Commit 4a36be37 authored by Ralf Jung's avatar Ralf Jung

apply feedback; fix compilation with coq 8.5

parent af7b6da1
...@@ -956,22 +956,25 @@ Proof. ...@@ -956,22 +956,25 @@ Proof.
Qed. Qed.
(** Sigma *) (** Sigma *)
Class LimitPreserving {A : ofeT} `{!Cofe A} (P : A Prop) : Prop :=
limit_preserving : c : chain A, ( n, P (c n)) P (compl c).
Section sigma. Section sigma.
Context {A : ofeT} {f : A Prop}. Context {A : ofeT} {P : A Prop}.
(* TODO: Find a better place for this Equiv instance. It also (* TODO: Find a better place for this Equiv instance. It also
should not depend on A being an OFE. *) should not depend on A being an OFE. *)
Instance sig_equiv : Equiv (sig f) := Instance sig_equiv : Equiv (sig P) :=
λ x1 x2, (proj1_sig x1) (proj1_sig x2). λ x1 x2, (proj1_sig x1) (proj1_sig x2).
Instance sig_dist : Dist (sig f) := Instance sig_dist : Dist (sig P) :=
λ n x1 x2, (proj1_sig x1) {n} (proj1_sig x2). λ n x1 x2, (proj1_sig x1) {n} (proj1_sig x2).
Global Lemma exist_ne : Lemma exist_ne :
n x1 x2, x1 {n} x2 n x1 x2, x1 {n} x2
(H1 : f x1) (H2 : f x2), (exist f x1 H1) {n} (exist f x2 H2). (H1 : P x1) (H2 : P x2), (exist P x1 H1) {n} (exist P x2 H2).
Proof. intros n ?? Hx ??. exact Hx. Qed. Proof. intros n ?? Hx ??. exact Hx. Qed.
Global Instance proj1_sig_ne : Proper (dist n ==> dist n) (@proj1_sig _ f). Global Instance proj1_sig_ne : Proper (dist n ==> dist n) (@proj1_sig _ P).
Proof. intros n [] [] ?. done. Qed. Proof. intros n [] [] ?. done. Qed.
Definition sig_ofe_mixin : OfeMixin (sig f). Definition sig_ofe_mixin : OfeMixin (sig P).
Proof. Proof.
split. split.
- intros x y. unfold dist, sig_dist, equiv, sig_equiv. - intros x y. unfold dist, sig_dist, equiv, sig_equiv.
...@@ -979,24 +982,24 @@ Section sigma. ...@@ -979,24 +982,24 @@ Section sigma.
- unfold dist, sig_dist. intros n. - unfold dist, sig_dist. intros n.
split; [intros [] | intros [] [] | intros [] [] []]; simpl; try done. split; [intros [] | intros [] [] | intros [] [] []]; simpl; try done.
intros. by etrans. intros. by etrans.
- intros n [] []. unfold dist, sig_dist. apply dist_S. - intros n [??] [??]. unfold dist, sig_dist. simpl. apply dist_S.
Qed. Qed.
Canonical Structure sigC : ofeT := OfeT (sig f) sig_ofe_mixin. Canonical Structure sigC : ofeT := OfeT (sig P) sig_ofe_mixin.
Global Class LimitPreserving `{Cofe A} : Prop := (* FIXME: WTF, it seems that within these braces {...} the ofe argument of LimitPreserving
limit_preserving : c : chain A, ( n, f (c n)) f (compl c). suddenyl becomes explicit...? *)
Program Definition sig_compl `{LimitPreserving} : Compl sigC := Program Definition sig_compl `{LimitPreserving _ P} : Compl sigC :=
λ c, exist f (compl (chain_map proj1_sig c)) _. λ c, exist P (compl (chain_map proj1_sig c)) _.
Next Obligation. Next Obligation.
intros ? Hlim c. apply Hlim. move=>n /=. destruct (c n). done. intros ? Hlim c. apply Hlim. move=>n /=. destruct (c n). done.
Qed. Qed.
Program Definition sig_cofe `{LimitPreserving} : Cofe sigC := Program Definition sig_cofe `{LimitPreserving _ P} : Cofe sigC :=
{| compl := sig_compl |}. {| compl := sig_compl |}.
Next Obligation. Next Obligation.
intros ? Hlim n c. apply (conv_compl n (chain_map proj1_sig c)). intros ? Hlim n c. apply (conv_compl n (chain_map proj1_sig c)).
Qed. Qed.
Global Instance sig_timeless (x : sig f) : Global Instance sig_timeless (x : sig P) :
Timeless (proj1_sig x) Timeless x. Timeless (proj1_sig x) Timeless x.
Proof. intros ? y. destruct x, y. unfold dist, sig_dist, equiv, sig_equiv. apply (timeless _). Qed. Proof. intros ? y. destruct x, y. unfold dist, sig_dist, equiv, sig_equiv. apply (timeless _). Qed.
Global Instance sig_discrete_cofe : Discrete A Discrete sigC. Global Instance sig_discrete_cofe : Discrete A Discrete sigC.
......
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