Commit ff508ad9 authored by Ralf Jung's avatar Ralf Jung
Browse files

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

parents c55672d8 b90854c7
...@@ -833,21 +833,31 @@ Proof. done. Qed. ...@@ -833,21 +833,31 @@ Proof. done. Qed.
Lemma valid_weaken {A : cmraT} (a b : A) : (a b) a. Lemma valid_weaken {A : cmraT} (a b : A) : (a b) a.
Proof. intros r n _; apply cmra_validN_op_l. Qed. Proof. intros r n _; apply cmra_validN_op_l. Qed.
(* Own and valid derived *)
Lemma ownM_invalid (a : M) : ¬ {0} a uPred_ownM a False.
Proof. by intros; rewrite ownM_valid valid_elim. Qed.
Global Instance ownM_mono : Proper (flip () ==> ()) (@uPred_ownM M).
Proof. move=>a b [c H]. rewrite H ownM_op. eauto. Qed.
(* Products *)
Lemma prod_equivI {A B : cofeT} (x y : A * B) : Lemma prod_equivI {A B : cofeT} (x y : A * B) :
(x y)%I (x.1 y.1 x.2 y.2 : uPred M)%I. (x y)%I (x.1 y.1 x.2 y.2 : uPred M)%I.
Proof. done. Qed. Proof. done. Qed.
Lemma prod_validI {A B : cmraT} (x : A * B) : Lemma prod_validI {A B : cmraT} (x : A * B) :
( x)%I ( x.1 x.2 : uPred M)%I. ( x)%I ( x.1 x.2 : uPred M)%I.
Proof. done. Qed. Proof. done. Qed.
(* Later *)
Lemma later_equivI {A : cofeT} (x y : later A) : Lemma later_equivI {A : cofeT} (x y : later A) :
(x y)%I ( (later_car x later_car y) : uPred M)%I. (x y)%I ( (later_car x later_car y) : uPred M)%I.
Proof. done. Qed. Proof. done. Qed.
(* Own and valid derived *) (* Discrete *)
Lemma ownM_invalid (a : M) : ¬ {0} a uPred_ownM a False. (* For equality, there already is timeless_eq *)
Proof. by intros; rewrite ownM_valid valid_elim. Qed. Lemma discrete_validI {A : cofeT} `{ x : A, Timeless x}
Global Instance ownM_mono : Proper (flip () ==> ()) (@uPred_ownM M). `{Op A, Valid A, Unit A, Minus A} (ra : RA A) (x : discreteRA ra) :
Proof. move=>a b [c H]. rewrite H ownM_op. eauto. Qed. ( x)%I ( x : uPred M)%I.
Proof. done. Qed.
(* Timeless *) (* Timeless *)
Lemma timelessP_spec P : TimelessP P x n, {n} x P 0 x P n x. Lemma timelessP_spec P : TimelessP P x n, {n} x P 0 x P n x.
...@@ -962,23 +972,9 @@ Proof. by rewrite -(always_always Q); apply always_entails_r'. Qed. ...@@ -962,23 +972,9 @@ Proof. by rewrite -(always_always Q); apply always_entails_r'. Qed.
End uPred_logic. End uPred_logic.
Section discrete.
Context {A : cofeT} `{ x : A, Timeless x}.
Context {op : Op A} {v : Valid A} `{Unit A, Minus A} (ra : RA A).
(** Internalized properties of discrete RAs *)
(* For equality, there already is timeless_eq *)
Lemma discrete_validI {M} (x : discreteRA ra) :
( x)%I ( x : uPred M)%I.
Proof.
apply (anti_symm ()).
- move=>? n ?. done.
- move=>? n ? ?. by apply: discrete_valid.
Qed.
End discrete.
(* Hint DB for the logic *) (* Hint DB for the logic *)
Create HintDb I. Create HintDb I.
Hint Resolve const_intro.
Hint Resolve or_elim or_intro_l' or_intro_r' : I. Hint Resolve or_elim or_intro_l' or_intro_r' : I.
Hint Resolve and_intro and_elim_l' and_elim_r' : I. Hint Resolve and_intro and_elim_l' and_elim_r' : I.
Hint Resolve always_mono : I. Hint Resolve always_mono : I.
......
...@@ -30,7 +30,7 @@ Proof. ...@@ -30,7 +30,7 @@ Proof.
by rewrite -wp_let' //= ?to_of_val ?subst_empty. by rewrite -wp_let' //= ?to_of_val ?subst_empty.
Qed. Qed.
Lemma wp_skip E Q : (Q (LitV LitUnit)) wp E Skip Q. Lemma wp_skip E Q : (Q (LitV LitUnit)) wp E Skip Q.
Proof. rewrite -wp_seq -wp_value // -wp_value //. Qed. Proof. rewrite -wp_seq -wp_value // -wp_value //. Qed.
Lemma wp_le E (n1 n2 : Z) P Q : Lemma wp_le E (n1 n2 : Z) P Q :
......
...@@ -76,13 +76,12 @@ Proof. ...@@ -76,13 +76,12 @@ Proof.
Qed. Qed.
(** Base axioms for core primitives of the language: Stateless reductions *) (** Base axioms for core primitives of the language: Stateless reductions *)
Lemma wp_fork E e : Lemma wp_fork E e Q :
wp (Σ:=Σ) coPset_all e (λ _, True) wp E (Fork e) (λ v, v = LitV LitUnit). ( Q (LitV LitUnit) wp (Σ:=Σ) coPset_all e (λ _, True)) wp E (Fork e) Q.
Proof. Proof.
rewrite -(wp_lift_pure_det_step (Fork e) (Lit LitUnit) (Some e)) //=; rewrite -(wp_lift_pure_det_step (Fork e) (Lit LitUnit) (Some e)) //=;
last by intros; inv_step; eauto. last by intros; inv_step; eauto.
apply later_mono, sep_intro_True_l; last done. rewrite later_sep -(wp_value _ _ (Lit _)) //.
by rewrite -(wp_value _ _ (Lit _)) //; apply const_intro.
Qed. Qed.
(* For the lemmas involving substitution, we only derive a preliminary version. (* For the lemmas involving substitution, we only derive a preliminary version.
......
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