continue ...

Makefile.coq

@@ -102,7 +102,8 @@ VFILES:=sync.v\
   sync_stack.v\
   protocol.v\
   misc.v\
-  atomic_pair.v
+  atomic_pair.v\
+  srv.v
 
 ifneq ($(filter-out archclean clean cleanall printenv,$(MAKECMDGOALS)),)
 -include $(addsuffix .d,$(VFILES))

_CoqProject

@@ -6,3 +6,4 @@ sync_stack.v
 protocol.v
 misc.v
 atomic_pair.v
+srv.v

misc.v

-From iris.program_logic Require Export weakestpre hoare.
-From iris.proofmode Require Import invariants ghost_ownership.
-From iris.heap_lang Require Export lang.
-From iris.heap_lang Require Import proofmode notation.
-From iris.heap_lang.lib Require Import spin_lock.
-From iris.tests Require Import atomic.
-From iris.algebra Require Import dec_agree frac gmap upred_big_op.
-From iris.program_logic Require Import auth.
-Import uPred.
-
-Section lemmas.
-  Lemma frac_op': forall (p q: Qp), (p ⋅ q) = (p + q)%Qp.
-  Proof. done. Qed.
-  
-  Lemma pair_l_frac_update (g g': val):
-    ((1 / 2)%Qp, DecAgree g) ⋅ ((1 / 2)%Qp, DecAgree g) ~~> ((1 / 2)%Qp, DecAgree g') ⋅ ((1 / 2)%Qp, DecAgree g').
-  Proof.
-    repeat rewrite pair_op dec_agree_idemp.
-    rewrite frac_op' Qp_div_2.
-    eapply cmra_update_exclusive.
-    done.
-  Qed.
-  
-  Lemma pair_l_frac_op (p q: Qp) (g g': val):
-    (((p, DecAgree g') ⋅ (q, DecAgree g'))) ~~> ((p + q)%Qp, DecAgree g').
-  Proof. by rewrite pair_op dec_agree_idemp frac_op'. Qed.
-
-  Lemma pair_l_frac_op' (p q: Qp) (g g': val):
-     ((p + q)%Qp, DecAgree g') ~~> (((p, DecAgree g') ⋅ (q, DecAgree g'))).
-  Proof. by rewrite pair_op dec_agree_idemp frac_op'. Qed.
-
-  Lemma pair_l_frac_op_1' (g g': val):
-     (1%Qp, DecAgree g') ~~> (((1/2)%Qp, DecAgree g') ⋅ ((1/2)%Qp, DecAgree g')).
-  Proof. by rewrite pair_op dec_agree_idemp frac_op' Qp_div_2. Qed.
-
-  Lemma split_mapk
-        {Σ} {K: Type} `{Countable K} {V: cmraT}
-        (m: gmapUR K V) (k: K) (v: V) (R: K → iProp Σ) :
-    m !! k = Some v → ([★ map] k ↦ v ∈ m, R k) ⊢ R k ★ ([★ map] k ↦ v ∈ delete k m, R k).
-  Proof. iIntros (?) "HRm". by iApply (big_sepM_delete (fun k _ => R k)). Qed.
-
-  Lemma merge_mapk
-        {Σ} {K: Type} `{Countable K} {V: cmraT}
-        (m: gmapUR K V) (k: K) (v: V) (R: K → iProp Σ) :
-    R k ★ ([★ map] k ↦ v ∈ delete k m, R k) ⊢ ([★ map] k ↦ v ∈ m, R k).
-  Proof.
-    iIntros "[Hk HRs]".
-    destruct (m !! k) eqn:Heqn.
-    - iApply (big_sepM_delete (fun k _ => R k))=>//. iFrame.
-    - rewrite delete_notin=>//.
-  Qed.
-  
-  Lemma split_mapv
-        {Σ} {K: Type} `{Countable K} {V: cmraT}
-        (m: gmapUR K V) (k: K) (v: V) (R: V → iProp Σ) :
-    m !! k = Some v → ([★ map] k ↦ v ∈ m, R v) ⊢ R v ★ ([★ map] k ↦ v ∈ delete k m, R v).
-  Proof. iIntros (?) "HRm". by iApply (big_sepM_delete (fun _ v => R v)). Qed.
-
-  Lemma merge_mapv
-        {Σ} {K: Type} `{Countable K} {V: cmraT}
-        (m: gmapUR K V) (k: K) (v: V) (R: V → iProp Σ) :
-    m !! k = Some v → R v ★ ([★ map] k ↦ v ∈ delete k m, R v) ⊢ ([★ map] k ↦ v ∈ m, R v).
-  Proof. iIntros (?) "HRm". iApply (big_sepM_delete (fun _ v => R v))=>//. Qed.
-
-  Lemma map_agree {A: cmraT} m m' (hd: loc) (p q: A) x y:
-    m !! hd = Some (p, DecAgree y) →
-    x ≠ y → m = {[hd := (q, DecAgree x)]} ⋅ m' → False.
-  Proof.
-    intros H1 H2 H3.
-    subst. rewrite lookup_op lookup_singleton in H1.
-    destruct (m' !! hd) as [[b [c|]]|] eqn:Heqn; rewrite Heqn in H1; inversion H1=>//.
-    destruct (decide (x = c)) as [->|Hneq3]=>//.
-    - rewrite dec_agree_idemp in H3. by inversion H3.        
-    - rewrite dec_agree_ne in H3=>//.
-  Qed.
-
-  Lemma map_agree_none {A: cmraT} m m' (hd: loc) (q: A) (x: val):
-    m !! hd = None → m = {[hd := (q, DecAgree x)]} ⋅ m' → False.
-  Proof.
-    intros H1 H2. subst. rewrite lookup_op lookup_singleton in H1.
-    destruct (m' !! hd)=>//.
-  Qed.
-End lemmas.
-
-
-Section heap_extra.
-  Context `{heapG Σ}.
-
-  Lemma bogus_heap p (q1 q2: Qp) a b:
-    ~((q1 + q2)%Qp ≤ 1%Qp)%Qc →
-    heap_ctx ★ p ↦{q1} a ★ p ↦{q2} b ⊢ False.
-  Proof.
-    iIntros (?) "(#Hh & Hp1 & Hp2)".
-    iCombine "Hp1" "Hp2" as "Hp".
-    iDestruct (heap_mapsto_op_1 with "Hp") as "[_ Hp]".
-    rewrite heap_mapsto_eq. iDestruct (auth_own_valid with "Hp") as %H'.
-    apply singleton_valid in H'. destruct H' as [H' _].
-    auto.
-  Qed.
-  
-End heap_extra.