Minor cleanup

theories/examples/queue/proof_per_elem_graph.v

@@ -27,41 +27,39 @@ Context {Σ : gFunctors} `{noprolG Σ, inG Σ (graphR qevent)}.
 #[local] Notation iProp := (iProp Σ).
 #[local] Notation vProp := (vProp Σ).
 
-Variable N : namespace.
 Hypothesis msq : weak_queue_spec Σ.
 
-Variable P : Z → vProp.
-Variable q : loc.
+Implicit Types (N : namespace) (P : Z → vProp) (q : loc).
 
-Definition queue_resources G : vProp :=
+Definition queue_resources P G : vProp :=
   ([∗ set] eid ∈ filter (unmatched_enq_2 G) (to_set G.(Es)),
       match G.(Es) !! eid with
       | Some (mkGraphEvent (Enq v) V _) => @{V.(dv_in)} P v
       | _ => emp (* this is impossible *)
       end)%I.
 
-Instance queue_resources_objective G : Objective (queue_resources G).
+Instance queue_resources_objective P G : Objective (queue_resources P G).
 Proof.
   apply big_sepS_objective => e.
   destruct (G.(Es) !! e) as [[ ge ??]|]; [|apply _].
   destruct ge; apply _.
 Qed.
 
-Definition QueuePerElemInv γg : vProp :=
-  ∃ G, msq.(QueueInv) γg G ∗ queue_resources G.
+Definition QueuePerElemInv P γg : vProp :=
+  ∃ G, msq.(QueueInv) γg G ∗ queue_resources P G.
 
 Local Existing Instance QueueInv_Objective.
-Instance QueuePerElemInv_objective γg : Objective (QueuePerElemInv γg) := _.
+Instance QueuePerElemInv_objective P γg : Objective (QueuePerElemInv P γg) := _.
 
-Definition QueuePerElem γg : vProp :=
+Definition QueuePerElem N P γg q : vProp :=
   ∃ G M, msq.(QueueLocal) (N .@ "que") γg q G M ∗
-         inv (N .@ "iinv") (QueuePerElemInv γg).
+         inv (N .@ "iinv") (QueuePerElemInv P γg).
 
 (* TODO: we can prove logically-atomic spec here. *)
-Lemma per_elem_enqueue (DISJ: N ## histN) γg (x: Z) tid (NZ: 0 < x) :
-  {{{ QueuePerElem γg ∗ ▷ P x}}}
+Lemma per_elem_enqueue N P γg q (x: Z) tid (DISJ: N ## histN) (NZ: 0 < x) :
+  {{{ QueuePerElem N P γg q ∗ ▷ P x}}}
       msq.(enqueue) [ #q; #x] @ tid; ⊤
-  {{{ RET #☠; QueuePerElem γg }}}.
+  {{{ RET #☠; QueuePerElem N P γg q }}}.
 Proof.
   iIntros (Φ) "[Queue P] Post".
   iDestruct "Queue" as (G0 M0) "[Queue #QPI]".
@@ -86,7 +84,7 @@ Proof.
   { by rewrite EsG' Eqenq lookup_app_1_eq. }
 
   iIntros "!>".
-  iAssert (▷ queue_resources G')%I with "[P Elems]" as "Elems'".
+  iAssert (▷ queue_resources P G')%I with "[P Elems]" as "Elems'".
   { iNext. rewrite /queue_resources.
     have UMe : unmatched_enq_2 G' enqId.
     { split.
@@ -123,10 +121,10 @@ Proof.
     iExists _, _. by iFrame.
 Qed.
 
-Lemma per_elem_dequeue (DISJ: N ## histN) γg tid :
-  {{{ QueuePerElem γg }}}
+Lemma per_elem_dequeue N P γg q tid (DISJ: N ## histN) :
+  {{{ QueuePerElem N P γg q }}}
       msq.(dequeue) [ #q] @ tid; ⊤
-  {{{ (x: Z), RET #x; QueuePerElem γg ∗ (⌜x = 0⌝ ∨ ▷ P x) }}}.
+  {{{ (x: Z), RET #x; QueuePerElem N P γg q ∗ (⌜x = 0⌝ ∨ ▷ P x) }}}.
 Proof.
   iIntros (Φ) "QI Post". iDestruct "QI" as (G0 M0) "[Queue #QPI]".
   iApply (wp_step_fupd _ _ ⊤ _ (∀ _, _-∗ _)%I with "[$Post]"); [auto..|].
@@ -190,7 +188,7 @@ Proof.
   have EqEm' : G'.(Es) !! enqId = Some (mkGraphEvent (Enq x) Venq Menq).
   { rewrite EsG' lookup_app_1_ne; [done|by rewrite -Eqdeq]. }
 
-  iAssert (▷ (@{Venq.(dv_in)} P x ∗ queue_resources G'))%I
+  iAssert (▷ (@{Venq.(dv_in)} P x ∗ queue_resources P G'))%I
     with "[Elems]" as "[Px Elems]".
   { iNext. rewrite /queue_resources.
     rewrite (_: (@{Venq.(dv_in)} P x)%I
@@ -260,19 +258,19 @@ From gpfsl.examples.queue Require Import code_ms proof_ms_graph.
 (* TODO: use ther spec_per_elem one. Need try_enq and try_deq *)
 Section RSL_instance.
 Context {Σ : gFunctors} `{noprolG Σ, !msqueueG Σ, !atomicG Σ}.
-Context (P : lit → vProp Σ) (q: loc).
 
-Let is_queue N := QueuePerElem N (msqueue_impl_weak Σ).
+Let is_queue := QueuePerElem (msqueue_impl_weak Σ).
 
-Lemma per_elem_enqueue_inst N (DISJ: N ## histN) γg (x: Z) tid (NZ: (0 < x)%Z) :
-  {{{ is_queue N P q γg ∗ ▷ P x }}}
+Lemma per_elem_enqueue_inst N P γg q (x: Z) tid
+  (NZ: (0 < x)%Z) (DISJ: N ## histN) :
+  {{{ is_queue N P γg q ∗ ▷ P x }}}
     enqueue [ #q ; #x] @ tid; ⊤
-  {{{ RET #☠; is_queue N P q γg }}}.
+  {{{ RET #☠; is_queue N P γg q }}}.
 Proof. by apply : per_elem_enqueue. Qed.
 
-Lemma per_elem_dequeue_inst N (DISJ: N ## histN) γg tid :
-  {{{ is_queue N P q γg }}}
+Lemma per_elem_dequeue_inst N P γg q tid (DISJ: N ## histN) :
+  {{{ is_queue N P γg q }}}
     dequeue [ #q] @ tid; ⊤
-  {{{ (x: Z), RET #x; is_queue N P q γg ∗ (⌜x = 0⌝ ∨ ▷ P x) }}}.
+  {{{ (x: Z), RET #x; is_queue N P γg q ∗ (⌜x = 0⌝ ∨ ▷ P x) }}}.
 Proof. by apply : per_elem_dequeue. Qed.
 End RSL_instance.