Commit ff935fd4 authored by Robbert Krebbers's avatar Robbert Krebbers

Define FromOp type class and use it in the proof mode.

parent fc77fc3a
Pipeline #2766 passed with stage
in 9 minutes and 33 seconds
......@@ -132,6 +132,10 @@ Proof. rewrite /FromAnd=> <-. by rewrite later_and. Qed.
(* FromSep *)
Global Instance from_sep_sep P1 P2 : FromSep (P1 P2) P1 P2 | 100.
Proof. done. Qed.
Global Instance from_sep_ownM (a b1 b2 : M) :
FromOp a b1 b2
FromSep (uPred_ownM a) (uPred_ownM b1) (uPred_ownM b2).
Proof. intros. by rewrite /FromSep -ownM_op from_op. Qed.
Global Instance from_sep_always P Q1 Q2 :
FromSep P Q1 Q2 FromSep ( P) ( Q1) ( Q2).
Proof. rewrite /FromSep=> <-. by rewrite always_sep. Qed.
......@@ -142,9 +146,6 @@ Global Instance from_sep_rvs P Q1 Q2 :
FromSep P Q1 Q2 FromSep (|=r=> P) (|=r=> Q1) (|=r=> Q2).
Proof. rewrite /FromSep=><-. apply rvs_sep. Qed.
Global Instance from_sep_ownM (a b : M) :
FromSep (uPred_ownM (a b)) (uPred_ownM a) (uPred_ownM b) | 99.
Proof. by rewrite /FromSep ownM_op. Qed.
Global Instance from_sep_big_sepM
`{Countable K} {A} (Φ Ψ1 Ψ2 : K A uPred M) m :
( k x, FromSep (Φ k x) (Ψ1 k x) (Ψ2 k x))
......@@ -160,6 +161,20 @@ Proof.
rewrite /FromSep=> ?. rewrite -big_sepS_sepS. by apply big_sepS_mono.
Qed.
(* FromOp *)
Global Instance from_op_op {A : cmraT} (a b : A) : FromOp (a b) a b.
Proof. by rewrite /FromOp. Qed.
Global Instance from_op_persistent {A : cmraT} (a : A) :
Persistent a FromOp a a a.
Proof. intros. by rewrite /FromOp -(persistent_dup a). Qed.
Global Instance from_op_pair {A B : cmraT} (a b1 b2 : A) (a' b1' b2' : B) :
FromOp a b1 b2 FromOp a' b1' b2'
FromOp (a,a') (b1,b1') (b2,b2').
Proof. by constructor. Qed.
Global Instance from_op_Some {A : cmraT} (a : A) b1 b2 :
FromOp a b1 b2 FromOp (Some a) (Some b1) (Some b2).
Proof. by constructor. Qed.
(* IntoOp *)
Global Instance into_op_op {A : cmraT} (a b : A) : IntoOp (a b) a b.
Proof. by rewrite /IntoOp. Qed.
......
......@@ -39,6 +39,9 @@ Global Arguments into_and : clear implicits.
Lemma mk_into_and_sep p P Q1 Q2 : (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 {_} _ _ _ {_}.
Class IntoOp {A : cmraT} (a b1 b2 : A) := into_op : a b1 b2.
Global Arguments into_op {_} _ _ _ {_}.
......
......@@ -9,7 +9,7 @@ Implicit Types a b : A.
Global Instance into_and_own p γ a b1 b2 :
IntoOp a b1 b2 IntoAnd p (own γ a) (own γ b1) (own γ b2).
Proof. intros. apply mk_into_and_sep. by rewrite (into_op a) own_op. Qed.
Global Instance from_sep_own γ a b :
FromSep (own γ (a b)) (own γ a) (own γ b) | 90.
Proof. by rewrite /FromSep own_op. Qed.
Global Instance from_sep_own γ a b1 b2 :
FromOp a b1 b2 FromSep (own γ a) (own γ b1) (own γ b2).
Proof. intros. by rewrite /FromSep -own_op from_op. Qed.
End ghost.
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