Declare [Hint Mode] instances for proof mode.

This fixes issue #62.

theories/base_logic/lib/fancy_updates.v

@@ -155,8 +155,10 @@ Section proofmode_classes.
   Proof. rewrite /FromAssumption=>->. apply bupd_fupd. Qed.
 
   Global Instance into_wand_fupd E1 E2 R P Q :
-    IntoWand R P Q → IntoWand R (|={E1,E2}=> P) (|={E1,E2}=> Q) | 100.
-  Proof. rewrite /IntoWand=>->. apply wand_intro_l. by rewrite fupd_wand_r. Qed.
+    IntoWand R P Q → IntoWand' R (|={E1,E2}=> P) (|={E1,E2}=> Q) | 100.
+  Proof.
+    rewrite /IntoWand' /IntoWand=>->. apply wand_intro_l. by rewrite fupd_wand_r.
+  Qed.
 
   Global Instance from_sep_fupd E P Q1 Q2 :
     FromSep P Q1 Q2 → FromSep (|={E}=> P) (|={E}=> Q1) (|={E}=> Q2).
@@ -179,8 +181,8 @@ Section proofmode_classes.
   Global Instance is_except_0_fupd E1 E2 P : IsExcept0 (|={E1,E2}=> P).
   Proof. by rewrite /IsExcept0 except_0_fupd. Qed.
 
-  Global Instance into_modal_fupd E P : IntoModal P (|={E}=> P).
-  Proof. rewrite /IntoModal. apply fupd_intro. Qed.
+  Global Instance from_modal_fupd E P : FromModal (|={E}=> P) P.
+  Proof. rewrite /FromModal. apply fupd_intro. Qed.
 
   (* Put a lower priority compared to [elim_modal_fupd_fupd], so that
      it is not taken when the first parameter is not specified (in

theories/proofmode/class_instances.v

@@ -219,15 +219,22 @@ Proof. apply and_elim_r', impl_wand. Qed.
 
 Global Instance into_wand_always R P Q : IntoWand R P Q → IntoWand (□ R) P Q.
 Proof. rewrite /IntoWand=> ->. apply always_elim. Qed.
+
 Global Instance into_wand_later (R1 R2 P Q : uPred M) :
-  IntoLaterN 1 R1 R2 → IntoWand R2 P Q → IntoWand R1 (▷ P) (▷ Q) | 99.
-Proof. rewrite /IntoLaterN /IntoWand=> -> ->. by rewrite -later_wand. Qed.
+  IntoLaterN 1 R1 R2 → IntoWand R2 P Q → IntoWand' R1 (▷ P) (▷ Q) | 99.
+Proof.
+  rewrite /IntoLaterN /IntoWand' /IntoWand=> -> ->. by rewrite -later_wand.
+Qed.
 Global Instance into_wand_laterN n (R1 R2 P Q : uPred M) :
-  IntoLaterN n R1 R2 → IntoWand R2 P Q → IntoWand R1 (▷^n P) (▷^n Q) | 100.
-Proof. rewrite /IntoLaterN /IntoWand=> -> ->. by rewrite -laterN_wand. Qed.
+  IntoLaterN n R1 R2 → IntoWand R2 P Q → IntoWand' R1 (▷^n P) (▷^n Q) | 100.
+Proof.
+  rewrite /IntoLaterN /IntoWand' /IntoWand=> -> ->. by rewrite -laterN_wand.
+Qed.
 Global Instance into_wand_bupd R P Q :
-  IntoWand R P Q → IntoWand R (|==> P) (|==> Q) | 98.
-Proof. rewrite /IntoWand=>->. apply wand_intro_l. by rewrite bupd_wand_r. Qed.
+  IntoWand R P Q → IntoWand' R (|==> P) (|==> Q) | 98.
+Proof.
+  rewrite /IntoWand' /IntoWand=> ->. apply wand_intro_l. by rewrite bupd_wand_r.
+Qed.
 
 (* FromAnd *)
 Global Instance from_and_and P1 P2 : FromAnd (P1 ∧ P2) P1 P2.
@@ -564,12 +571,12 @@ Global Instance into_exist_laterN {A} n P (Φ : A → uPred M) :
   IntoExist P Φ → Inhabited A → IntoExist (▷^n P) (λ a, ▷^n (Φ a))%I.
 Proof. rewrite /IntoExist=> HP ?. by rewrite HP laterN_exist. Qed.
 
-(* IntoModal *)
-Global Instance into_modal_later P : IntoModal P (▷ P).
+(* FromModal *)
+Global Instance from_modal_later P : FromModal (▷ P) P.
 Proof. apply later_intro. Qed.
-Global Instance into_modal_bupd P : IntoModal P (|==> P).
+Global Instance from_modal_bupd P : FromModal (|==> P) P.
 Proof. apply bupd_intro. Qed.
-Global Instance into_modal_except_0 P : IntoModal P (◇ P).
+Global Instance from_modal_except_0 P : FromModal (◇ P) P.
 Proof. apply except_0_intro. Qed.
 
 (* ElimModal *)

theories/proofmode/classes.v

@@ -2,77 +2,102 @@ From iris.base_logic Require Export base_logic.
 Set Default Proof Using "Type".
 Import uPred.
 
-Section classes.
-Context {M : ucmraT}.
-Implicit Types P Q : uPred M.
-
-Class FromAssumption (p : bool) (P Q : uPred M) := from_assumption : □?p P ⊢ Q.
-Global Arguments from_assumption _ _ _ {_}.
-
-Class IntoPure (P : uPred M) (φ : Prop) := into_pure : P ⊢ ⌜φ⌝.
-Global Arguments into_pure : clear implicits.
-
-Class FromPure (P : uPred M) (φ : Prop) := from_pure : ⌜φ⌝ ⊢ P.
-Global Arguments from_pure : clear implicits.
-
-Class IntoPersistentP (P Q : uPred M) := into_persistentP : P ⊢ □ Q.
-Global Arguments into_persistentP : clear implicits.
-
-Class IntoLaterN (n : nat) (P Q : uPred M) := into_laterN : P ⊢ ▷^n Q.
-Global Arguments into_laterN _ _ _ {_}.
-
-Class FromLaterN (n : nat) (P Q : uPred M) := from_laterN : ▷^n Q ⊢ P.
-Global Arguments from_laterN _ _ _ {_}.
-
-Class IntoWand (R P Q : uPred M) := into_wand : R ⊢ P -∗ Q.
-Global Arguments into_wand : clear implicits.
-
-Class FromAnd (P Q1 Q2 : uPred M) := from_and : Q1 ∧ Q2 ⊢ P.
-Global Arguments from_and : clear implicits.
-
-Class FromSep (P Q1 Q2 : uPred M) := from_sep : Q1 ∗ Q2 ⊢ P.
-Global Arguments from_sep : clear implicits.
-
-Class IntoAnd (p : bool) (P Q1 Q2 : uPred M) :=
+Class FromAssumption {M} (p : bool) (P Q : uPred M) :=
+  from_assumption : □?p P ⊢ Q.
+Arguments from_assumption {_} _ _ _ {_}.
+Hint Mode FromAssumption + + ! - : typeclass_instances.
+
+Class IntoPure {M} (P : uPred M) (φ : Prop) := into_pure : P ⊢ ⌜φ⌝.
+Arguments into_pure {_} _ _ {_}.
+Hint Mode IntoPure + ! - : typeclass_instances.
+
+Class FromPure {M} (P : uPred M) (φ : Prop) := from_pure : ⌜φ⌝ ⊢ P.
+Arguments from_pure {_} _ _ {_}.
+Hint Mode FromPure + ! - : typeclass_instances.
+
+Class IntoPersistentP {M} (P Q : uPred M) := into_persistentP : P ⊢ □ Q.
+Arguments into_persistentP {_} _ _ {_}.
+Hint Mode IntoPersistentP + ! - : typeclass_instances.
+
+Class IntoLaterN {M} (n : nat) (P Q : uPred M) := into_laterN : P ⊢ ▷^n Q.
+Arguments into_laterN {_} _ _ _ {_}.
+Hint Mode IntoLaterN + - ! - : typeclass_instances.
+
+Class FromLaterN {M} (n : nat) (P Q : uPred M) := from_laterN : ▷^n Q ⊢ P.
+Arguments from_laterN {_} _ _ _ {_}.
+Hint Mode FromLaterN + - ! - : typeclass_instances.
+
+Class IntoWand {M} (R P Q : uPred M) := into_wand : R ⊢ P -∗ Q.
+Arguments into_wand {_} _ _ _ {_}.
+Hint Mode IntoWand + ! - - : typeclass_instances.
+
+Class IntoWand' {M} (R P Q : uPred M) := into_wand' :> IntoWand R P Q.
+Arguments into_wand' {_} _ _ _ {_}.
+Hint Mode IntoWand' + ! ! - : typeclass_instances.
+Hint Mode IntoWand' + ! - ! : typeclass_instances.
+
+Class FromAnd {M} (P Q1 Q2 : uPred M) := from_and : Q1 ∧ Q2 ⊢ P.
+Arguments from_and {_} _ _ _ {_}.
+Hint Mode FromAnd + ! - - : typeclass_instances.
+
+Class FromSep {M} (P Q1 Q2 : uPred M) := from_sep : Q1 ∗ Q2 ⊢ P.
+Arguments from_sep {_} _ _ _ {_}.
+Hint Mode FromSep + ! - - : typeclass_instances.
+Hint Mode FromSep + - ! ! : typeclass_instances. (* For iCombine *)
+
+Class IntoAnd {M} (p : bool) (P Q1 Q2 : uPred M) :=
   into_and : P ⊢ if p then Q1 ∧ Q2 else Q1 ∗ Q2.
-Global Arguments into_and : clear implicits.
-
-Lemma mk_into_and_sep p P Q1 Q2 : (P ⊢ Q1 ∗ Q2) → IntoAnd p P Q1 Q2.
+Arguments into_and {_} _ _ _ _ {_}.
+Hint Mode IntoAnd + + ! - - : typeclass_instances.
+Lemma mk_into_and_sep {M} p (P Q1 Q2 : uPred M) :
+  (P ⊢ Q1 ∗ Q2) → IntoAnd p P Q1 Q2.
 Proof. rewrite /IntoAnd=>->. destruct p; auto using sep_and. Qed.
 
 Class FromOp {A : cmraT} (a b1 b2 : A) := from_op : b1 ⋅ b2 ≡ a.
-Global Arguments from_op {_} _ _ _ {_}.
+Arguments from_op {_} _ _ _ {_}.
+Hint Mode FromOp + ! - - : typeclass_instances.
+Hint Mode FromOp + - ! ! : typeclass_instances. (* For iCombine *)
 
 Class IntoOp {A : cmraT} (a b1 b2 : A) := into_op : a ≡ b1 ⋅ b2.
-Global Arguments into_op {_} _ _ _ {_}.
+Arguments into_op {_} _ _ _ {_}.
+(* No [Hint Mode] since we want to turn [?x] into [?x1 ⋅ ?x2], for example
+when having [H : own ?x]. *)
 
-Class Frame (R P Q : uPred M) := frame : R ∗ Q ⊢ P.
-Global Arguments frame : clear implicits.
+Class Frame {M} (R P Q : uPred M) := frame : R ∗ Q ⊢ P.
+Arguments frame {_} _ _ _ {_}.
+Hint Mode Frame + ! ! - : typeclass_instances.
 
-Class FromOr (P Q1 Q2 : uPred M) := from_or : Q1 ∨ Q2 ⊢ P.
-Global Arguments from_or : clear implicits.
+Class FromOr {M} (P Q1 Q2 : uPred M) := from_or : Q1 ∨ Q2 ⊢ P.
+Arguments from_or {_} _ _ _ {_}.
+Hint Mode FromOr + ! - - : typeclass_instances.
 
-Class IntoOr P Q1 Q2 := into_or : P ⊢ Q1 ∨ Q2.
-Global Arguments into_or : clear implicits.
+Class IntoOr {M} (P Q1 Q2 : uPred M) := into_or : P ⊢ Q1 ∨ Q2.
+Arguments into_or {_} _ _ _ {_}.
+Hint Mode IntoOr + ! - - : typeclass_instances.
 
-Class FromExist {A} (P : uPred M) (Φ : A → uPred M) :=
+Class FromExist {M A} (P : uPred M) (Φ : A → uPred M) :=
   from_exist : (∃ x, Φ x) ⊢ P.
-Global Arguments from_exist {_} _ _ {_}.
+Arguments from_exist {_ _} _ _ {_}.
+Hint Mode FromExist + - ! - : typeclass_instances.
 
-Class IntoExist {A} (P : uPred M) (Φ : A → uPred M) :=
+Class IntoExist {M A} (P : uPred M) (Φ : A → uPred M) :=
   into_exist : P ⊢ ∃ x, Φ x.
-Global Arguments into_exist {_} _ _ {_}.
+Arguments into_exist {_ _} _ _ {_}.
+Hint Mode IntoExist + - ! - : typeclass_instances.
 
-Class IntoModal (P Q : uPred M) := into_modal : P ⊢ Q.
-Global Arguments into_modal : clear implicits.
+Class FromModal {M} (P Q : uPred M) := from_modal : Q ⊢ P.
+Arguments from_modal {_} _ _ {_}.
+Hint Mode FromModal + ! - : typeclass_instances.
 
-Class ElimModal (P P' : uPred M) (Q Q' : uPred M) :=
+Class ElimModal {M} (P P' : uPred M) (Q Q' : uPred M) :=
   elim_modal : P ∗ (P' -∗ Q') ⊢ Q.
-Global Arguments elim_modal _ _ _ _ {_}.
+Arguments elim_modal {_} _ _ _ _ {_}.
+Hint Mode ElimModal + ! - ! - : typeclass_instances.
+Hint Mode ElimModal + - ! - ! : typeclass_instances.
 
-Lemma elim_modal_dummy P Q : ElimModal P P Q Q.
+Lemma elim_modal_dummy {M} (P Q : uPred M) : ElimModal P P Q Q.
 Proof. by rewrite /ElimModal wand_elim_r. Qed.
 
-Class IsExcept0 (Q : uPred M) := is_except_0 : ◇ Q ⊢ Q.
-Global Arguments is_except_0 : clear implicits.
-End classes.
+Class IsExcept0 {M} (Q : uPred M) := is_except_0 : ◇ Q ⊢ Q.
+Arguments is_except_0 {_} _ {_}.
+Hint Mode IsExcept0 + ! : typeclass_instances.

theories/proofmode/coq_tactics.v

@@ -832,8 +832,8 @@ Proof.
 Qed.
 
 (** * Modalities *)
-Lemma tac_modal_intro Δ P Q : IntoModal Q P → (Δ ⊢ Q) → Δ ⊢ P.
-Proof. rewrite /IntoModal. by intros <- ->. Qed.
+Lemma tac_modal_intro Δ P Q : FromModal P Q → (Δ ⊢ Q) → Δ ⊢ P.
+Proof. rewrite /FromModal. by intros <- ->. Qed.
 
 Lemma tac_modal_elim Δ Δ' i p P' P Q Q' :
   envs_lookup i Δ = Some (p, P) →
@@ -845,3 +845,5 @@ Proof.
   rewrite right_id HΔ always_if_elim. by apply elim_modal.
 Qed.
 End tactics.
+
+Hint Mode ForallSpecialize + - - ! - : typeclass_instances.

theories/proofmode/tactics.v

@@ -642,7 +642,7 @@ Tactic Notation "iNext":= iNext _.
 Tactic Notation "iModIntro" :=
   iStartProof;
   eapply tac_modal_intro;
-    [let P := match goal with |- IntoModal _ ?P => P end in
+    [let P := match goal with |- FromModal ?P _ => P end in
      apply _ || fail "iModIntro:" P "not a modality"|].
 
 Tactic Notation "iModCore" constr(H) :=