Define type pbit for readable adequacy lemmas.

theories/heap_lang/adequacy.v

@@ -16,7 +16,7 @@ Proof. solve_inG. Qed.
 
 Definition heap_adequacy Σ `{heapPreG Σ} e σ φ :
   (∀ `{heapG Σ}, WP e {{ v, ⌜φ v⌝ }}%I) →
-  adequate true e σ φ.
+  adequate progress e σ φ.
 Proof.
   intros Hwp; eapply (wp_adequacy _ _); iIntros (?) "".
   iMod (own_alloc (● to_gen_heap σ)) as (γ) "Hh".

theories/heap_lang/proofmode.v

@@ -27,7 +27,7 @@ Ltac wp_value_head := eapply tac_wp_value; [apply _|lazy beta].
 Tactic Notation "wp_pure" open_constr(efoc) :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) => reshape_expr e ltac:(fun K e' =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) => reshape_expr e ltac:(fun K e' =>
     unify e' efoc;
     eapply (tac_wp_pure K);
     [simpl; apply _                 (* PureExec *)
@@ -66,7 +66,7 @@ Ltac wp_bind_core K :=
 Tactic Notation "wp_bind" open_constr(efoc) :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     reshape_expr e ltac:(fun K e' => unify e' efoc; wp_bind_core K)
     || fail "wp_bind: cannot find" efoc "in" e
   | _ => fail "wp_bind: not a 'wp'"
@@ -151,7 +151,7 @@ End heap.
 Tactic Notation "wp_apply" open_constr(lem) :=
   iPoseProofCore lem as false true (fun H =>
     lazymatch goal with
-    | |- envs_entails _ (wp true ?E ?e ?Q) =>
+    | |- envs_entails _ (wp progress ?E ?e ?Q) =>
       reshape_expr e ltac:(fun K e' =>
         wp_bind_core K; iApplyHyp H; try iNext; simpl) ||
       lazymatch iTypeOf H with
@@ -163,7 +163,7 @@ Tactic Notation "wp_apply" open_constr(lem) :=
 Tactic Notation "wp_alloc" ident(l) "as" constr(H) :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     first
       [reshape_expr e ltac:(fun K e' =>
          eapply (tac_wp_alloc _ _ _ H K); [apply _|..])
@@ -182,7 +182,7 @@ Tactic Notation "wp_alloc" ident(l) :=
 Tactic Notation "wp_load" :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     first
       [reshape_expr e ltac:(fun K e' => eapply (tac_wp_load _ _ _ _ K))
       |fail 1 "wp_load: cannot find 'Load' in" e];
@@ -196,7 +196,7 @@ Tactic Notation "wp_load" :=
 Tactic Notation "wp_store" :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     first
       [reshape_expr e ltac:(fun K e' =>
          eapply (tac_wp_store _ _ _ _ _ K); [apply _|..])
@@ -212,7 +212,7 @@ Tactic Notation "wp_store" :=
 Tactic Notation "wp_cas_fail" :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     first
       [reshape_expr e ltac:(fun K e' =>
          eapply (tac_wp_cas_fail _ _ _ _ K); [apply _|apply _|..])
@@ -228,7 +228,7 @@ Tactic Notation "wp_cas_fail" :=
 Tactic Notation "wp_cas_suc" :=
   iStartProof;
   lazymatch goal with
-  | |- envs_entails _ (wp true ?E ?e ?Q) =>
+  | |- envs_entails _ (wp progress ?E ?e ?Q) =>
     first
       [reshape_expr e ltac:(fun K e' =>
          eapply (tac_wp_cas_suc _ _ _ _ _ K); [apply _|apply _|..])

theories/program_logic/adequacy.v

@@ -34,24 +34,24 @@ Proof.
 Qed.
 
 (* Program logic adequacy *)
-Record adequate {Λ} (p : bool) (e1 : expr Λ) (σ1 : state Λ) (φ : val Λ → Prop) := {
+Record adequate {Λ} (p : pbit) (e1 : expr Λ) (σ1 : state Λ) (φ : val Λ → Prop) := {
   adequate_result t2 σ2 v2 :
    rtc step ([e1], σ1) (of_val v2 :: t2, σ2) → φ v2;
   adequate_safe t2 σ2 e2 :
-   p →
+   p = progress →
    rtc step ([e1], σ1) (t2, σ2) →
    e2 ∈ t2 → progressive e2 σ2
 }.
 
 Theorem adequate_tp_safe {Λ} (e1 : expr Λ) t2 σ1 σ2 φ :
-  adequate true e1 σ1 φ →
+  adequate progress e1 σ1 φ →
   rtc step ([e1], σ1) (t2, σ2) →
   Forall (λ e, is_Some (to_val e)) t2 ∨ ∃ t3 σ3, step (t2, σ2) (t3, σ3).
 Proof.
   intros Had ?.
   destruct (decide (Forall (λ e, is_Some (to_val e)) t2)) as [|Ht2]; [by left|].
   apply (not_Forall_Exists _), Exists_exists in Ht2; destruct Ht2 as (e2&?&He2).
-  destruct (adequate_safe true e1 σ1 φ Had t2 σ2 e2) as [?|(e3&σ3&efs&?)];
+  destruct (adequate_safe progress e1 σ1 φ Had t2 σ2 e2) as [?|(e3&σ3&efs&?)];
     rewrite ?eq_None_not_Some; auto.
   { exfalso. eauto. }
   destruct (elem_of_list_split t2 e2) as (t2'&t2''&->); auto.
@@ -59,7 +59,7 @@ Proof.
 Qed.
 
 Section adequacy.
-Context `{irisG Λ Σ} (p : bool).
+Context `{irisG Λ Σ} (p : pbit).
 Implicit Types e : expr Λ.
 Implicit Types P Q : iProp Σ.
 Implicit Types Φ : val Λ → iProp Σ.
@@ -187,7 +187,7 @@ Proof.
     iMod wsat_alloc as (Hinv) "[Hw HE]".
     rewrite fupd_eq in Hwp; iMod (Hwp with "[$Hw $HE]") as ">(Hw & HE & Hwp)".
     iDestruct "Hwp" as (Istate) "[HI Hwp]".
-    iApply (@wptp_safe _ _ (IrisG _ _ Hinv Istate) true); eauto with iFrame.
+    iApply (@wptp_safe _ _ (IrisG _ _ Hinv Istate) progress); eauto with iFrame.
 Qed.
 
 Theorem wp_invariance Σ Λ `{invPreG Σ} p e σ1 t2 σ2 φ :

theories/program_logic/ectx_lifting.v

@@ -6,7 +6,7 @@ Set Default Proof Using "Type".
 Section wp.
 Context {expr val ectx state} {Λ : EctxLanguage expr val ectx state}.
 Context `{irisG (ectx_lang expr) Σ} {Hinh : Inhabited state}.
-Implicit Types p : bool.
+Implicit Types p : pbit.
 Implicit Types P : iProp Σ.
 Implicit Types Φ : val → iProp Σ.
 Implicit Types v : val.

theories/program_logic/hoare.v

@@ -3,7 +3,7 @@ From iris.base_logic.lib Require Export viewshifts.
 From iris.proofmode Require Import tactics.
 Set Default Proof Using "Type".
 
-Definition ht `{irisG Λ Σ} (p : bool) (E : coPset) (P : iProp Σ)
+Definition ht `{irisG Λ Σ} (p : pbit) (E : coPset) (P : iProp Σ)
     (e : expr Λ) (Φ : val Λ → iProp Σ) : iProp Σ :=
   (□ (P -∗ WP e @ p; E {{ Φ }}))%I.
 Instance: Params (@ht) 5.
@@ -11,38 +11,38 @@ Instance: Params (@ht) 5.
 Notation "{{ P } } e @ p ; E {{ Φ } }" := (ht p E P%I e%E Φ%I)
   (at level 20, P, e, Φ at level 200,
    format "{{  P  } }  e  @  p ;  E  {{  Φ  } }") : C_scope.
-Notation "{{ P } } e @ E {{ Φ } }" := (ht true E P%I e%E Φ%I)
+Notation "{{ P } } e @ E {{ Φ } }" := (ht progress E P%I e%E Φ%I)
   (at level 20, P, e, Φ at level 200,
    format "{{  P  } }  e  @  E  {{  Φ  } }") : C_scope.
-Notation "{{ P } } e @ E ? {{ Φ } }" := (ht false E P%I e%E Φ%I)
+Notation "{{ P } } e @ E ? {{ Φ } }" := (ht noprogress E P%I e%E Φ%I)
   (at level 20, P, e, Φ at level 200,
    format "{{  P  } }  e  @  E  ? {{  Φ  } }") : C_scope.
-Notation "{{ P } } e {{ Φ } }" := (ht true ⊤ P%I e%E Φ%I)
+Notation "{{ P } } e {{ Φ } }" := (ht progress ⊤ P%I e%E Φ%I)
   (at level 20, P, e, Φ at level 200,
    format "{{  P  } }  e  {{  Φ  } }") : C_scope.
-Notation "{{ P } } e ? {{ Φ } }" := (ht false ⊤ P%I e%E Φ%I)
+Notation "{{ P } } e ? {{ Φ } }" := (ht noprogress ⊤ P%I e%E Φ%I)
   (at level 20, P, e, Φ at level 200,
    format "{{  P  } }  e  ? {{  Φ  } }") : C_scope.
 
 Notation "{{ P } } e @ p ; E {{ v , Q } }" := (ht p E P%I e%E (λ v, Q)%I)
   (at level 20, P, e, Q at level 200,
    format "{{  P  } }  e  @  p ;  E  {{  v ,  Q  } }") : C_scope.
-Notation "{{ P } } e @ E {{ v , Q } }" := (ht true E P%I e%E (λ v, Q)%I)
+Notation "{{ P } } e @ E {{ v , Q } }" := (ht progress E P%I e%E (λ v, Q)%I)
   (at level 20, P, e, Q at level 200,
    format "{{  P  } }  e  @  E  {{  v ,  Q  } }") : C_scope.
-Notation "{{ P } } e @ E ? {{ v , Q } }" := (ht false E P%I e%E (λ v, Q)%I)
+Notation "{{ P } } e @ E ? {{ v , Q } }" := (ht noprogress E P%I e%E (λ v, Q)%I)
   (at level 20, P, e, Q at level 200,
    format "{{  P  } }  e  @  E  ? {{  v ,  Q  } }") : C_scope.
-Notation "{{ P } } e {{ v , Q } }" := (ht true ⊤ P%I e%E (λ v, Q)%I)
+Notation "{{ P } } e {{ v , Q } }" := (ht progress ⊤ P%I e%E (λ v, Q)%I)
   (at level 20, P, e, Q at level 200,
    format "{{  P  } }  e  {{  v ,  Q  } }") : C_scope.
-Notation "{{ P } } e ? {{ v , Q } }" := (ht false ⊤ P%I e%E (λ v, Q)%I)
+Notation "{{ P } } e ? {{ v , Q } }" := (ht noprogress ⊤ P%I e%E (λ v, Q)%I)
   (at level 20, P, e, Q at level 200,
    format "{{  P  } }  e  ? {{  v ,  Q  } }") : C_scope.
 
 Section hoare.
 Context `{irisG Λ Σ}.
-Implicit Types p : bool.
+Implicit Types p : pbit.
 Implicit Types P Q : iProp Σ.
 Implicit Types Φ Ψ : val Λ → iProp Σ.
 Implicit Types v : val Λ.
@@ -77,7 +77,7 @@ Proof.
 Qed.
 
 Lemma ht_atomic' p E1 E2 P P' Φ Φ' e :
-  StronglyAtomic e ∨ p ∧ Atomic e →
+  StronglyAtomic e ∨ p = progress ∧ Atomic e →
   (P ={E1,E2}=> P') ∧ {{ P' }} e @ p; E2 {{ Φ' }} ∧ (∀ v, Φ' v ={E2,E1}=> Φ v)
   ⊢ {{ P }} e @ p; E1 {{ Φ }}.
 Proof.

theories/program_logic/lifting.v

@@ -5,7 +5,7 @@ Set Default Proof Using "Type".
 
 Section lifting.
 Context `{irisG Λ Σ}.
-Implicit Types p : bool.
+Implicit Types p : pbit.
 Implicit Types v : val Λ.
 Implicit Types e : expr Λ.
 Implicit Types σ : state Λ.

theories/program_logic/ownp.v

@@ -70,7 +70,7 @@ Qed.
 (** Lifting *)
 Section lifting.
   Context `{ownPG Λ Σ}.
-  Implicit Types p : bool.
+  Implicit Types p : pbit.
   Implicit Types e : expr Λ.
   Implicit Types Φ : val Λ → iProp Σ.
 
@@ -197,7 +197,7 @@ Section ectx_lifting.
   Import ectx_language.
   Context {expr val ectx state} {Λ : EctxLanguage expr val ectx state}.
   Context `{ownPG (ectx_lang expr) Σ} {Hinh : Inhabited state}.
-  Implicit Types p : bool.
+  Implicit Types p : pbit.
   Implicit Types Φ : val → iProp Σ.
   Implicit Types e : expr.
   Hint Resolve head_prim_reducible head_reducible_prim_step.

theories/program_logic/weakestpre.v

@@ -11,7 +11,9 @@ Class irisG' (Λstate : Type) (Σ : gFunctors) := IrisG {
 }.
 Notation irisG Λ Σ := (irisG' (state Λ) Σ).
 
-Definition wp_pre `{irisG Λ Σ} (p : bool)
+CoInductive pbit := progress | noprogress.
+
+Definition wp_pre `{irisG Λ Σ} (p : pbit)
     (wp : coPset -c> expr Λ -c> (val Λ -c> iProp Σ) -c> iProp Σ) :
     coPset -c> expr Λ -c> (val Λ -c> iProp Σ) -c> iProp Σ := λ E e1 Φ,
   match to_val e1 with
@@ -41,32 +43,32 @@ Instance: Params (@wp) 6.
 Notation "'WP' e @ p ; E {{ Φ } }" := (wp p E e%E Φ)
   (at level 20, e, Φ at level 200,
    format "'[' 'WP'  e  '/' @  p ;  E  {{  Φ  } } ']'") : uPred_scope.
-Notation "'WP' e @ E {{ Φ } }" := (wp true E e%E Φ)
+Notation "'WP' e @ E {{ Φ } }" := (wp progress E e%E Φ)
   (at level 20, e, Φ at level 200,
    format "'[' 'WP'  e  '/' @  E  {{  Φ  } } ']'") : uPred_scope.
-Notation "'WP' e @ E ? {{ Φ } }" := (wp false E e%E Φ)
+Notation "'WP' e @ E ? {{ Φ } }" := (wp noprogress E e%E Φ)
   (at level 20, e, Φ at level 200,
    format "'[' 'WP'  e  '/' @  E  ? {{  Φ  } } ']'") : uPred_scope.
-Notation "'WP' e {{ Φ } }" := (wp true ⊤ e%E Φ)
+Notation "'WP' e {{ Φ } }" := (wp progress ⊤ e%E Φ)
   (at level 20, e, Φ at level 200,
    format "'[' 'WP'  e  '/' {{  Φ  } } ']'") : uPred_scope.
-Notation "'WP' e ? {{ Φ } }" := (wp false ⊤ e%E Φ)
+Notation "'WP' e ? {{ Φ } }" := (wp noprogress ⊤ e%E Φ)
   (at level 20, e, Φ at level 200,
    format "'[' 'WP'  e  '/' ? {{  Φ  } } ']'") : uPred_scope.
 
 Notation "'WP' e @ p ; E {{ v , Q } }" := (wp p E e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'[' 'WP'  e  '/' @  p ;  E  {{  v ,  Q  } } ']'") : uPred_scope.
-Notation "'WP' e @ E {{ v , Q } }" := (wp true E e%E (λ v, Q))
+Notation "'WP' e @ E {{ v , Q } }" := (wp progress E e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'[' 'WP'  e  '/' @  E  {{  v ,  Q  } } ']'") : uPred_scope.
-Notation "'WP' e @ E ? {{ v , Q } }" := (wp false E e%E (λ v, Q))
+Notation "'WP' e @ E ? {{ v , Q } }" := (wp noprogress E e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'[' 'WP'  e  '/' @  E  ? {{  v ,  Q  } } ']'") : uPred_scope.
-Notation "'WP' e {{ v , Q } }" := (wp true ⊤ e%E (λ v, Q))
+Notation "'WP' e {{ v , Q } }" := (wp progress ⊤ e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'[' 'WP'  e  '/' {{  v ,  Q  } } ']'") : uPred_scope.
-Notation "'WP' e ? {{ v , Q } }" := (wp false ⊤ e%E (λ v, Q))
+Notation "'WP' e ? {{ v , Q } }" := (wp noprogress ⊤ e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'[' 'WP'  e  '/' ? {{  v ,  Q  } } ']'") : uPred_scope.
 
@@ -165,7 +167,7 @@ Notation "'{{{' P } } } e ? {{{ 'RET' pat ; Q } } }" :=
 
 Section wp.
 Context `{irisG Λ Σ}.
-Implicit Types p : bool.
+Implicit Types p : pbit.
 Implicit Types P : iProp Σ.
 Implicit Types Φ : val Λ → iProp Σ.
 Implicit Types v : val Λ.
@@ -234,7 +236,7 @@ Lemma wp_fupd p E e Φ : WP e @ p; E {{ v, |={E}=> Φ v }} ⊢ WP e @ p; E {{ Φ
 Proof. iIntros "H". iApply (wp_strong_mono p E); try iFrame; auto. Qed.
 
 Lemma wp_atomic' p E1 E2 e Φ :
-  StronglyAtomic e ∨ p ∧ Atomic e →
+  StronglyAtomic e ∨ p = progress ∧ Atomic e →
   (|={E1,E2}=> WP e @ p; E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ p; E1 {{ Φ }}.
 Proof.
   iIntros (Hatomic) "H". rewrite !wp_unfold /wp_pre.

theories/tests/heap_lang.v

@@ -86,5 +86,5 @@ Section LiftingTests.
   Proof. iIntros "". wp_apply Pred_spec. wp_let. by wp_apply Pred_spec. Qed.
 End LiftingTests.
 
-Lemma heap_e_adequate σ : adequate true heap_e σ (= #2).
+Lemma heap_e_adequate σ : adequate progress heap_e σ (= #2).
 Proof. eapply (heap_adequacy heapΣ)=> ?. by apply heap_e_spec. Qed.