Remove unused and not really maintained Hoare lifiting lemmas.

_CoqProject

@@ -64,7 +64,6 @@ algebra/gset.v
 algebra/coPset.v
 program_logic/model.v
 program_logic/adequacy.v
-program_logic/hoare_lifting.v
 program_logic/lifting.v
 program_logic/invariants.v
 program_logic/viewshifts.v

program_logic/hoare_lifting.v

-From iris.algebra Require Import upred_tactics.
-From iris.program_logic Require Export hoare lifting.
-From iris.program_logic Require Import ownership.
-From iris.proofmode Require Import tactics pviewshifts.
-
-Local Notation "{{ P } } ef ?@ E {{ v , Q } }" :=
-  (default True%I ef (λ e, ht E P e (λ v, Q)))
-  (at level 20, P, ef, Q at level 200,
-   format "{{  P  } }  ef  ?@  E  {{  v ,  Q  } }") : uPred_scope.
-Local Notation "{{ P } } ef ?@ E {{ v , Q } }" :=
-  (True ⊢ default True ef (λ e, ht E P e (λ v, Q)))
-  (at level 20, P, ef, Q at level 200,
-   format "{{  P  } }  ef  ?@  E  {{  v ,  Q  } }") : C_scope.
-
-Section lifting.
-Context {Λ : language} {Σ : iFunctor}.
-Implicit Types e : expr Λ.
-Implicit Types P Q R : iProp Λ Σ.
-Implicit Types Ψ : val Λ → iProp Λ Σ.
-
-Lemma ht_lift_step E1 E2 P Pσ1 Φ1 Φ2 Ψ e1 :
-  E2 ⊆ E1 → to_val e1 = None →
-  (P ={E1,E2}=> ∃ σ1, ■ reducible e1 σ1 ∧ ▷ ownP σ1 ★ ▷ Pσ1 σ1) ∧
-    (∀ σ1 e2 σ2 ef, ■ prim_step e1 σ1 e2 σ2 ef ★ ownP σ2 ★ Pσ1 σ1
-                  ={E2,E1}=> Φ1 e2 σ2 ef ★ Φ2 e2 σ2 ef) ∧
-    (∀ e2 σ2 ef, {{ Φ1 e2 σ2 ef }} e2 @ E1 {{ Ψ }}) ∧
-    (∀ e2 σ2 ef, {{ Φ2 e2 σ2 ef }} ef ?@ ⊤ {{ _, True }})
-  ⊢ {{ P }} e1 @ E1 {{ Ψ }}.
-Proof.
-  iIntros (??) "#(#Hvs&HΦ&He2&Hef) ! HP".
-  iApply (wp_lift_step E1 E2 _ e1); auto.
-  iPvs ("Hvs" with "HP") as (σ1) "(%&Hσ&HP)"; first set_solver.
-  iPvsIntro. iExists σ1. repeat iSplit. by eauto. iFrame.
-  iNext. iIntros (e2 σ2 ef) "[#Hstep Hown]".
-  iSpecialize ("HΦ" $! σ1 e2 σ2 ef with "[-]"). by iFrame "Hstep HP Hown".
-  iPvs "HΦ" as "[H1 H2]"; first by set_solver. iPvsIntro. iSplitL "H1".
-  - by iApply "He2".
-  - destruct ef as [e|]; last done. by iApply ("Hef" $! _ _ (Some e)).
-Qed.
-
-Lemma ht_lift_atomic_step E P e1 σ1 :
-  atomic e1 →
-  reducible e1 σ1 →
-  (∀ e2 σ2 ef, {{ ■ prim_step e1 σ1 e2 σ2 ef ★ P }} ef ?@ ⊤ {{ _, True }}) ⊢
-  {{ ▷ ownP σ1 ★ ▷ P }} e1 @ E {{ v, ∃ σ2 ef, ownP σ2
-                                       ★ ■ prim_step e1 σ1 (of_val v) σ2 ef }}.
-Proof.
-  iIntros (? Hsafe) "#Hef".
-  iApply (ht_lift_step E E _ (λ σ1', P ∧ σ1 = σ1')%I
-           (λ e2 σ2 ef, ownP σ2 ★ ■ (is_Some (to_val e2) ∧ prim_step e1 σ1 e2 σ2 ef))%I
-           (λ e2 σ2 ef, ■ prim_step e1 σ1 e2 σ2 ef ★ P)%I);
-    try by (eauto using reducible_not_val).
-  repeat iSplit.
-  - iIntros "![Hσ1 HP]". iExists σ1. iPvsIntro.
-    iSplit. by eauto. iFrame. by auto.
-  - iIntros (? e2 σ2 ef) "! (%&Hown&HP&%)". iPvsIntro. subst.
-    iFrame. iSplit; iPureIntro; auto. split; eauto.
-  - iIntros (e2 σ2 ef) "! [Hown #Hφ]"; iDestruct "Hφ" as %[[v2 <-%of_to_val] ?].
-    iApply wp_value'. iExists σ2, ef. by iSplit.
-  - done.
-Qed.
-
-Lemma ht_lift_pure_step E P P' Ψ e1 :
-  to_val e1 = None →
-  (∀ σ1, reducible e1 σ1) →
-  (∀ σ1 e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → σ1 = σ2) →
-  (∀ e2 ef σ, {{ ■ prim_step e1 σ e2 σ ef ★ P }} e2 @ E {{ Ψ }}) ∧
-    (∀ e2 ef σ, {{ ■ prim_step e1 σ e2 σ ef ★ P' }} ef ?@ ⊤ {{ _, True }})
-  ⊢ {{ ▷(P ★ P') }} e1 @ E {{ Ψ }}.
-Proof.
-  iIntros (? Hsafe Hpure) "[#He2 #Hef] ! HP". iApply wp_lift_pure_step; auto.
-  iNext; iIntros (e2 ef σ Hstep). iDestruct "HP" as "[HP HP']"; iSplitL "HP".
-  - iApply "He2"; by iSplit.
-  - destruct ef as [e|]; last done. iApply ("Hef" $! _ (Some e)); by iSplit.
-Qed.
-
-Lemma ht_lift_pure_det_step E P P' Ψ e1 e2 ef :
-  to_val e1 = None →
-  (∀ σ1, reducible e1 σ1) →
-  (∀ σ1 e2' σ2 ef', prim_step e1 σ1 e2' σ2 ef' → σ1 = σ2 ∧ e2 = e2' ∧ ef = ef')→
-  {{ P }} e2 @ E {{ Ψ }} ∧ {{ P' }} ef ?@ ⊤ {{ _, True }}
-  ⊢ {{ ▷(P ★ P') }} e1 @ E {{ Ψ }}.
-Proof.
-  iIntros (? Hsafe Hpuredet) "[#He2 #Hef]".
-  iApply ht_lift_pure_step; eauto. by intros; eapply Hpuredet.
-  iSplit; iIntros (e2' ef' σ).
-  - iIntros "! [% ?]". edestruct Hpuredet as (_&->&->). done. by iApply "He2".
-  - destruct ef' as [e'|]; last done.
-    iIntros "! [% ?]". edestruct Hpuredet as (_&->&->). done. by iApply "Hef".
-Qed.
-End lifting.