Get rid of the `pure.v` file

_CoqProject

@@ -55,7 +55,6 @@ theories/base_logic/lib/core.v
 theories/base_logic/lib/fancy_updates_from_vs.v
 theories/program_logic/adequacy.v
 theories/program_logic/lifting.v
-theories/program_logic/pure.v
 theories/program_logic/weakestpre.v
 theories/program_logic/hoare.v
 theories/program_logic/language.v

theories/heap_lang/lifting.v

 From iris.base_logic Require Export gen_heap.
-From iris.program_logic Require Export weakestpre pure.
+From iris.program_logic Require Export weakestpre lifting.
 From iris.program_logic Require Import ectx_lifting.
 From iris.heap_lang Require Export lang.
 From iris.heap_lang Require Import tactics.
@@ -195,7 +195,7 @@ Qed.
 Lemma wp_seq E e1 e2 Φ :
   is_Some (to_val e1) → Closed [] e2 →
   ▷ WP e2 @ E {{ Φ }} ⊢ WP Seq e1 e2 @ E {{ Φ }}.
-Proof. iIntros ([? ?] ?). rewrite -wp_pure'; by eauto. Qed.
+Proof. iIntros ([? ?] ?). rewrite -wp_pure_step_later; by eauto. Qed.
 
 Lemma wp_skip E Φ : ▷ Φ (LitV LitUnit) ⊢ WP Skip @ E {{ Φ }}.
 Proof. rewrite -wp_seq; last eauto. by rewrite -wp_value. Qed.
@@ -203,11 +203,11 @@ Proof. rewrite -wp_seq; last eauto. by rewrite -wp_value. Qed.
 Lemma wp_match_inl E e0 x1 e1 x2 e2 Φ :
   is_Some (to_val e0) → Closed (x1 :b: []) e1 →
   ▷ WP subst' x1 e0 e1 @ E {{ Φ }} ⊢ WP Match (InjL e0) x1 e1 x2 e2 @ E {{ Φ }}.
-Proof. iIntros ([? ?] ?) "?". rewrite -!wp_pure'; by eauto. Qed.
+Proof. iIntros ([? ?] ?) "?". rewrite -!wp_pure_step_later; by eauto. Qed.
 
 Lemma wp_match_inr E e0 x1 e1 x2 e2 Φ :
   is_Some (to_val e0) → Closed (x2 :b: []) e2 →
   ▷ WP subst' x2 e0 e2 @ E {{ Φ }} ⊢ WP Match (InjR e0) x1 e1 x2 e2 @ E {{ Φ }}.
-Proof. iIntros ([? ?] ?) "?". rewrite -!wp_pure'; by eauto. Qed.
+Proof. iIntros ([? ?] ?) "?". rewrite -!wp_pure_step_later; by eauto. Qed.
 
 End lifting.

theories/heap_lang/proofmode.v

@@ -47,7 +47,7 @@ Lemma tac_wp_pure `{heapG Σ} K Δ Δ' E e1 e2 φ Φ :
   (Δ ⊢ WP fill K e1 @ E {{ Φ }}).
 Proof.
   intros ??? HΔ'. rewrite into_laterN_env_sound /=.
-  rewrite -lifting.wp_bind HΔ' -wp_pure' //.
+  rewrite -lifting.wp_bind HΔ' -wp_pure_step_later //.
   by rewrite -ectx_lifting.wp_ectx_bind_inv.
 Qed.
 

theories/program_logic/ectx_language.v

@@ -150,6 +150,18 @@ Section ectx_language.
       exists (fill K' e2''); rewrite -fill_comp; split; auto.
       econstructor; eauto.
   Qed.
+
+  Lemma det_head_step_pureexec e1 e2 :
+    (∀ σ, head_reducible e1 σ) →
+    (∀ σ1 e2' σ2 efs, head_step e1 σ1 e2' σ2 efs → σ1 = σ2 ∧ e2=e2' ∧ efs = []) →
+    PureExec True e1 e2.
+  Proof.
+    intros Hp1 Hp2. split.
+    - intros σ _. destruct (Hp1 σ) as (e2' & σ2 & efs & ?).
+      eexists e2', σ2, efs.
+      eapply (Ectx_step _ _ _ _ _ empty_ectx); eauto using fill_empty.
+    - intros σ1 e2' σ2 efs _ ?%head_reducible_prim_step; eauto.
+  Qed.
 End ectx_language.
 
 Arguments ectx_lang _ {_ _ _ _}.

theories/program_logic/language.v

@@ -93,4 +93,16 @@ Section language.
     exists (tl' ++ e2 :: tr' ++ efs); split; [|by econstructor].
     by rewrite -!Permutation_middle !assoc_L Ht.
   Qed.
+
+  Class PureExec (P : Prop) (e1 e2 : expr Λ) := {
+    pure_exec_safe σ :
+      P → reducible e1 σ;
+    pure_exec_puredet σ1 e2' σ2 efs :
+      P → prim_step e1 σ1 e2' σ2 efs → σ1 = σ2 ∧ e2 = e2' ∧ efs = [];
+  }.
+
+  Lemma hoist_pred_pureexec (P : Prop) (e1 e2 : expr Λ) :
+    (P → PureExec True e1 e2) →
+    PureExec P e1 e2.
+  Proof. intros HPE. split; intros; eapply HPE; eauto. Qed.
 End language.

theories/program_logic/lifting.v

@@ -68,4 +68,22 @@ Proof.
   iApply (step_fupd_wand with "H"); iIntros "H".
   by iIntros (e' efs' σ (_&->&->)%Hpuredet).
 Qed.
+
+Lemma wp_pure_step_fupd `{Inhabited (state Λ)} E E' e1 e2 φ Φ :
+  PureExec φ e1 e2 →
+  φ →
+  (|={E,E'}▷=> WP e2 @ E {{ Φ }}) ⊢ WP e1 @ E {{ Φ }}.
+Proof.
+  iIntros ([??] Hφ) "HWP".
+  iApply (wp_lift_pure_det_step with "[HWP]"); [eauto|naive_solver|].
+  rewrite big_sepL_nil right_id //.
+Qed.
+
+Lemma wp_pure_step_later `{Inhabited (state Λ)} E e1 e2 φ Φ :
+  PureExec φ e1 e2 →
+  φ →
+  ▷ WP e2 @ E {{ Φ }} ⊢ WP e1 @ E {{ Φ }}.
+Proof.
+  intros ??. rewrite -wp_pure_step_fupd //. rewrite -step_fupd_intro //.
+Qed.
 End lifting.

theories/program_logic/pure.v

-From iris.proofmode Require Import tactics.
-From iris.program_logic Require Import lifting language ectx_language.
-Set Default Proof Using "Type".
-
-Section pure_language.
-Context `{irisG Λ Σ}.
-Implicit Types Φ : val Λ → iProp Σ.
-Implicit Types φ : Prop.
-Implicit Types e : expr Λ.
-
-Class PureExec (P : Prop) (e1 e2 : expr Λ) := {
-  pure_exec_safe : 
-    P -> ∀ σ, language.reducible e1 σ;
-  pure_exec_puredet : 
-    P -> ∀ σ1 e2' σ2 efs, language.prim_step e1 σ1 e2' σ2 efs -> σ1=σ2 /\ e2=e2' /\ [] = efs;
-  }.
-
-Lemma wp_pure `{Inhabited (state Λ)} E E' e1 e2 φ Φ :
-  PureExec φ e1 e2 →
-  φ →
-  (|={E,E'}▷=> WP e2 @ E {{ Φ }}) ⊢ WP e1 @ E {{ Φ }}.
-Proof.
-  iIntros (? Hφ) "HWP".
-  iApply (wp_lift_pure_det_step with "[HWP]").
-  { apply (pure_exec_safe Hφ). }
-  { apply (pure_exec_puredet Hφ). }
-  rewrite big_sepL_nil right_id //.
-Qed.
-
-Lemma wp_pure' `{Inhabited (state Λ)} E e1 e2 φ Φ :
-  PureExec φ e1 e2 →
-  φ →
-  (▷ WP e2 @ E {{ Φ }}) ⊢ WP e1 @ E {{ Φ }}.
-Proof. 
-  intros ? ?.
-  rewrite -wp_pure //.
-  rewrite -step_fupd_intro //.
-Qed.
-
-Lemma hoist_pred_pureexec (P : Prop) (e1 e2 : expr Λ) :
-  (P → PureExec True e1 e2) →
-  PureExec P e1 e2.
-Proof.
-  intros HPE.
-  split; intros HP; destruct (HPE HP); eauto.
-Qed.
-
-End pure_language.
-
-Section pure_ectx_language.
-Context {expr val ectx state} {Λ : EctxLanguage expr val ectx state}.
-Context `{irisG (ectx_lang expr) Σ} {Hinh : Inhabited state}.
-
-Lemma det_head_step_pureexec (e1 e2 : expr) :
-  (∀ σ, head_reducible e1 σ) →
-  (∀ σ1 e2' σ2 efs, head_step e1 σ1 e2' σ2 efs -> σ1=σ2 /\ e2=e2' /\ [] = efs) →
-  PureExec True e1 e2.
-Proof.
-  intros Hp1 Hp2.
-  split; intros _.
-  - intros σ. destruct (Hp1 σ) as (? & ? & ? & ?).
-    do 3 eexists. simpl.
-    eapply (Ectx_step _ _ _ _ _ empty_ectx); eauto using fill_empty.
-  - move => σ1 e2' σ2 efs /=.
-    intros ?%head_reducible_prim_step; eauto.
-Qed.
-
-End pure_ectx_language.