Commit 2dc8d5d8 authored by Jonas Kastberg's avatar Jonas Kastberg

Squashed commit of the following:

commit e0d15199
Author: jihgfee <jihgfee@gmail.com>
Date:   Wed Sep 16 14:20:00 2020 +0200

    Refactoring - Moved spar to own file and renamed as par_start

commit fd7dc61d
Author: jihgfee <jihgfee@gmail.com>
Date:   Wed Sep 16 13:10:42 2020 +0200

    Proved spar using typing rule instead of breaking abstraction

commit 821a4c23
Author: jihgfee <jihgfee@gmail.com>
Date:   Tue Sep 15 17:11:20 2020 +0200

    Whitespace cleanup

commit eb01938a
Author: jihgfee <jihgfee@gmail.com>
Date:   Tue Sep 15 17:10:37 2020 +0200

    Added a parallel composition for lambdas over channels
parent fd9a4c7a
Pipeline #34199 passed with stage
in 5 minutes and 47 seconds
......@@ -36,6 +36,7 @@ theories/logrel/term_typing_judgment.v
theories/logrel/subtyping_rules.v
theories/logrel/term_typing_rules.v
theories/logrel/lib/mutex.v
theories/logrel/lib/par_start.v
theories/logrel/examples/double.v
theories/logrel/examples/pair.v
theories/logrel/examples/rec_subtyping.v
......
From actris.logrel Require Export term_typing_rules environments.
From actris.channel Require Import proofmode.
Section properties.
Context `{heapG Σ}.
Context `{chanG Σ}.
Context `{spawnG Σ}.
Definition par_start : expr :=
(λ: "e1" "e2",
let: "c" := new_chan #() in
let: "c1" := Fst "c" in
let: "c2" := Snd "c" in
("e1" "c1") ||| ("e2" "c2"))%E.
Lemma ltyped_par_start Γ S A B :
Γ par_start : ((chan S) A) (chan (lty_dual S) B) A * B.
Proof.
iApply ltyped_lam; [ iApply env_split_id_l | ].
iApply ltyped_lam; [ iApply env_split_id_r | ].
iApply ltyped_let.
{ iApply ltyped_app; [ iApply ltyped_unit | iApply ltyped_new_chan ]. }
iApply ltyped_let; [ by iApply ltyped_fst | ].
rewrite insert_insert.
iApply ltyped_let; [ by iApply ltyped_snd | ].
rewrite /binder_insert (insert_commute _ "c1" "c") // insert_insert.
iApply (ltyped_par).
- iApply env_split_right; last first.
{ rewrite (insert_commute _ "c1" "e2"); [ | eauto ].
rewrite (insert_commute _ "c" "e2"); [ | eauto ].
iApply env_split_right; last by iApply env_split_id_r.
eauto. eauto. }
eauto. eauto.
- iApply ltyped_app; by iApply ltyped_var.
- iApply ltyped_app; by iApply ltyped_var.
- rewrite insert_insert.
rewrite (insert_commute _ "c2" "e2") // insert_insert.
rewrite (insert_commute _ "c1" "c") // insert_insert.
rewrite (insert_commute _ "c1" "e1") //
(insert_commute _ "c" "e1") // insert_insert.
iApply env_split_left=> //; last first.
iApply env_split_left=> //; last first.
iApply env_split_left=> //; last first.
iApply env_split_id_l.
eauto. eauto. eauto.
Qed.
End properties.
......@@ -6,7 +6,8 @@ From iris.bi.lib Require Import core.
From iris.base_logic.lib Require Import invariants.
From iris.heap_lang Require Import metatheory.
From iris.heap_lang.lib Require Export spawn par assert.
From actris.logrel Require Export subtyping term_typing_judgment operators session_types.
From actris.logrel Require Export subtyping term_typing_judgment operators
session_types.
From actris.logrel Require Import environments.
From actris.utils Require Import switch.
From actris.channel Require Import proofmode.
......@@ -438,12 +439,12 @@ Section properties.
(** Parallel composition properties *)
Lemma ltyped_par Γ Γ' Γ1 Γ1' Γ2 Γ2' e1 e2 A B :
env_split Γ Γ1 Γ2 -
env_split Γ' Γ1' Γ2' -
(Γ1 e1 : A Γ1') -
(Γ2 e2 : B Γ2') -
env_split Γ' Γ1' Γ2' -
Γ e1 ||| e2 : A * B Γ'.
Proof.
iIntros "#Hsplit #Hsplit' #H1 #H2" (vs) "!> HΓ /=".
iIntros "#Hsplit #H1 #H2 #Hsplit'" (vs) "!> HΓ /=".
iDestruct ("Hsplit" with "HΓ") as "[HΓ1 HΓ2]".
wp_apply (wp_par with "[HΓ1] [HΓ2]").
- iApply ("H1" with "HΓ1").
......@@ -460,10 +461,10 @@ Section properties.
Context `{chanG Σ}.
Lemma ltyped_new_chan Γ S :
Γ new_chan : () (chan S * chan (lty_dual S)) Γ.
Γ new_chan : () (chan S * chan (lty_dual S)) Γ.
Proof.
iIntros (vs) "!> HΓ /=". iApply wp_value. iFrame "HΓ".
iIntros "!>" (u) ">->".
iIntros (u) ">->".
iApply (new_chan_spec with "[//]"); iIntros (c1 c2) "!> [Hp1 Hp2]".
iExists c1, c2. iSplit=>//. iFrame "Hp1 Hp2".
Qed.
......
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