Support for framing pure hypotheses.

This closes issue 32.

ProofMode.md

@@ -81,11 +81,16 @@ Elimination of logical connectives
 Separating logic specific tactics
 ---------------------------------
 
-- `iFrame "H0 ... Hn"` : cancel the hypotheses `H0 ... Hn` in the goal. The
-  symbol `★` can be used to frame as much of the spatial context as possible,
-  and the symbol `#` can be used to repeatedly frame as much of the persistent
-  context as possible. When without arguments, it attempts to frame all spatial
-  hypotheses.
+- `iFrame (t1 .. tn) "H0 ... Hn"` : cancel the Coq terms (or Coq hypotheses)
+  `t1 ... tn` and Iris hypotheses `H0 ... Hn` in the goal. Apart from
+  hypotheses, the following symbols can be used:
+
+  + `%` : repeatedly frame hypotheses from the Coq context.
+  + `#` : repeatedly frame hypotheses from the persistent context.
+  + `★` : frame as much of the spatial context as possible.
+
+  Notice that framing spatial hypotheses makes them disappear, but framing Coq
+  or persistent hypotheses does not make them disappear.
 - `iCombine "H1" "H2" as "H"` : turns `H1 : P1` and `H2 : P2` into
   `H : P1 ★ P2`.
 

proofmode/class_instances.v

@@ -219,6 +219,8 @@ Qed.
 (* Frame *)
 Global Instance frame_here R : Frame R R True.
 Proof. by rewrite /Frame right_id. Qed.
+Global Instance frame_here_pure φ Q : FromPure Q φ → Frame (■ φ) Q True.
+Proof. rewrite /FromPure /Frame=> ->. by rewrite right_id. Qed.
 
 Class MakeSep (P Q PQ : uPred M) := make_sep : P ★ Q ⊣⊢ PQ.
 Global Instance make_sep_true_l P : MakeSep True P P.

proofmode/coq_tactics.v

@@ -685,6 +685,10 @@ Proof.
 Qed.
 
 (** * Framing *)
+Lemma tac_frame_pure Δ (φ : Prop) P Q :
+  φ → Frame (■ φ) P Q → (Δ ⊢ Q) → Δ ⊢ P.
+Proof. intros ?? ->. by rewrite -(frame (■ φ) P) pure_equiv // left_id. Qed.
+
 Lemma tac_frame Δ Δ' i p R P Q :
   envs_lookup_delete i Δ = Some (p, R, Δ') → Frame R P Q →
   ((if p then Δ else Δ') ⊢ Q) → Δ ⊢ P.

proofmode/tactics.v

@@ -430,6 +430,11 @@ Tactic Notation "iCombine" constr(H1) constr(H2) "as" constr(H) :=
     |env_cbv; reflexivity || fail "iCombine:" H "not fresh"|].
 
 (** Framing *)
+Local Ltac iFramePure t :=
+  let φ := type of t in
+  eapply (tac_frame_pure _ _ _ _ t);
+    [apply _ || fail "iFrame: cannot frame" φ|].
+
 Local Ltac iFrameHyp H :=
   eapply tac_frame with _ H _ _ _;
     [env_cbv; reflexivity || fail "iFrame:" H "not found"
@@ -437,7 +442,10 @@ Local Ltac iFrameHyp H :=
      apply _ || fail "iFrame: cannot frame" R
     |lazy iota beta].
 
-Local Ltac iFramePersistent :=
+Local Ltac iFrameAnyPure :=
+  repeat match goal with H : _ |- _ => iFramePure H end.
+
+Local Ltac iFrameAnyPersistent :=
   let rec go Hs :=
     match Hs with [] => idtac | ?H :: ?Hs => repeat iFrameHyp H; go Hs end in
   match goal with
@@ -445,7 +453,7 @@ Local Ltac iFramePersistent :=
      let Hs := eval cbv in (env_dom (env_persistent Δ)) in go Hs
   end.
 
-Local Ltac iFrameSpatial :=
+Local Ltac iFrameAnySpatial :=
   let rec go Hs :=
     match Hs with [] => idtac | ?H :: ?Hs => try iFrameHyp H; go Hs end in
   match goal with
@@ -453,17 +461,60 @@ Local Ltac iFrameSpatial :=
      let Hs := eval cbv in (env_dom (env_spatial Δ)) in go Hs
   end.
 
+Tactic Notation "iFrame" := iFrameAnySpatial.
+
+Tactic Notation "iFrame" "(" constr(t1) ")" :=
+  iFramePure t1.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) ")" :=
+  iFramePure t1; iFrame ( t2 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) ")" :=
+  iFramePure t1; iFrame ( t2 t3 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4) ")" :=
+  iFramePure t1; iFrame ( t2 t3 t4 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) ")" :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) ")" :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) constr(t7) ")" :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 ).
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) constr(t7) constr(t8)")" :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 t8 ).
+
 Tactic Notation "iFrame" constr(Hs) :=
   let rec go Hs :=
     match Hs with
     | [] => idtac
-    | "#" :: ?Hs => iFramePersistent; go Hs
-    | "★" :: ?Hs => iFrameSpatial; go Hs
+    | "%" :: ?Hs => iFrameAnyPure; go Hs
+    | "#" :: ?Hs => iFrameAnyPersistent; go Hs
+    | "★" :: ?Hs => iFrameAnySpatial; go Hs
     | ?H :: ?Hs => iFrameHyp H; go Hs
     end
   in let Hs := words Hs in go Hs.
-
-Tactic Notation "iFrame" := iFrameSpatial.
+Tactic Notation "iFrame" "(" constr(t1) ")" constr(Hs) :=
+  iFramePure t1; iFrame Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) ")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) ")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4) ")"
+    constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 t4 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) ")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) ")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) constr(t7) ")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 ) Hs.
+Tactic Notation "iFrame" "(" constr(t1) constr(t2) constr(t3) constr(t4)
+    constr(t5) constr(t6) constr(t7) constr(t8)")" constr(Hs) :=
+  iFramePure t1; iFrame ( t2 t3 t4 t5 t6 t7 t8 ) Hs.
 
 (** * Existential *)
 Tactic Notation "iExists" uconstr(x1) :=

tests/proofmode.v

@@ -100,3 +100,7 @@ Section iris.
     - done.
   Qed.
 End iris.
+
+Lemma demo_9 (M : ucmraT) (x y z : M) :
+  ✓ x → ■ (y ≡ z) ⊢ (✓ x ∧ ✓ x ∧ y ≡ z : uPred M).
+Proof. iIntros (Hv) "Hxy". by iFrame (Hv Hv) "Hxy". Qed.