Commit e67181e6 authored by Robbert's avatar Robbert

Merge branch 'ci/robbert/overloaded_wp' into 'gen_proofmode'

Typeclass to overload WP notation.

See merge request FP/iris-coq!146
parents 83a8c02a f2a18f5a
Pipeline #9778 passed with stage
in 26 minutes and 33 seconds
......@@ -38,6 +38,7 @@ theories/bi/bi.v
theories/bi/tactics.v
theories/bi/monpred.v
theories/bi/embedding.v
theories/bi/weakestpre.v
theories/bi/lib/counter_examples.v
theories/bi/lib/fixpoint.v
theories/bi/lib/fractional.v
......
......@@ -35,7 +35,7 @@
Σ : gFunctors
H : heapG Σ
fun1, fun2, fun3 : expr
Φ : language.val heap_lang → iProp Σ
Φ : language.val heap_lang → iPropI Σ
============================
--------------------------------------∗
WP let: "val1" := fun1 #() in
......@@ -48,7 +48,7 @@
Σ : gFunctors
H : heapG Σ
fun1, fun2, fun3 : expr
Φ : language.val heap_lang → iProp Σ
Φ : language.val heap_lang → iPropI Σ
E : coPset
============================
--------------------------------------∗
......
This diff is collapsed.
......@@ -50,142 +50,13 @@ Qed.
Definition twp_def `{irisG Λ Σ} (s : stuckness) (E : coPset)
(e : expr Λ) (Φ : val Λ iProp Σ) :
iProp Σ := bi_least_fixpoint (twp_pre' s) (E,e,Φ).
Definition twp_aux : seal (@twp_def). by eexists. Qed.
Definition twp := twp_aux.(unseal).
Definition twp_eq : @twp = @twp_def := twp_aux.(seal_eq).
Arguments twp {_ _ _} _ _ _%E _.
Instance: Params (@twp) 6.
(* Note that using '[[' instead of '[{' results in conflicts with the list
notations. *)
Notation "'WP' e @ s ; E [{ Φ } ]" := (twp s E e%E Φ)
(at level 20, e, Φ at level 200,
format "'[' 'WP' e '/' @ s ; E [{ Φ } ] ']'") : bi_scope.
Notation "'WP' e @ E [{ Φ } ]" := (twp NotStuck E e%E Φ)
(at level 20, e, Φ at level 200,
format "'[' 'WP' e '/' @ E [{ Φ } ] ']'") : bi_scope.
Notation "'WP' e @ E ? [{ Φ } ]" := (twp MaybeStuck E e%E Φ)
(at level 20, e, Φ at level 200,
format "'[' 'WP' e '/' @ E ? [{ Φ } ] ']'") : bi_scope.
Notation "'WP' e [{ Φ } ]" := (twp NotStuck e%E Φ)
(at level 20, e, Φ at level 200,
format "'[' 'WP' e '/' [{ Φ } ] ']'") : bi_scope.
Notation "'WP' e ? [{ Φ } ]" := (twp MaybeStuck e%E Φ)
(at level 20, e, Φ at level 200,
format "'[' 'WP' e '/' ? [{ Φ } ] ']'") : bi_scope.
Notation "'WP' e @ s ; E [{ v , Q } ]" := (twp s E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' @ s ; E [{ v , Q } ] ']'") : bi_scope.
Notation "'WP' e @ E [{ v , Q } ]" := (twp NotStuck E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' @ E [{ v , Q } ] ']'") : bi_scope.
Notation "'WP' e @ E ? [{ v , Q } ]" := (twp MaybeStuck E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' @ E ? [{ v , Q } ] ']'") : bi_scope.
Notation "'WP' e [{ v , Q } ]" := (twp NotStuck e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' [{ v , Q } ] ']'") : bi_scope.
Notation "'WP' e ? [{ v , Q } ]" := (twp MaybeStuck e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' ? [{ v , Q } ] ']'") : bi_scope.
(* Texan triples *)
Notation "'[[{' P } ] ] e @ s ; E [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ s; E [{ Φ }])%I
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ s ; E [[{ x .. y , RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ E [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E [{ Φ }])%I
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ E [[{ x .. y , RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ E ? [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E ?[{ Φ }])%I
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ E ? [[{ x .. y , RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e [{ Φ }])%I
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e [[{ x .. y , RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e ? [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e ?[{ Φ }])%I
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e ? [[{ x .. y , RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ s ; E [[{ 'RET' pat ; Q } ] ]" :=
( Φ, P - (Q - Φ pat%V) - WP e @ s; E [{ Φ }])%I
(at level 20,
format "[[{ P } ] ] e @ s ; E [[{ RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ E [[{ 'RET' pat ; Q } ] ]" :=
( Φ, P - (Q - Φ pat%V) - WP e @ E [{ Φ }])%I
(at level 20,
format "[[{ P } ] ] e @ E [[{ RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ E ? [[{ 'RET' pat ; Q } ] ]" :=
( Φ, P - (Q - Φ pat%V) - WP e @ E ?[{ Φ }])%I
(at level 20,
format "[[{ P } ] ] e @ E ? [[{ RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e [[{ 'RET' pat ; Q } ] ]" :=
( Φ, P - (Q - Φ pat%V) - WP e [{ Φ }])%I
(at level 20,
format "[[{ P } ] ] e [[{ RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e ? [[{ 'RET' pat ; Q } ] ]" :=
( Φ, P - (Q - Φ pat%V) - WP e ?[{ Φ }])%I
(at level 20,
format "[[{ P } ] ] e ? [[{ RET pat ; Q } ] ]") : bi_scope.
Notation "'[[{' P } ] ] e @ s ; E [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ s; E [{ Φ }])
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ s ; E [[{ x .. y , RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e @ E [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E [{ Φ }])
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ E [[{ x .. y , RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e @ E ? [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E ?[{ Φ }])
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e @ E ? [[{ x .. y , RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e [{ Φ }])
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e [[{ x .. y , RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e ? [[{ x .. y , 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e ?[{ Φ }])
(at level 20, x closed binder, y closed binder,
format "[[{ P } ] ] e ? [[{ x .. y , RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e @ s ; E [[{ 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ s; E [{ Φ }])
(at level 20,
format "[[{ P } ] ] e @ s ; E [[{ RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e @ E [[{ 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ E [{ Φ }])
(at level 20,
format "[[{ P } ] ] e @ E [[{ RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e @ E ? [[{ 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ E ?[{ Φ }])
(at level 20,
format "[[{ P } ] ] e @ E ? [[{ RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e [[{ 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e [{ Φ }])
(at level 20,
format "[[{ P } ] ] e [[{ RET pat ; Q } ] ]") : stdpp_scope.
Notation "'[[{' P } ] ] e ? [[{ 'RET' pat ; Q } ] ]" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e ?[{ Φ }])
(at level 20,
format "[[{ P } ] ] e ? [[{ RET pat ; Q } ] ]") : stdpp_scope.
Definition twp_aux `{irisG Λ Σ} : seal (@twp_def Λ Σ _). by eexists. Qed.
Instance twp' `{irisG Λ Σ} : Twp Λ (iProp Σ) stuckness := twp_aux.(unseal).
Definition twp_eq `{irisG Λ Σ} : twp = @twp_def Λ Σ _ := twp_aux.(seal_eq).
Section twp.
Context `{irisG Λ Σ}.
Implicit Types s : stuckness.
Implicit Types P : iProp Σ.
Implicit Types Φ : val Λ iProp Σ.
Implicit Types v : val Λ.
......@@ -210,12 +81,12 @@ Proof.
Qed.
Global Instance twp_ne s E e n :
Proper (pointwise_relation _ (dist n) ==> dist n) (@twp Λ Σ _ s E e).
Proper (pointwise_relation _ (dist n) ==> dist n) (twp (PROP:=iProp Σ) s E e).
Proof.
intros Φ1 Φ2 HΦ. rewrite !twp_eq. by apply (least_fixpoint_ne _), pair_ne, HΦ.
Qed.
Global Instance twp_proper s E e :
Proper (pointwise_relation _ () ==> ()) (@twp Λ Σ _ s E e).
Proper (pointwise_relation _ () ==> ()) (twp (PROP:=iProp Σ) s E e).
Proof.
by intros Φ Φ' ?; apply equiv_dist=>n; apply twp_ne=>v; apply equiv_dist.
Qed.
......@@ -339,7 +210,7 @@ Lemma twp_mask_mono s E1 E2 e Φ :
E1 E2 WP e @ s; E1 [{ Φ }] - WP e @ s; E2 [{ Φ }].
Proof. iIntros (?) "H"; iApply (twp_strong_mono with "H"); auto. Qed.
Global Instance twp_mono' s E e :
Proper (pointwise_relation _ () ==> ()) (@twp Λ Σ _ s E e).
Proper (pointwise_relation _ () ==> ()) (twp (PROP:=iProp Σ) s E e).
Proof. by intros Φ Φ' ?; apply twp_mono. Qed.
Lemma twp_value s E Φ e v `{!IntoVal e v} : Φ v - WP e @ s; E [{ Φ }].
......
From iris.base_logic.lib Require Export fancy_updates.
From iris.program_logic Require Export language.
From iris.bi Require Export weakestpre.
From iris.proofmode Require Import tactics classes.
Set Default Proof Using "Type".
Import uPred.
......@@ -11,20 +12,6 @@ Class irisG' (Λstate : Type) (Σ : gFunctors) := IrisG {
Notation irisG Λ Σ := (irisG' (state Λ) Σ).
Global Opaque iris_invG.
Inductive stuckness := NotStuck | MaybeStuck.
Definition stuckness_leb (s1 s2 : stuckness) : bool :=
match s1, s2 with
| MaybeStuck, NotStuck => false
| _, _ => true
end.
Instance stuckness_le : SqSubsetEq stuckness := stuckness_leb.
Instance stuckness_le_po : PreOrder stuckness_le.
Proof. split; by repeat intros []. Qed.
Definition stuckness_to_atomicity (s : stuckness) : atomicity :=
if s is MaybeStuck then StronglyAtomic else WeaklyAtomic.
Definition wp_pre `{irisG Λ Σ} (s : stuckness)
(wp : coPset -c> expr Λ -c> (val Λ -c> iProp Σ) -c> iProp Σ) :
coPset -c> expr Λ -c> (val Λ -c> iProp Σ) -c> iProp Σ := λ E e1 Φ,
......@@ -45,119 +32,9 @@ Qed.
Definition wp_def `{irisG Λ Σ} (s : stuckness) :
coPset expr Λ (val Λ iProp Σ) iProp Σ := fixpoint (wp_pre s).
Definition wp_aux : seal (@wp_def). by eexists. Qed.
Definition wp := wp_aux.(unseal).
Definition wp_eq : @wp = @wp_def := wp_aux.(seal_eq).
Arguments wp {_ _ _} _ _ _%E _.
Instance: Params (@wp) 6.
(* Notations without binder -- only parsing because they overlap with the
notations with binder. *)
Notation "'WP' e @ s ; E {{ Φ } }" := (wp s E e%E Φ)
(at level 20, e, Φ at level 200, only parsing) : bi_scope.
Notation "'WP' e @ E {{ Φ } }" := (wp NotStuck E e%E Φ)
(at level 20, e, Φ at level 200, only parsing) : bi_scope.
Notation "'WP' e @ E ? {{ Φ } }" := (wp MaybeStuck E e%E Φ)
(at level 20, e, Φ at level 200, only parsing) : bi_scope.
Notation "'WP' e {{ Φ } }" := (wp NotStuck e%E Φ)
(at level 20, e, Φ at level 200, only parsing) : bi_scope.
Notation "'WP' e ? {{ Φ } }" := (wp MaybeStuck e%E Φ)
(at level 20, e, Φ at level 200, only parsing) : bi_scope.
(* Notations with binder. The indentation for the inner format block is chosen
such that *if* one has a single-character mask (e.g. [E]), the second line
should align with the binder(s) on the first line. *)
Notation "'WP' e @ s ; E {{ v , Q } }" := (wp s E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' '[ ' @ s ; E {{ v , Q } } ']' ']'") : bi_scope.
Notation "'WP' e @ E {{ v , Q } }" := (wp NotStuck E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' '[ ' @ E {{ v , Q } } ']' ']'") : bi_scope.
Notation "'WP' e @ E ? {{ v , Q } }" := (wp MaybeStuck E e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' '[ ' @ E ? {{ v , Q } } ']' ']'") : bi_scope.
Notation "'WP' e {{ v , Q } }" := (wp NotStuck e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' '[ ' {{ v , Q } } ']' ']'") : bi_scope.
Notation "'WP' e ? {{ v , Q } }" := (wp MaybeStuck e%E (λ v, Q))
(at level 20, e, Q at level 200,
format "'[' 'WP' e '/' '[ ' ? {{ v , Q } } ']' ']'") : bi_scope.
(* Texan triples *)
Notation "'{{{' P } } } e @ s ; E {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ s; E {{ Φ }})%I
(at level 20, x closed binder, y closed binder,
format "'[hv' {{{ P } } } '/ ' e '/' @ s ; E {{{ x .. y , RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e @ E {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E {{ Φ }})%I
(at level 20, x closed binder, y closed binder,
format "'[hv' {{{ P } } } '/ ' e '/' @ E {{{ x .. y , RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e @ E ? {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E ?{{ Φ }})%I
(at level 20, x closed binder, y closed binder,
format "'[hv' {{{ P } } } '/ ' e '/' @ E ? {{{ x .. y , RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e {{ Φ }})%I
(at level 20, x closed binder, y closed binder,
format "'[hv' {{{ P } } } '/ ' e '/' {{{ x .. y , RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e ? {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e ?{{ Φ }})%I
(at level 20, x closed binder, y closed binder,
format "'[hv' {{{ P } } } '/ ' e '/' ? {{{ x .. y , RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e @ s ; E {{{ 'RET' pat ; Q } } }" :=
( Φ, P - (Q - Φ pat%V) - WP e @ s; E {{ Φ }})%I
(at level 20,
format "'[hv' {{{ P } } } '/ ' e '/' @ s ; E {{{ RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e @ E {{{ 'RET' pat ; Q } } }" :=
( Φ, P - (Q - Φ pat%V) - WP e @ E {{ Φ }})%I
(at level 20,
format "'[hv' {{{ P } } } '/ ' e '/' @ E {{{ RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e @ E ? {{{ 'RET' pat ; Q } } }" :=
( Φ, P - (Q - Φ pat%V) - WP e @ E ?{{ Φ }})%I
(at level 20,
format "'[hv' {{{ P } } } '/ ' e '/' @ E ? {{{ RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e {{{ 'RET' pat ; Q } } }" :=
( Φ, P - (Q - Φ pat%V) - WP e {{ Φ }})%I
(at level 20,
format "'[hv' {{{ P } } } '/ ' e '/' {{{ RET pat ; Q } } } ']'") : bi_scope.
Notation "'{{{' P } } } e ? {{{ 'RET' pat ; Q } } }" :=
( Φ, P - (Q - Φ pat%V) - WP e ?{{ Φ }})%I
(at level 20,
format "'[hv' {{{ P } } } '/ ' e '/' ? {{{ RET pat ; Q } } } ']'") : bi_scope.
(* Aliases for stdpp scope -- they inherit the levels and format from above. *)
Notation "'{{{' P } } } e @ s ; E {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ s; E {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e @ E {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e @ E ? {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e @ E ?{{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e ? {{{ x .. y , 'RET' pat ; Q } } }" :=
( Φ : _ uPred _,
P - ( x, .. ( y, Q - Φ pat%V) .. ) - WP e ?{{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e @ s ; E {{{ 'RET' pat ; Q } } }" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ s; E {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e @ E {{{ 'RET' pat ; Q } } }" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ E {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e @ E ? {{{ 'RET' pat ; Q } } }" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e @ E ?{{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e {{{ 'RET' pat ; Q } } }" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e {{ Φ }}) : stdpp_scope.
Notation "'{{{' P } } } e ? {{{ 'RET' pat ; Q } } }" :=
( Φ : _ uPred _, P - (Q - Φ pat%V) - WP e ?{{ Φ }}) : stdpp_scope.
Definition wp_aux `{irisG Λ Σ} : seal (@wp_def Λ Σ _). by eexists. Qed.
Instance wp' `{irisG Λ Σ} : Wp Λ (iProp Σ) stuckness := wp_aux.(unseal).
Definition wp_eq `{irisG Λ Σ} : wp = @wp_def Λ Σ _ := wp_aux.(seal_eq).
Section wp.
Context `{irisG Λ Σ}.
......@@ -168,11 +45,12 @@ Implicit Types v : val Λ.
Implicit Types e : expr Λ.
(* Weakest pre *)
Lemma wp_unfold s E e Φ : WP e @ s; E {{ Φ }} wp_pre s (wp s) E e Φ.
Lemma wp_unfold s E e Φ :
WP e @ s; E {{ Φ }} wp_pre s (wp (PROP:=iProp Σ) s) E e Φ.
Proof. rewrite wp_eq. apply (fixpoint_unfold (wp_pre s)). Qed.
Global Instance wp_ne s E e n :
Proper (pointwise_relation _ (dist n) ==> dist n) (@wp Λ Σ _ s E e).
Proper (pointwise_relation _ (dist n) ==> dist n) (wp (PROP:=iProp Σ) s E e).
Proof.
revert e. induction (lt_wf n) as [n _ IH]=> e Φ Ψ HΦ.
rewrite !wp_unfold /wp_pre.
......@@ -183,7 +61,7 @@ Proof.
intros v. eapply dist_le; eauto with omega.
Qed.
Global Instance wp_proper s E e :
Proper (pointwise_relation _ () ==> ()) (@wp Λ Σ _ s E e).
Proper (pointwise_relation _ () ==> ()) (wp (PROP:=iProp Σ) s E e).
Proof.
by intros Φ Φ' ?; apply equiv_dist=>n; apply wp_ne=>v; apply equiv_dist.
Qed.
......@@ -294,7 +172,7 @@ Proof. apply wp_stuck_mono. by destruct s. Qed.
Lemma wp_mask_mono s E1 E2 e Φ : E1 E2 WP e @ s; E1 {{ Φ }} WP e @ s; E2 {{ Φ }}.
Proof. iIntros (?) "H"; iApply (wp_strong_mono with "H"); auto. Qed.
Global Instance wp_mono' s E e :
Proper (pointwise_relation _ () ==> ()) (@wp Λ Σ _ s E e).
Proper (pointwise_relation _ () ==> ()) (wp (PROP:=iProp Σ) s E e).
Proof. by intros Φ Φ' ?; apply wp_mono. Qed.
Lemma wp_value s E Φ e v `{!IntoVal e v} : Φ v WP e @ s; E {{ Φ }}.
......@@ -411,5 +289,4 @@ Section proofmode_classes.
iApply (wp_wand with "[Hinner Hα]"); first by iApply "Hinner".
iIntros (v) ">[Hβ HΦ]". iApply "HΦ". by iApply "Hclose".
Qed.
End proofmode_classes.
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