Nuprl Definition : fifo+property
11,40
postcript
pdf
fifo+property(
es
;
codes
;
decodes
;
C
;
S
;
R
;
T
;
Req
;
Ack
;
i
;
f
)
==
e
.
j
:
C
. (
S
(
j
,
i
,
e
))
f
e
.
R
(
i
,
e
)
==
& (
e
:{
e
:E|
R
(
i
,
e
)} ,
j
:{
j
:
C
|
S
(
j
,
i
,
f
(
e
))} .
== & (
decodes
(
i
,
e
,(state when
e
)) =
codes
(
j
,
i
,
f
(
e
),(state when
f
(
e
))))
==
& (
e
,
e'
:{
e
:E|
R
(
i
,
e
)} ,
j
:
C
. (
S
(
j
,
i
,
f
(
e
)))
(
S
(
j
,
i
,
f
(
e'
)))
f
(
e
) c
f
(
e'
)
e
c
e'
)
==
& (
j
:
C
.
== & (
req
:{
e
:E|
Ack
(
j
,
i
,
e
)}
{
e
:E|
S
(
j
,
i
,
e
) &
Req
(
j
,
e
)}
== & (
(
e
.
S
(
j
,
i
,
e
) &
Req
(
j
,
e
)
req
e
.
Ack
(
j
,
i
,
e
)
== & (
& (
a
:{
e
:E|
Ack
(
j
,
i
,
e
)} .
e
:{
e
:E|
R
(
i
,
e
)} . (
f
(
e
) =
req
(
a
) &
e
c
a
))
== & (
&
e
.
req
(
e
) is c< preserving on
e
.
Ack
(
j
,
i
,
e
)))
latex
clarification:
fifo+property(
es
;
codes
;
decodes
;
C
;
S
;
R
;
T
;
Req
;
Ack
;
i
;
f
)
== antecedent-surjection(
es
;
e
.
R
(
i
,
e
);
e
.
j
:
C
. (
S
(
j
,
i
,
e
));
f
)
==
& (
e
:{
e
:es-E(
es
)|
R
(
i
,
e
)} ,
j
:{
j
:
C
|
S
(
j
,
i
,
f
(
e
))} .
== & (
decodes
(
i
,
e
,es-state-when(
es
;
e
)) =
codes
(
j
,
i
,
f
(
e
),es-state-when(
es
;
f
(
e
)))
T
)
==
& (
e
:{
e
:es-E(
es
)|
R
(
i
,
e
)} ,
e'
:{
e
:es-E(
es
)|
R
(
i
,
e
)} ,
j
:
C
.
== & (
(
S
(
j
,
i
,
f
(
e
)))
(
S
(
j
,
i
,
f
(
e'
)))
es-causle(
es
;
f
(
e
);
f
(
e'
))
es-causle(
es
;
e
;
e'
))
==
& (
j
:
C
.
== & (
req
:{
e
:es-E(
es
)|
Ack
(
j
,
i
,
e
)}
{
e
:es-E(
es
)|
S
(
j
,
i
,
e
) &
Req
(
j
,
e
)}
== & (
(antecedent-surjection(
es
;
e
.
Ack
(
j
,
i
,
e
);
e
.
S
(
j
,
i
,
e
) &
Req
(
j
,
e
);
req
)
== & (
& (
a
:{
e
:es-E(
es
)|
Ack
(
j
,
i
,
e
)} .
== & (
& (
e
:{
e
:es-E(
es
)|
R
(
i
,
e
)} . (
f
(
e
) =
req
(
a
)
es-E(
es
) & es-causle(
es
;
e
;
a
)))
== & (
& causal-order-preserving(
es
;
e
.
req
(
e
);
e
.
Ack
(
j
,
i
,
e
))))
latex
Definitions
(state when
e
)
,
P
Q
,
x
:
A
B
(
x
)
,
Q
f
P
,
x
.
A
(
x
)
,
x
:
A
.
B
(
x
)
,
x
:
A
.
B
(
x
)
,
{
x
:
A
|
B
(
x
)}
,
P
&
Q
,
s
=
t
,
E
,
e
c
e'
,
a
.
f
(
a
) is c< preserving on
e
.
P
(
e
)
,
f
(
a
)
FDL editor aliases
fifo+property
origin