New concurrent stack formalization

theories/concurrent_stacks/spec.v

-From stdpp Require Import namespaces.
-From iris.program_logic Require Export weakestpre.
-From iris.heap_lang Require Export proofmode notation.
-
-(** General (HoCAP-style) spec for a concurrent bag ("per-elemt spec") *)
-Record concurrent_bag {Σ} `{!heapG Σ} := ConcurrentBag {
-  mk_bag : val;
-  mk_bag_spec (N : namespace) (P : val → iProp Σ) :
-    {{{ True }}}
-      mk_bag #()
-    {{{ (f₁ f₂ : val), RET (f₁, f₂);
-        (□ WP f₁ #() {{ v, (∃ (v' : val), v ≡ SOMEV v' ∗ P v')  ∨  v ≡ NONEV }})
-        ∗ (∀ (v : val), □ (P v -∗ WP f₂ v {{ v, True }}))
-    }}}
-}.
-Arguments concurrent_bag _ {_}.
-
-(** General (HoCAP-style) spec for a concurrent stack *)
-
-Record concurrent_stack {Σ} `{!heapG Σ} := ConcurrentStack {
-  mk_stack : val;
-  mk_stack_spec (N : namespace) (P : list val → iProp Σ)
-    (Q : val → iProp Σ) (Q' Q'' : iProp Σ) :
-    {{{ P [] }}}
-      mk_stack #()
-    {{{ (f₁ f₂ : val), RET (f₁, f₂);
-        (□ ( (∀ v vs, P (v :: vs) ={⊤ ∖ ↑ N}=∗ Q v ∗ P vs)
-             ∧ (P [] ={⊤ ∖ ↑ N}=∗ Q' ∗ P []) -∗
-            WP f₁ #() {{ v, (∃ (v' : val), v ≡ SOMEV v' ∗ Q v') ∨ (v ≡ NONEV ∗ Q')}}))
-        ∗ (∀ (v : val),
-             □ ((∀ vs, P vs ={⊤ ∖ ↑ N}=∗ P (v :: vs) ∗ Q'') -∗ WP f₂ v {{ v, Q'' }}))
-    }}}
-}.
-Arguments concurrent_stack _ {_}.