Make more use of the `direction` enum in the proof mode tactics.

_CoqProject

@@ -75,7 +75,7 @@ theories/heap_lang/lib/ticket_lock.v
 theories/heap_lang/lib/counter.v
 theories/heap_lang/proofmode.v
 theories/heap_lang/adequacy.v
-theories/proofmode/strings.v
+theories/proofmode/base.v
 theories/proofmode/tokens.v
 theories/proofmode/coq_tactics.v
 theories/proofmode/environments.v

theories/proofmode/strings.v → theories/proofmode/base.v

-From stdpp Require Import strings.
-From iris.algebra Require Import base.
+From stdpp Require Export strings.
+From iris.algebra Require Export base.
 From Coq Require Import Ascii.
 Set Default Proof Using "Type".
 
+(* Directions of rewrites *)
+Inductive direction := Left | Right.
+
+(* Some specific versions of operations on strings for the proof mode. We need
+those so that we can make [cbv] unfold just them, but not the actual operations
+that may appear in users' proofs. *)
 Local Notation "b1 && b2" := (if b1 then b2 else false) : bool_scope.
 
 Lemma lazy_andb_true (b1 b2 : bool) : b1 && b2 = true ↔ b1 = true ∧ b2 = true.

theories/proofmode/coq_tactics.v

 From iris.base_logic Require Export base_logic.
 From iris.base_logic Require Import big_op tactics.
-From iris.proofmode Require Export environments classes.
+From iris.proofmode Require Export base environments classes.
 From stdpp Require Import stringmap hlist.
 Set Default Proof Using "Type".
 Import uPred.
@@ -108,12 +108,12 @@ Fixpoint envs_split_go {M}
      if p then envs_split_go js Δ1 Δ2 else
      envs_split_go js Δ1' (envs_snoc Δ2 false j P)
   end.
-(* if [lr = true] then [result = (remaining hyps, hyps named js)] and
-   if [lr = false] then [result = (hyps named js, remaining hyps)] *)
-Definition envs_split {M} (lr : bool)
+(* if [d = Right] then [result = (remaining hyps, hyps named js)] and
+   if [d = Left] then [result = (hyps named js, remaining hyps)] *)
+Definition envs_split {M} (d : direction)
     (js : list string) (Δ : envs M) : option (envs M * envs M) :=
   '(Δ1,Δ2) ← envs_split_go js Δ (envs_clear_spatial Δ);
-  if lr then Some (Δ1,Δ2) else Some (Δ2,Δ1).
+  if d is Right then Some (Δ1,Δ2) else Some (Δ2,Δ1).
 
 (* Coq versions of the tactics *)
 Section tactics.
@@ -215,11 +215,11 @@ Proof.
   apply wand_intro_l; destruct p; simpl.
   - apply sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using Esnoc_wf.
-      intros j; destruct (strings.string_beq_reflect j i); naive_solver.
+      intros j; destruct (string_beq_reflect j i); naive_solver.
     + by rewrite persistently_sep assoc.
   - apply sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using Esnoc_wf.
-      intros j; destruct (strings.string_beq_reflect j i); naive_solver.
+      intros j; destruct (string_beq_reflect j i); naive_solver.
     + solve_sep_entails.
 Qed.
 
@@ -341,15 +341,15 @@ Proof.
     - rewrite envs_lookup_envs_delete_ne // envs_lookup_snoc_ne //. eauto. }
   rewrite (envs_snoc_sound Δ2 false j P) /= ?wand_elim_r; eauto.
 Qed.
-Lemma envs_split_sound Δ lr js Δ1 Δ2 :
-  envs_split lr js Δ = Some (Δ1,Δ2) → Δ ⊢ Δ1 ∗ Δ2.
+Lemma envs_split_sound Δ d js Δ1 Δ2 :
+  envs_split d js Δ = Some (Δ1,Δ2) → Δ ⊢ Δ1 ∗ Δ2.
 Proof.
   rewrite /envs_split=> ?. rewrite -(idemp uPred_and Δ).
   rewrite {2}envs_clear_spatial_sound sep_elim_l and_sep_r.
   destruct (envs_split_go _ _) as [[Δ1' Δ2']|] eqn:HΔ; [|done].
   apply envs_split_go_sound in HΔ as ->; last first.
   { intros j P. by rewrite envs_lookup_envs_clear_spatial=> ->. }
-  destruct lr; simplify_eq; solve_sep_entails.
+  destruct d; simplify_eq; solve_sep_entails.
 Qed.
 
 Global Instance envs_Forall2_refl (R : relation (uPred M)) :
@@ -601,10 +601,10 @@ Proof.
     by rewrite right_id assoc (into_wand _ R) persistently_if_elim wand_elim_r wand_elim_r.
 Qed.
 
-Lemma tac_specialize_assert Δ Δ' Δ1 Δ2' j q lr js R P1 P2 P1' Q :
+Lemma tac_specialize_assert Δ Δ' Δ1 Δ2' j q neg js R P1 P2 P1' Q :
   envs_lookup_delete j Δ = Some (q, R, Δ') →
   IntoWand false R P1 P2 → ElimModal P1' P1 Q Q →
-  ('(Δ1,Δ2) ← envs_split lr js Δ';
+  ('(Δ1,Δ2) ← envs_split (if neg is true then Right else Left) js Δ';
     Δ2' ← envs_app false (Esnoc Enil j P2) Δ2;
     Some (Δ1,Δ2')) = Some (Δ1,Δ2') → (* does not preserve position of [j] *)
   (Δ1 ⊢ P1') → (Δ2' ⊢ Q) → Δ ⊢ Q.
@@ -704,9 +704,9 @@ Proof.
   by rewrite -(idemp uPred_and Δ) {1}(persistent Δ) {1}HP // HPQ impl_elim_r.
 Qed.
 
-Lemma tac_assert Δ Δ1 Δ2 Δ2' lr js j P P' Q :
+Lemma tac_assert Δ Δ1 Δ2 Δ2' neg js j P P' Q :
   ElimModal P' P Q Q →
-  envs_split lr js Δ = Some (Δ1,Δ2) →
+  envs_split (if neg is true then Right else Left) js Δ = Some (Δ1,Δ2) →
   envs_app false (Esnoc Enil j P) Δ2 = Some Δ2' →
   (Δ1 ⊢ P') → (Δ2' ⊢ Q) → Δ ⊢ Q.
 Proof.
@@ -715,8 +715,8 @@ Proof.
   by rewrite right_id HP HQ.
 Qed.
 
-Lemma tac_assert_persistent Δ Δ1 Δ2 Δ' lr js j P Q :
-  envs_split lr js Δ = Some (Δ1,Δ2) →
+Lemma tac_assert_persistent Δ Δ1 Δ2 Δ' neg js j P Q :
+  envs_split (if neg is true then Right else Left) js Δ = Some (Δ1,Δ2) →
   envs_app false (Esnoc Enil j P) Δ = Some Δ' →
   Persistent P →
   (Δ1 ⊢ P) → (Δ' ⊢ Q) → Δ ⊢ Q.
@@ -765,34 +765,34 @@ Proof.
 Qed.
 
 (** * Rewriting *)
-Lemma tac_rewrite Δ i p Pxy (lr : bool) Q :
+Lemma tac_rewrite Δ i p Pxy d Q :
   envs_lookup i Δ = Some (p, Pxy) →
   ∀ {A : ofeT} (x y : A) (Φ : A → uPred M),
     (Pxy ⊢ x ≡ y) →
-    (Q ⊣⊢ Φ (if lr then y else x)) →
+    (Q ⊣⊢ Φ (if d is Left then y else x)) →
     (NonExpansive Φ) →
-    (Δ ⊢ Φ (if lr then x else y)) → Δ ⊢ Q.
+    (Δ ⊢ Φ (if d is Left then x else y)) → Δ ⊢ Q.
 Proof.
   intros ? A x y ? HPxy -> ?; apply internal_eq_rewrite; auto.
   rewrite {1}envs_lookup_sound' //; rewrite sep_elim_l HPxy.
-  destruct lr; auto using internal_eq_sym.
+  destruct d; auto using internal_eq_sym.
 Qed.
 
-Lemma tac_rewrite_in Δ i p Pxy j q P (lr : bool) Q :
+Lemma tac_rewrite_in Δ i p Pxy j q P d Q :
   envs_lookup i Δ = Some (p, Pxy) →
   envs_lookup j Δ = Some (q, P) →
   ∀ {A : ofeT} Δ' x y (Φ : A → uPred M),
     (Pxy ⊢ x ≡ y) →
-    (P ⊣⊢ Φ (if lr then y else x)) →
+    (P ⊣⊢ Φ (if d is Left then y else x)) →
     (NonExpansive Φ) →
-    envs_simple_replace j q (Esnoc Enil j (Φ (if lr then x else y))) Δ = Some Δ' →
+    envs_simple_replace j q (Esnoc Enil j (Φ (if d is Left then x else y))) Δ = Some Δ' →
     (Δ' ⊢ Q) → Δ ⊢ Q.
 Proof.
   intros ?? A Δ' x y Φ HPxy HP ?? <-.
   rewrite -(idemp uPred_and Δ) {2}(envs_lookup_sound' _ i) //.
   rewrite sep_elim_l HPxy and_sep_r.
   rewrite (envs_simple_replace_sound _ _ j) //; simpl.
-  rewrite HP right_id -assoc; apply wand_elim_r'. destruct lr.
+  rewrite HP right_id -assoc; apply wand_elim_r'. destruct d.
   - apply (internal_eq_rewrite x y (λ y, □?q Φ y -∗ Δ')%I);
       eauto with I. solve_proper.
   - apply (internal_eq_rewrite y x (λ y, □?q Φ y -∗ Δ')%I);
@@ -806,9 +806,9 @@ Lemma tac_and_split Δ P Q1 Q2 :
 Proof. intros. rewrite -(from_and true P). by apply and_intro. Qed.
 
 (** * Separating conjunction splitting *)
-Lemma tac_sep_split Δ Δ1 Δ2 lr js P Q1 Q2 :
+Lemma tac_sep_split Δ Δ1 Δ2 d js P Q1 Q2 :
   FromAnd false P Q1 Q2 →
-  envs_split lr js Δ = Some (Δ1,Δ2) →
+  envs_split d js Δ = Some (Δ1,Δ2) →
   (Δ1 ⊢ Q1) → (Δ2 ⊢ Q2) → Δ ⊢ P.
 Proof.
   intros. rewrite envs_split_sound // -(from_and false P). by apply sep_mono.
@@ -851,13 +851,13 @@ Qed.
 (* Using this tactic, one can destruct a (non-separating) conjunction in the
 spatial context as long as one of the conjuncts is thrown away. It corresponds
 to the principle of "external choice" in linear logic. *)
-Lemma tac_and_destruct_choice Δ Δ' i p (lr : bool) j P P1 P2 Q :
+Lemma tac_and_destruct_choice Δ Δ' i p d j P P1 P2 Q :
   envs_lookup i Δ = Some (p, P) → IntoAnd true P P1 P2 →
-  envs_simple_replace i p (Esnoc Enil j (if lr then P1 else P2)) Δ = Some Δ' →
+  envs_simple_replace i p (Esnoc Enil j (if d is Left then P1 else P2)) Δ = Some Δ' →
   (Δ' ⊢ Q) → Δ ⊢ Q.
 Proof.
   intros. rewrite envs_simple_replace_sound //; simpl.
-  rewrite right_id (into_and true P). destruct lr.
+  rewrite right_id (into_and true P). destruct d.
   - by rewrite and_elim_l wand_elim_r.
   - by rewrite and_elim_r wand_elim_r.
 Qed.

theories/proofmode/environments.v

 From stdpp Require Export strings.
-From iris.proofmode Require Import strings.
+From iris.proofmode Require Import base.
 From iris.algebra Require Export base.
 From stdpp Require Import stringmap.
 Set Default Proof Using "Type".

theories/proofmode/intro_patterns.v

 From stdpp Require Export strings.
-From iris.proofmode Require Import tokens sel_patterns.
+From iris.proofmode Require Import base tokens sel_patterns.
 Set Default Proof Using "Type".
 
 Inductive intro_pat :=
@@ -11,7 +11,7 @@ Inductive intro_pat :=
   | IPureElim : intro_pat
   | IAlwaysElim : intro_pat → intro_pat
   | IModalElim : intro_pat → intro_pat
-  | IRewrite : direction → intro_pat (* true = ->, false = <- *)
+  | IRewrite : direction → intro_pat
   | IPureIntro : intro_pat
   | IAlwaysIntro : intro_pat
   | IModalIntro : intro_pat

theories/proofmode/sel_patterns.v

 From stdpp Require Export strings.
-From iris.proofmode Require Import tokens.
+From iris.proofmode Require Import base tokens.
 Set Default Proof Using "Type".
 
 Inductive sel_pat :=

theories/proofmode/tactics.v

 From iris.proofmode Require Import coq_tactics.
-From iris.proofmode Require Import intro_patterns spec_patterns sel_patterns.
+From iris.proofmode Require Import base intro_patterns spec_patterns sel_patterns.
 From iris.base_logic Require Export base_logic.
 From iris.proofmode Require Export classes notation.
 From iris.proofmode Require Import class_instances.
 From stdpp Require Import stringmap hlist.
-From iris.proofmode Require Import strings.
 Set Default Proof Using "Type".
 
 Declare Reduction env_cbv := cbv [
@@ -704,7 +703,7 @@ Tactic Notation "iSplit" :=
 Tactic Notation "iSplitL" constr(Hs) :=
   iStartProof;
   let Hs := words Hs in
-  eapply tac_sep_split with _ _ false Hs _ _; (* (js:=Hs) *)
+  eapply tac_sep_split with _ _ Left Hs _ _; (* (js:=Hs) *)
     [apply _ ||
      let P := match goal with |- FromAnd _ ?P _ _ => P end in
      fail "iSplitL:" P "not a separating conjunction"
@@ -716,7 +715,7 @@ Tactic Notation "iSplitL" constr(Hs) :=
 Tactic Notation "iSplitR" constr(Hs) :=
   iStartProof;
   let Hs := words Hs in
-  eapply tac_sep_split with _ _ true Hs _ _; (* (js:=Hs) *)
+  eapply tac_sep_split with _ _ Right Hs _ _; (* (js:=Hs) *)
     [apply _ ||
      let P := match goal with |- FromAnd _ ?P _ _ => P end in
      fail "iSplitR:" P "not a separating conjunction"
@@ -736,8 +735,8 @@ Local Tactic Notation "iAndDestruct" constr(H) "as" constr(H1) constr(H2) :=
      fail "iAndDestruct: cannot destruct" P
     |env_reflexivity || fail "iAndDestruct:" H1 "or" H2 " not fresh"|].
 
-Local Tactic Notation "iAndDestructChoice" constr(H) "as" constr(lr) constr(H') :=
-  eapply tac_and_destruct_choice with _ H _ lr H' _ _ _;
+Local Tactic Notation "iAndDestructChoice" constr(H) "as" constr(d) constr(H') :=
+  eapply tac_and_destruct_choice with _ H _ d H' _ _ _;
     [env_reflexivity || fail "iAndDestructChoice:" H "not found"
     |apply _ ||
      let P := match goal with |- IntoAnd _ ?P _ _ => P end in
@@ -848,14 +847,14 @@ Local Tactic Notation "iDestructHyp" constr(H) "as" constr(pat) :=
     | IFrame => iFrame Hz
     | IName ?y => iRename Hz into y
     | IList [[]] => iExFalso; iExact Hz
-    | IList [[?pat1; IDrop]] => iAndDestructChoice Hz as true Hz; go Hz pat1
-    | IList [[IDrop; ?pat2]] => iAndDestructChoice Hz as false Hz; go Hz pat2
+    | IList [[?pat1; IDrop]] => iAndDestructChoice Hz as Left Hz; go Hz pat1
+    | IList [[IDrop; ?pat2]] => iAndDestructChoice Hz as Right Hz; go Hz pat2
     | IList [[?pat1; ?pat2]] =>
        let Hy := iFresh in iAndDestruct Hz as Hz Hy; go Hz pat1; go Hy pat2
     | IList [[?pat1];[?pat2]] => iOrDestruct Hz as Hz Hz; [go Hz pat1|go Hz pat2]
     | IPureElim => iPure Hz as ?
-    | IRewrite tokens.Right => iPure Hz as ->
-    | IRewrite tokens.Left => iPure Hz as <-
+    | IRewrite Right => iPure Hz as ->
+    | IRewrite Left => iPure Hz as <-
     | IAlwaysElim ?pat => iPersistent Hz; go Hz pat
     | IModalElim ?pat => iModCore Hz; go Hz pat
     | _ => fail "iDestruct:" pat "invalid"
@@ -1637,8 +1636,8 @@ Local Tactic Notation "iRewriteCore" constr(lr) open_constr(lem) :=
       |iRewriteFindPred
       |intros ??? ->; reflexivity|lazy beta; iClear Heq]).
 
-Tactic Notation "iRewrite" open_constr(lem) := iRewriteCore false lem.
-Tactic Notation "iRewrite" "-" open_constr(lem) := iRewriteCore true lem.
+Tactic Notation "iRewrite" open_constr(lem) := iRewriteCore Right lem.
+Tactic Notation "iRewrite" "-" open_constr(lem) := iRewriteCore Left lem.
 
 Local Tactic Notation "iRewriteCore" constr(lr) open_constr(lem) "in" constr(H) :=
   iPoseProofCore lem as true true (fun Heq =>
@@ -1653,9 +1652,9 @@ Local Tactic Notation "iRewriteCore" constr(lr) open_constr(lem) "in" constr(H)
       |env_reflexivity|lazy beta; iClear Heq]).
 
 Tactic Notation "iRewrite" open_constr(lem) "in" constr(H) :=
-  iRewriteCore false lem in H.
+  iRewriteCore Right lem in H.
 Tactic Notation "iRewrite" "-" open_constr(lem) "in" constr(H) :=
-  iRewriteCore true lem in H.
+  iRewriteCore Left lem in H.
 
 Ltac iSimplifyEq := repeat (
   iMatchHyp (fun H P => match P with ⌜_ = _⌝%I => iDestruct H as %? end)

theories/proofmode/tokens.v

-From stdpp Require Export strings.
+From iris.proofmode Require Import base.
 Set Default Proof Using "Type".
 
-(* TODO: Move elsewhere *)
-Inductive direction := Left | Right.
-
 Inductive token :=
   | TName : string → token
   | TNat : nat → token