Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
10
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Iris
Actris
Commits
2efbf2f6
Commit
2efbf2f6
authored
Nov 15, 2019
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Better names for basic examples.
parent
df678f5f
Pipeline
#21262
passed with stage
in 17 minutes and 40 seconds
Changes
1
Pipelines
2
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
32 additions
and
32 deletions
+32
-32
theories/examples/basics.v
theories/examples/basics.v
+32
-32
No files found.
theories/examples/basics.v
View file @
2efbf2f6
...
...
@@ -5,17 +5,17 @@ From iris.heap_lang Require Import proofmode notation lib.spin_lock.
From
actris
.
utils
Require
Import
contribution
.
(** Basic *)
Definition
prog
1
:
val
:
=
λ
:
<>,
Definition
prog
:
val
:
=
λ
:
<>,
let
:
"c"
:
=
start_chan
(
λ
:
"c'"
,
send
"c'"
#
42
)
in
recv
"c"
.
(** Tranfering References *)
Definition
prog
1
_ref
:
val
:
=
λ
:
<>,
Definition
prog_ref
:
val
:
=
λ
:
<>,
let
:
"c"
:
=
start_chan
(
λ
:
"c'"
,
send
"c'"
(
ref
#
42
))
in
!
(
recv
"c"
).
(** Delegation, i.e. transfering channels *)
Definition
prog
1
_del
:
val
:
=
λ
:
<>,
Definition
prog_del
:
val
:
=
λ
:
<>,
let
:
"c1"
:
=
start_chan
(
λ
:
"c1'"
,
let
:
"cc2"
:
=
new_chan
#()
in
send
"c1'"
(
Fst
"cc2"
)
;;
...
...
@@ -23,18 +23,18 @@ Definition prog1_del : val := λ: <>,
recv
(
recv
"c1"
).
(** Dependent protocols *)
Definition
prog
2
:
val
:
=
λ
:
<>,
Definition
prog
_dep
:
val
:
=
λ
:
<>,
let
:
"c"
:
=
start_chan
(
λ
:
"c'"
,
let
:
"x"
:
=
recv
"c'"
in
send
"c'"
(
"x"
+
#
2
))
in
send
"c"
#
40
;;
recv
"c"
.
Definition
prog
2
_ref
:
val
:
=
λ
:
<>,
Definition
prog
_dep
_ref
:
val
:
=
λ
:
<>,
let
:
"c"
:
=
start_chan
(
λ
:
"c'"
,
let
:
"l"
:
=
recv
"c'"
in
"l"
<-
!
"l"
+
#
2
;;
send
"c'"
#())
in
let
:
"l"
:
=
ref
#
40
in
send
"c"
"l"
;;
recv
"c"
;;
!
"l"
.
Definition
prog
2
_del
:
val
:
=
λ
:
<>,
Definition
prog
_dep
_del
:
val
:
=
λ
:
<>,
let
:
"c1"
:
=
start_chan
(
λ
:
"c1'"
,
let
:
"cc2"
:
=
new_chan
#()
in
send
"c1'"
(
Fst
"cc2"
)
;;
...
...
@@ -42,7 +42,7 @@ Definition prog2_del : val := λ: <>,
let
:
"c2'"
:
=
recv
"c1"
in
send
"c2'"
#
40
;;
recv
"c2'"
.
(** Transfering higher-order functions *)
Definition
prog
3
:
val
:
=
λ
:
<>,
Definition
prog
_fun
:
val
:
=
λ
:
<>,
let
:
"c"
:
=
start_chan
(
λ
:
"c'"
,
let
:
"f"
:
=
recv
"c'"
in
send
"c'"
(
λ
:
<>,
"f"
#()
+
#
2
))
in
let
:
"r"
:
=
ref
#
40
in
...
...
@@ -61,27 +61,27 @@ Section proofs.
Context
`
{
heapG
Σ
,
proto_chanG
Σ
}.
(** Protocols for the respective programs *)
Definition
prot
1
:
iProto
Σ
:
=
Definition
prot
:
iProto
Σ
:
=
(<?>
MSG
#
42
;
END
)%
proto
.
Definition
prot
1
_ref
:
iProto
Σ
:
=
Definition
prot_ref
:
iProto
Σ
:
=
(<?>
l
:
loc
,
MSG
#
l
{{
l
↦
#
42
}}
;
END
)%
proto
.
Definition
prot
1
_del
:
iProto
Σ
:
=
(<?>
c
:
val
,
MSG
c
{{
c
↣
prot
1
}}
;
END
)%
proto
.
Definition
prot_del
:
iProto
Σ
:
=
(<?>
c
:
val
,
MSG
c
{{
c
↣
prot
}}
;
END
)%
proto
.
Definition
prot
2
:
iProto
Σ
:
=
Definition
prot
_dep
:
iProto
Σ
:
=
(<!>
x
:
Z
,
MSG
#
x
;
<?>
MSG
#(
x
+
2
)
;
END
)%
proto
.
Definition
prot
2
_ref
:
iProto
Σ
:
=
Definition
prot
_dep
_ref
:
iProto
Σ
:
=
(<!>
(
l
:
loc
)
(
x
:
Z
),
MSG
#
l
{{
l
↦
#
x
}}
;
<?>
MSG
#()
{{
l
↦
#(
x
+
2
)
}}
;
END
)%
proto
.
Definition
prot
2
_del
:
iProto
Σ
:
=
(<?>
c
:
val
,
MSG
c
{{
c
↣
prot
2
}}
;
END
)%
proto
.
Definition
prot
_dep
_del
:
iProto
Σ
:
=
(<?>
c
:
val
,
MSG
c
{{
c
↣
prot
_dep
}}
;
END
)%
proto
.
Definition
prot
3
:
iProto
Σ
:
=
Definition
prot
_fun
:
iProto
Σ
:
=
(<!>
(
P
:
iProp
Σ
)
(
Φ
:
Z
→
iProp
Σ
)
(
vf
:
val
),
MSG
vf
{{
{{{
P
}}}
vf
#()
{{{
x
,
RET
#
x
;
Φ
x
}}}
}}
;
<?>
(
vg
:
val
),
...
...
@@ -95,64 +95,64 @@ Fixpoint prot_lock (n : nat) : iProto Σ :=
end
%
proto
.
(** Specs and proofs of the respective programs *)
Lemma
prog
1
_spec
:
{{{
True
}}}
prog
1
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog_spec
:
{{{
True
}}}
prog
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
1
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot
)
;
iIntros
(
c
)
"Hc"
.
-
by
wp_send
with
"[]"
.
-
wp_recv
as
"_"
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog
1
_ref_spec
:
{{{
True
}}}
prog
1
_ref
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog_ref_spec
:
{{{
True
}}}
prog_ref
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
1
_ref
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot_ref
)
;
iIntros
(
c
)
"Hc"
.
-
wp_alloc
l
as
"Hl"
.
by
wp_send
with
"[$Hl]"
.
-
wp_recv
(
l
)
as
"Hl"
.
wp_load
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog
1
_del_spec
:
{{{
True
}}}
prog
1
_del
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog_del_spec
:
{{{
True
}}}
prog_del
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
1
_del
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot_del
)
;
iIntros
(
c
)
"Hc"
.
-
wp_apply
(
new_chan_proto_spec
with
"[//]"
).
iIntros
(
c2
c2'
)
"Hcc2"
.
iMod
(
"Hcc2"
$!
prot
1
)
as
"[Hc2 Hc2']"
.
iIntros
(
c2
c2'
)
"Hcc2"
.
iMod
(
"Hcc2"
$!
prot
)
as
"[Hc2 Hc2']"
.
wp_send
with
"[$Hc2]"
.
by
wp_send
with
"[]"
.
-
wp_recv
(
c2
)
as
"Hc2"
.
wp_recv
as
"_"
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog
2
_spec
:
{{{
True
}}}
prog
2
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog
_dep
_spec
:
{{{
True
}}}
prog
_dep
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
2
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot
_dep
)
;
iIntros
(
c
)
"Hc"
.
-
wp_recv
(
x
)
as
"_"
.
by
wp_send
with
"[]"
.
-
wp_send
with
"[//]"
.
wp_recv
as
"_"
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog2_ref_spec
:
{{{
True
}}}
prog
2
_ref
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog2_ref_spec
:
{{{
True
}}}
prog
_dep
_ref
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
2
_ref
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot
_dep
_ref
)
;
iIntros
(
c
)
"Hc"
.
-
wp_recv
(
l
x
)
as
"Hl"
.
wp_load
.
wp_store
.
by
wp_send
with
"[Hl]"
.
-
wp_alloc
l
as
"Hl"
.
wp_send
with
"[$Hl]"
.
wp_recv
as
"Hl"
.
wp_load
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog
2
_del_spec
:
{{{
True
}}}
prog
2
_del
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog
_dep
_del_spec
:
{{{
True
}}}
prog
_dep
_del
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
2
_del
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot
_dep
_del
)
;
iIntros
(
c
)
"Hc"
.
-
wp_apply
(
new_chan_proto_spec
with
"[//]"
).
iIntros
(
c2
c2'
)
"Hcc2"
.
iMod
(
"Hcc2"
$!
prot
2
)
as
"[Hc2 Hc2']"
.
iIntros
(
c2
c2'
)
"Hcc2"
.
iMod
(
"Hcc2"
$!
prot
_dep
)
as
"[Hc2 Hc2']"
.
wp_send
with
"[$Hc2]"
.
wp_recv
(
x
)
as
"_"
.
by
wp_send
with
"[]"
.
-
wp_recv
(
c2
)
as
"Hc2"
.
wp_send
with
"[//]"
.
wp_recv
as
"_"
.
by
iApply
"HΦ"
.
Qed
.
Lemma
prog
3
_spec
:
{{{
True
}}}
prog
3
#()
{{{
RET
#
42
;
True
}}}.
Lemma
prog
_fun
_spec
:
{{{
True
}}}
prog
_fun
#()
{{{
RET
#
42
;
True
}}}.
Proof
.
iIntros
(
Φ
)
"_ HΦ"
.
wp_lam
.
wp_apply
(
start_chan_proto_spec
prot
3
)
;
iIntros
(
c
)
"Hc"
.
wp_apply
(
start_chan_proto_spec
prot
_fun
)
;
iIntros
(
c
)
"Hc"
.
-
wp_recv
(
P
Ψ
vf
)
as
"#Hf"
.
wp_send
with
"[]"
;
last
done
.
iIntros
"!>"
(
Ψ
'
)
"HP HΨ'"
.
wp_apply
(
"Hf"
with
"HP"
)
;
iIntros
(
x
)
"HΨ"
.
wp_pures
.
by
iApply
"HΨ'"
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment