").
-    - iNext.
-      wp_apply (recv_st_spec (A:=Z) with "Hstr"); iIntros (v) "[Hstr HP]".
-      wp_apply (send_st_spec (A:=Z) with "[$Hstr //]"); iIntros "Hstr".
-      eauto.
-    - wp_apply (send_st_spec (A:=Z) with "[$Hstl //]"); iIntros "Hstl".
-      wp_apply (recv_st_spec (A:=Z) with "Hstl"); iIntros (v) "[Hstl %]".
-      iApply "HΦ". iPureIntro. lia.
-  Qed.
-
-  Lemma heaplet_proof :
-    {{{ True }}} heaplet_example {{{ v l, RET v; ⌜v = #5⌝ ∗ l ↦ v }}}.
-  Proof.
-    rewrite /heaplet_example.
-    iIntros (Φ _) "HΦ".
-    wp_apply (new_chan_st_spec nroot (<!> v @ (v ↦ #5), TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (wp_fork with "[Hstl]").
-    - iNext.
-      wp_alloc l as "HP".
-      wp_apply (send_st_spec (A:=loc) with "[$Hstl HP]")=> //; iIntros "Hstl".
-      eauto.
-    - wp_apply (recv_st_spec (A:=loc) with "Hstr"); iIntros (v) "[Hstr HP]".
-      wp_load.
-      iApply "HΦ".
-      by iFrame.
-  Qed.
-
-  Lemma channel_proof :
-    {{{ True }}} channel_example {{{ v, RET v; ⌜v = #5⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /channel_example.
-    wp_apply (new_chan_st_spec nroot
-      (<!> v @ (∃ γ, ⟦ v @ Right : <?> v @ ⌜v = 5⌝, TEnd ⟧{nroot,γ}),
-               TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (wp_fork with "[Hstl]").
-    - iNext.
-      wp_apply (new_chan_st_spec nroot (<!> v @ ⌜v = 5⌝, TEnd))=> //;
-        iIntros (c' γ') "[Hstl' Hstr']"=> /=.
-      wp_apply (send_st_spec (A:=val) with "[Hstl Hstr']");
-        first by eauto 10 with iFrame.
-      iIntros "Hstl".
-      wp_apply (send_st_spec (A:=Z) with "[$Hstl' //]"); iIntros "Hstl'".
-      eauto.
-    - wp_apply (recv_st_spec (A:=val) with "Hstr"); iIntros (v) "[Hstr Hstr']".
-      iDestruct "Hstr'" as (γ') "Hstr'".
-      wp_apply (recv_st_spec (A:=Z) with "Hstr'"); iIntros (v') "[Hstr' <-]".
-      by iApply "HΦ".
-  Qed.
-
-  Lemma bad_seq_proof :
-    {{{ True }}} bad_seq_example {{{ v, RET v; ⌜v = #5⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /bad_seq_example.
-    wp_apply (new_chan_st_spec nroot (<!> v @ ⌜v = 5⌝, TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (recv_st_spec (A:=Z) with "Hstr"); iIntros (v) "[Hstr ->]".
-    wp_apply (send_st_spec (A:=Z) with "[$Hstl //]"); iIntros "Hstl".
-    wp_pures.
-    by iApply "HΦ".
-  Qed.
-
-  Lemma bad_par_proof :
-    {{{ True }}} bad_par_example {{{ v, RET v; ⌜v = #5⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /bad_par_example.
-    wp_apply (new_chan_st_spec nroot (<!> v @ ⌜v = 5⌝, TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (wp_fork with "[Hstl]").
-    - iNext. by wp_finish.
-    - wp_apply (recv_st_spec (A:=Z) with "Hstr"); iIntros (v) "[Hstr ->]".
-      by iApply "HΦ".
-  Qed.
-
-  Lemma bad_interleave_proof :
-    {{{ True }}} bad_interleave_example {{{ v, RET v; ⌜v = #()⌝ }}}.
-  Proof.
-    iIntros (Φ _) "HΦ".
-    rewrite /bad_interleave_example.
-    wp_apply (new_chan_st_spec nroot (<!> v @ ⌜v = 5⌝, TEnd))=> //;
-    iIntros (c γ) "[Hstl Hstr]"=> /=.
-    wp_apply (new_chan_st_spec nroot (<?> v @ ⌜v = 5⌝, TEnd))=> //;
-    iIntros (c' γ') "[Hstl' Hstr']"=> /=.
-    wp_apply (wp_fork with "[Hstr Hstr']").
-    - iNext. wp_apply (recv_st_spec (A:=Z) with "Hstr"); iIntros (v) "[Hstr HP]".
-      wp_apply (send_st_spec (A:=Z) with "[$Hstr' //]"). eauto.
-    - wp_apply (recv_st_spec (A:=Z) with "[$Hstl' //]"); iIntros (v) "[Hstl' HP]".
-      wp_apply (send_st_spec (A:=Z) with "[$Hstl //]"); iIntros "Hstl".
-      by iApply "HΦ".
-  Qed.
-End ExampleProofsEnc.