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Type system and algebraic theory of Robust Ambients
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ETS-MTo ^ n g .@e Z'*q S b h' ;\
68 C?v R Gordon * Cardelli > R MA i ' % e ' ROAM @ " ,
è > R ? eo n ROAM @e xE;\ @o v 'e o4 e o44 c 8 xE;\ e d % $ R@e '
'c ! ROAM e Y% Z e U4Q V C ' Ce t;\b ek'} e ei '8 Y% Z e e d % > R,
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: 7C? Li ' |H c ! b ek,1 ROAM G h i G he U^'
&nYk ROAM 8 X" P ' e ZM TvG h } e C C? e Oql 8 âU' f (U) A v S 6 TvG h " P ' V U q @ " , > R !, TvG
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' f F ' SA U |2 A v S@ " y; 7 ROAM bZx SA
rZe C j J
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() Z TvG h?8e GECc !,h Z'*q Se GE \ ETS-MT ETS-MT H 4 @eW/ *9 o ^ HTns C @e Z
'*q S b h' ;\hE\ \ rs C I 'eF ETS-MT8
u M ^ o n# i. e P s Ci e I 'o ^ i e# i
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(u) /^ TvG h ei ' Ci ' fe > R @ " , + * g
.i i 8' ' f ? e ^ Levi * Sangiorgi % e > s 'C? Gordon
* Cardelli d xE;\ raeR a? i 'U+ | '
context lemma ek
,@ei ' |H "8 C? @ei ' |H * G h i eMS '
ek %k Zimmer eek ' a j5 k %Qk u hM @MS \TvG h
TYPE SYSTEM AND ALGEBRAIC THEORY
OF ROBUST AMBIENTS
ABSTRACT
The ambient calculus is a formal method modelling mobile systems and their interactions. This
thesis mainly focuses on the robust ambient calculus (ROAM) | a variation of the ambient calculus. Fundamental research on the operational semantics, type theory, behaviour equivalence and
expressiveness of ROAM are carried out in it.
Firstly, by analysing the inadequacies found in the existing mobile ambient calculus (MA) and
in the safe ambient calculus (SA), an approach that can improve those inadequacies by utilizing the
paramenters of co-actions is proposed. Based on this, the syntax and reduction semantics of ROAM
are given.
Secondly, the type system of ROAM is studied. The type evolution problem calls for a more
precise way to trace process behavior in type system for the ambient calculi. It has not been fully
addressed by many previous works. In this thesis, a type system named ETS-MT is proposed to fully
solve the problem. By storing both the current type and the future type in process type expressions,
and introducing special type syntax for capabilties, ETS-MT can track both the mobilty and threads
of a corresponding process, with full support for type evolution.
Thirdly, following Gordon and Cardelli's way in MA equivalence research, some process equivalence properties of ROAM are studied. By introducing a hardening relation that seperated the active
part of a process from the residue, a labelled transition semantics is given and proved sound with regard to the reduction semantics discussed before. Then, based on a simplied context called harness,
two results for proving the equivalence relations of processes are given, a context lemma that equates
the context equivalence relation with the harness equivalence relation, and an activity lemma that
enumerates the ways a process may interact with any given harness.
Fourthly, based on previous results on type system and process equivalences, some algebraic laws
for process equivalence are given, including a few single-threadness laws with and without contextual
constraints, a few uniform receptiveness laws, and a few corollaries. To demonstrate their usages,
the renaming example and the rewall-crossing example are proven through them, under certain
constraints. With simpler encoding and looser constraints, these examples illustrate the advanced
security features provided by ROAM.
Finally, the encoding of the -calculus into pure ROAM is given and the operational correspondence proved using the algebraic laws. It shows that by limiting the parameters of co-actions in
reduction, ROAM still holds the strong expressive power of its ancestors.
iii
iv
The main contributions of the thesis are summarized below.
The research on ROAM here shows that by further restricting the parameters of co-actions,
ROAM has better security control over SA, as is demonstrated by the renaming example and the
rewall-crossing example. Moreover, up-to-now, there is no evidence that ROAM is less expressive
than SA.
The type system ETS-MT provides a concise framework for the type evolution problem. It has
full subtyping support for both mobility and threads. Moreover, the basic structure supporting type
evolution can be extended with other type information, and the idea behind ETS-MT can be easily
adopted by other ambient calculi with co-actions.
This thesis also provides new proof method for equational laws, through Gordon and Cardelli's
context lemma. Moreover, the operational correspondence proof of the esc encoding is algebraic,
while the original proof by Zimmer is somewhat more complex.
KEY WORDS theory of computation, process algebra, type system, ambient calculus
||% .
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. . . . . . . . . . . . . . .
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{Bc &T }% dj .
9f . . . . . . . . . . . .
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4.2 c wDZ c X$ Y d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 & d(X$ Y d ch % . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
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7.1.2 & d . . . . . . . . . . . . .
7.2 esc E f . . . . . . . . . . . . . . . . .
7.2.1 N O . . . . . . . . . . . . .
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7.2.4 & B . . . . . . . . . . . . .
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7.2.6 ^ K6 . . . . . . . . . . . . .
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7.3.4 h&% caS % dj . . . . .
7.4 E fc h . . . . . . . . . . . . . .
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x
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x
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103
111
117
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M.
process
ambient name
capability
action
structural congruence relation
reduction relation
process type
capability type
pre-type
mobility
threads
type environment
concretion
hardening relation
label
labelled transition relation
context
observation, or barb
contextual equivalence
harness
harness equivalence
deep action
deep action observation
never occur in context
visible action
observation under restricted context
structural congruence relation
on prime
ix
{
15
15
15
17
17
18
24
24
24
24
24
29
37
38
38
38
45
45
46
47
48
61
62
63
63
63
111
x
=;9
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k 28] cp{ O 3Y Rt m %A c m Rt k h* 7 !p{H %L.) O T } Zimmer (>+ Ln . n'7 n m+p{ (0 p{& Rt=$U LRt cp{ :
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]~ n { 0Y; ~ % c imm T] Y imm c? T{3 h n Y; c E ~ imm c ! (3 G+ 7R Tn?n'{ d40Y;%h 5+N 6 = 67? u
& imm h! h &a,@~7>k 28] q c Z j~ Zimmer
7>k 29] 2? ! +I)c l @ h !! ^D +?c Y; H %(Rt cp{H %Ln m+
& Za | {c 7R O &I 4T]7R O#2> LL ? Tl + T |S{
% deterministric c F0f typing algorithm Cardelli h]7 >k 30] 2 k , $ ~ Z~ 5 MA c ! O % ? ! + i G \'U;T
R P _-y_W>i G \'U;T
;T n _-y_EaTp>i G \'U;T
>k 30] h 5 9 8"cp{H %(Y; H %u_ \ I ?6, 7~K 6c*) ( Fb
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] +c Rt m+ hXq a ^? ,b$ 'n6c O 7 6 c 31, 32, 33] h >k ``
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! MA v%&|eq _ C
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t " b + T RtE fc&I &-n 5 <ZU N T B>r c?h
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5] ( 19] c < P' a MA ch % >+ T] $4) _ Oec{ d! N -L3 > c context lemma ( activity lemma U& ] -L o + MA ?h % cdj= 6! context lemma v MA ? T*ad ~c~ `> h contextual equivalence Z h c
v4 harness c~B~`>q{d cE$QchZl 6 activity lemma b+Y
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40, 41]
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42, 43]
44 , 45, 46, 47, 48, 49]
50]
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ch % { &ab q S ?h % c{{G >k 96L /V+I)&E Xjq
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"c0 SA Efch B7c; ]6Tc~ N I`*
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& Z GSmrB +U Ojc" Z!7>k 16] c Zh 0
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l- . - ? ( Ic- 7 L&- c < PB$+ >k 16] k I l c !
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cX$c= r7h Z4TZ U T-L
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P
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(Struct Par Zero)
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P 0 P
(Struct Res Zero)
(Struct Res Res)
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6
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1
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m in n : P P ] n in m : Q Q ]
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1
j
2
1
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1
2
2
P
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P
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acquire n : P = open n : P
release n : P = n ] P
4
4
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4
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j
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j
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62
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(r)(P open r : Q)
P (r)(open r : Q)
P
(2.11)
(2.12)
(2.13)
(2.14)
(2.15)
P Q
= (r)(open r : P open r : Q r open] )
(r)(open r : P Q)
(r)(open r : P ) Q
Q
(2.16)
(2.17)
(2.18)
(2.19)
(2.20)
j
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hGG376 ec?h%L* Xy^70
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b+~ MA heXhRt c>75 Ah?c s= MA c;@hX? ;: R
t > v}l 4h ` h7 ROAM n7 rs c ? ;: Rt A~ ~{c F . ; @ s =
] `$_c !6 'T ~ Fb Rt @ 45 A W Xc 5 A s =n{ d k `
n
)
P +m
Q = (r)(open n : (nopen] open r : (open n P ))
open m : (mopen] open r : (open m Q))
ropen])
4
)
j
j
j
j
j
j
7 ] ~{ d ; @ open na T open m 6 2 h c nopen]a T mopen] 3 4 +
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(n P + m Q) n open]
(n P + m Q) m open]
)
)
)
j
)
;!
j
;!
P (r)(open m : (mopen]
Q (r)(open n : (nopen]
j
j
j
r : (open m Q))) (2.21)
open r : (open n P))) (2.22)
open
j
j
j
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7!um&z] nopen] ( mopen] c(h
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9( Cardelli ( Gordon 7 MA Tb+RtOmc&
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4
j
in
5 ]
m
U LRt n c? n be m : P Tn$ Rt cm+ n t7 & T ' T] 6 ' cm+
m
nn be m : P Q]
= nm out n : open n : P] in m Q]
m open n : P] n in m Q]
m open n : P nQ] ]
mP Q]
j
j
;!
j
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;!
j
j
j
j
(2.23)
(2.24)
(2.25)
(2.26)
(2.27)
7 ROAM 0h`{d_c Om s =
n
be
m : P = m out n : in n : open n]
L 4
j
out
nn be m : P Q]
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mP Q]
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ta Fb n m c? ? Q h $ n 7 O m a'Y; h U n .$` MA c O
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&
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B L c O Kc 0 a( 3P ( D m b + ROAM c (c - s Z c &
daT & ROAM cy @ d(Z B b 9+? Tl cXj 64 cL* ] 4
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h 8%TYJ
}%&
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Z type system T|jS{d c&n{? ZB(c s= 9d7 &
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MA c cB B k Y;%(*R ,r c
MA SA !O
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< P p Q ( KQLc
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~ Xj LRtc~ %k w B LRt 1 0 2 ! ?c "6'c `; @3 ; @
c(;@cuQnRtm q6'c l4 cS{ N;@s c~%
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b ; @7 h c? nm c? l 4 s ! Fb ; @?c { d N6,? Fb
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57 ]
27, 28, 29]
34 , 31, 32]
16 , 58]
54 ]
1
27, 28, 29, 34, 31, 58]
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j
(3.1)
4 Rt n c? in m : open : 0 Y Y; ~ %TV n 7 m ? Fb 6Rz T]
Jy??m m Rt n c Y; ~ %a8n m m U? 7Fb. 6 TDc@;
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?c;y~%?% m< P?cKQ% 7| N
B L + ROAM c T | ED Z ETS-MT " ~ ~Bc Z B(G 3 +? Z B(c r o h ( Imo h n33]Z +Fb y @. 6 ?c h ~ %, - ~Bc
s = ! m0]+RtEfcEDBB Lc N;h 2 ETS-MTIb!
k`>d9Zq+ gKc?H %b'b+n]gK l mobilty ( ]g
3 threads &H%ca07+?ZB(YEDBc~{-s(
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1
23
Dh Y$2VOL
24
b + ETS-MTc9 f typing algorithm n] 7 b {c J K `t f? R
t c9 dj+9 f caS % soundness ()>% completeness 9
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2
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3
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3
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25
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TD cr B
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h c ~ %k 0Y;(Y; & y @W 2s ! Zh Y; c~ %Q p ( Q p 72
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0
0
0
0
z
y
:
:
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y
y
y y y
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1
1
1
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1
t
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2
2
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4
1
2
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1
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0
4
4
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Dh Y$2VOL
26
!73P? P P c-Y#\i P : T P : T 3]`^@;{L
(1). T T ` 4 Q n T = U : T = U 4 P P c n ~ U u U Z+
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& ] Q p c? a ~- T3 *p c (2). T T T]4 Q T]4ED h, T = U T = U T] 4
P 7 ; @ open s ! . Zh4 U c~ %j 6Zh4 T %a ~c- $` P P c P c~ % 7 P ; @ open cs ! . 6# n hl 4 P c~ % U N @ ~
7 U ( T ~]`$ P P c
(3). T T #4ED B P P c 0 ~ - Y l4 & ]a ~c open ; @s ! c
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1
1
2
1
2
1
1
1
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2
0
1
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2
2
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1
2
2
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1
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4
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y
y
y y y
j
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0
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1
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2
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1
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1
j
j
j
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2
2
1
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1
j
1
j
2
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1
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1
2
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1
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2
2
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2
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2
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1
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=
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= MAX(U j U )
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;
4
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1
i1
in
3k
2
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3
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2j
1
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2
i
3
1
2
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3.3
x
27
c? T U Ts97? s =c@ ~ f3 0 )Vc a , M +NT]
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0
0
0
x3.3
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2tA cI Z&Zs~0 %k T]_ int c
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0
T
Z
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28
]` 3 T & Z c& 0
_
0
y ]
0
1
0
_
_
0
_
_
0
_
0
y!
y
y
y!
y! ]
y! y!]
]]
y! y! y!] ]
_
_
0
1
0
(3.2)
(3.3)
(3.4)
(3.5)
(3.6)
` e b + 2f = t ( jt c T % 7 U % 7nn' t ( jt c{ d `$ l2 3.1
_Qui z y u t \Y|Q
(Dot Zero Z )
zZ=Z
(Dot Zero Y ) 0 y Y = Y
(Dot Zero U )
uU =U
(Dot Zero T )
tT =T
(Dot Symm Z ) Z z Z = Z z Z
(Dot Symm Y ) Y y Y = Y y Y
(Dot Symm U ) U u U = U u U
(Dot Assoc Z ) (Z z Z ) z Z = Z z (Z z Z )
(Dot Assoc Y ) (Y y Y ) y Y = Y y (Y y Y )
(Dot Assoc U ) (U u U ) u U = U u (U u U )
(Dot Assoc T ) (U t U ) t T = U t (U t T)
(Dot Strict Z ) Z Z = Z z Z Z z Z
(Dot Strict Y ) Y Y = Y y Y Y y Y
(Dot Strict U ) U U = U u U U u U
(Dot Strict T ) U U = U t T U t T
_ 0
_
_
l2 3.2
0
1
1
1
2
2
1
1
1
2
1
2
2
1
3
3
1
)
1
1
2
)
1
1
2
)
1
2
1
)
2
1
3
2
2
3
3
2
2
3
3
2
2
3
2
1
1
2
1
2
1
3
2
1
2
2
1
2
3
3
3
_Qui z y u t \Y|Q
(Par Zero Z )
zZ=Z
(Par Zero Y ) 0 y Y = Y
(Par Zero U )
uU =U
(Par Zero T )
tT =T
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(Par Symm Y ) Y y Y = Y y Y
(Par Symm U ) U u U = U u U
(Par Symm T ) T t T = T t T
(Par Assoc Z ) (Z z Z ) z Z = Z z (Z z Z )
(Par Assoc Y ) (Y y Y ) y Y = Y y (Y y Y )
j
j
j
j
_ j
j
0
_
j
0
_
j
1
j
1
j
1
j
1
j
2
2
2
2
j
1
j
2
2
2
j
j
j
1
1
j
2
2
1
j
2
j
1
1
3
3
1
1
j
j
2
2
j
j
3
3
2V@ g
3.4
x
(Par Assoc U )
(Par Assoc T )
(Par Strict Z )
(Par Strict Y )
(Par Strict U )
(Par Strict T )
29
(U u U ) u U = U u (U u U )
(T t T ) t T = T t (T t T )
Z Z = Z zZ Z zZ
Y Y = Y yY Y yY
U U = U uU U uU
T T = T tT T tT
1
j
1
j
2
1
2
1
1
1
j
2
3
j
3
)
)
2
)
2
j
j
1
1
3
j
3
j
2
j
3
j
2
2
3
3
2
3
j
2
2
3
j
1
j
j
1
1
)
2
1
3
j
3
j
3
U %7Xj+ 2f= t ( t cT cB~%7` e { Bcdj ~$
U %7
x3.4
j
q j. 3)"
B *70 ETS-MTc { B typing rules U B ~ 7 T]b {c J K `Y-? P (- W c
{>dNb{q WXc n J K typing environment T]JK
~ ; Z+ uYk ` c cB - s n : T nk : Tk ! n nk 4=hr c R
t m ~ dom(;) Z +U Rt m6'c h-T] wc J K ~ Z + ETS-MTc { judgement ]` ^ ( (1). ; ` } Z + ; 4T] aSc J K n ; c Rt m =h -
(2). ; ` n : T Z + b { J K ; Rt m n Y T (3). ; ` M : W Z + b { J K ; M Y W (4). ; ` P : T Z + b { J K ; ? P Y T ETS-MTc { Bk Ù B 3 't ]n3
1
1
||a5 JK(Rtm { B
(Env Empty)
(Env Intro)
(ET Name)
1
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n dom(;)
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; n : T
; n : T n : T
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62
` }
` }
`
|a5 { B
(ET Empty)
(ET Cap Mbl)
(ET Cap Imm)
(ET Open)
;
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t
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t (T t )
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2 f
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1
;
2 f
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Dh Y$2VOL
30
;
(ET Co-open)
; open : ]
; M :W ; M :W
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1
1
;
`
1
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1
2
2
1
2
2
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(ET Inact)
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;
; 0:
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; M : P : W (T)
; P :T ; Q:T T tT =
; P Q:T tT
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; !P : T t T
; n : T P : T
; (n : T )P : T
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0
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6
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1
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2
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1
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6
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1
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2
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2
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1
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2
1
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2
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2
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È$Q
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c[k EDB+N~B O>d#{ P : T gD? open : P c
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open n y@n ] W" ) ' Rt n c L. Y ED - s UT ] :7Fb y @ ) ' 6 n 7/c? P : T (? P a~2!n-?c4 T jt T % open n 23T]0
Y; c ; @ l 4 open n : P c sL4 _ t (T jt T ) z 4 7 Rt n c 4 UT ] c.
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0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
1
2
2
1
1
2
2
2V@ g!ejWi<
3.5
x
31
%(p Q`Y v}l 4 T]-Rt c 4 _ 9 6? n ] & B
?!/I
3P ~K { B h ~` ]` -L n { B`$c? # 3 c
0
r 3.3 (Validity) 1w ; P : T '# T = `
6
?
* 3P ; P : T c-Y~ ]3 B (ET Act) (ET Par) ( (ET Repl)
c. n'n` `
7 ETS-MT3PB (ET Par) ( (ET Repl) n]hk>7&]a] ~c open ;
@a2!B?30 ck ! open open : P open : Q `40?
]`T] &Xj ETS-MT Bc$ ~
7 ; = n : UnTn] m : Um B ; in m : in n : open n : y t t t (Tn t ) V%
m c4TQh ?Fbl4 open m 7 ; `30cL n YED
l4 n 0] Q30cl4G &Z 0 c /I4 n c Un Tn] Q T3X n Y ED Rt n c? L. v s !T] open ; @ % U T s? 0
G >$ j
1
`
_
_
q j. 3)"x+
x3.5
1
_
1
j
;
0
~ / n ,0
B * N dj~K ETS-MT { Bc & T } % subject reduction nk ; ` P : T
: P ;! Q, zW ; ` Q : T : T T { 3.9 > d 7~K % 7 3.1 3.2 (T n c c
$~dj-s?c rn 3.8 j65dj { Bc & T }% {
3.9 7 ; ` J Z+aa]`t{jT ; ` } ; ` M : W aT ; ` P : T ~ fn(J) Z+
J n 4 M Q n 4 P h c)m 0
r 3.4
0
1w ; n : T J '# n dom(;) `
62
* zB (Env Intro) X7JKE~c% L Bc. 9d+qn
mcm+3hFc l47qnB -Yc-LJ Kcm+ hX F h
r 3.5 (Implied judgement) 1w ; ; J '# ;
1
2
`
1
` }
* ; cc]Q?! }
k ; = zWn' (Env Empty) n` "
k ; = ; n : T n ; n : T ; J }#i ;
n dom(; ) " ~ (Env Intro) n` ; n : T
n ;
1
` }
1
1
62
0
0
1
1
2
0
0
1
1
`
` }
1
0
1
` }
n 3.4 i
` }
r 3.6 (Strengthening) 1w ; n : T J - n fn(J) '# ; J `
62
`
Dh Y$2VOL
32
* n fn(J) n J cq&Om O m $` J h h n U L 7
; n : T J c - Y n : T hX? $ ~l 4n r~L c & `$ ; J 62
`
`
r 3.7 (Weakening) 1w ; J - n dom(;) '# E n : T J `
62
`
* > d ; J " ~n 3.5 i ; 5" ~ (Env Intro) n` ; n : T
c $~ $ ~ ; J r c Bn ] `$ ; n : T J `
` }
`
` }
74
`
r 3.8 (Subject congruence) 1w ; P : T - P Q s ; Q : T `
`
n 3.8 cdj u K B 1 r 3.9 (Subject reduction) 1w ; P : T - P
`
;!
Q, '# ; Q : T - T
`
0
0
T
{ 3.9 cdj u K B 1 x3.6
B d q j: %
{ B b +q - c { T3&Z c>7 { B
h GS b T] ?Yc~ %B * b T] 7 b { - J K `` J Rt( ?
9cf a dj Lf caS%()>%
a ab {c - J K ; ;
t f M Rt m n ( ? P c f 3
]~ Type(; M) Type(; n) ( Type(; P ) Z + r { d k `
` }
(Type Name)
(Type Empty)
(Type In)
(Type Co-in)
(Type Out)
(Type Co-out)
(Type Open)
(Type Co-open)
(Type Path)
(Type Inact)
T ype((; n : T ; ) n) = T
0
00
T ype(; ) =
Type(; n) = T
T ype(; in n) = y t
Type(; n) = T
T ype(; in n) =
t
Type(; n) = T
T ype(; out n) = y t
Type(; n) = T
T ype(; out n) =
t
Type(; n) = UT ]
T ype(; open n) =
t (T t )
;
1
_
;
1
1
_
1
_
;
;
1
;
j
;
T ype(; open) = ]
T ype(; M) = W T ype(; M ) = W
Type(; M : M ) = W(W )
_
1
;
0
0
T ype(; 0) =
_
0
0
0
3.6
x
oU2VJ"
(Type Act)
(Type Par)
(Type Repl)
(Type Res)
(Type Amb)
33
Type(; M) = W Type(; P ) = T W(T) =
T ype(; M : P ) = W (T)
Type(; P ) = T Type(; P ) = T T t T =
T ype(; P P ) = T t T
Type(; P ) = T T t T =
T ype(; ! P) = T t T
Type((; n : Tn ) P ) = T
Type(; (n : Tn )P) = T
Type(; n) = Tn Type(; P ) = T T Tn
T ype(; nP] ) =
6
0
j
j
0
0
6
j
j
0
6
?
?
0
?
j
_
0
f n ]t f- c Rt m ( ? E _ f 7! M n a P ~0"kG ~Kf `- BZ +! 3 0 c
~Kfc{dcB~_ { Bc;hh j(7 (Type Amb) c T Tn K + (ET Sub) B f caS % soundness ()>% completeness ` ec& ] { 9 d r 3.10 )1l
(1). 1w Type(; n) = T '# ; n : T "
(2). 1w Type(; M) = W '# ; M : W "
(3). 1w Type(; P) = T '# ; P : T `
`
`
* fc B?!} `dIn3@;# h`" ~ }#n'`$-L
!3P (Type Amb) +N*$~T7 (ET Sub) r 3.11 GPl
(1). 1w ; n : T '#WBeq n 4h - Type(; n) = T "
(2). 1w ; M : W '#WBeq M 4h - T ype(; M) = W "
(3). 1w ; P : T '#WBeq P 4h - T ype(; P) T `
`
`
* { B? ! } ` d! }#c" ~N~ $ %7 3.1 (% 7 3.2 ~]3!c (Dot Strict T ) ( (Par Strict T ) ~K&]{n]- Lk `7 ETS-MTqY - cRt (?# Y
T] 9 : L 9 a !4 f c- 96E_s~~K{ b f` ?9 c & T} %
T
r 3.12 1w Type(; P) = T - P
;!
Q sWBeq Q 4h - T ype(; Q)
* T ype(; P) = T " ~ { 3.10 ni ; P : T 7 P Q " ~ { 3.9 n`
; Q : T : T T 5" ~ { 3.11 Type(; Q) T l 4 Type(; Q) T `
`
0
0
;!
0
Dh Y$2VOL
34
x3.7
bu
B * b T]0Y;?K *c& Xj ETS-MT7r B ED& ec 7L&T]- P?K* Server h<hK Agent JcQX?K *( K
`)c{d k`
Server = s ! in a : open a : Collect]
Agent = a in s : open : Data]
U#{? Collect ( Data #Y0Y;cQ
>7 *] K kl)2 !I @ 4 K o?K c ?K * s VOW5 o?K4
+>$U T s ?K * L> c T] ~ % T3 0Y;%V % 7h g ED c Z ?K*NFbYY;% cK ]J`QX ?K*c L.Q4Y; c
7 ETS-MT?K*c0Y;%TncED`$0]#{ ; 3T]6,c s : Ts
( a : Ta c -J K :R4 Type(; Data) = Y Type(; Collect) = Y E _ f t f Ts ( Ta ncJtk `
(1) Type(; s) = Ts
\i
(2) Type(; in s) = y t
(1)+(Type In)
(3) Type(; open) = ]
(Type Co-open)
(4) Type(; in s : open) = y t( ] )
(2)(3)+(Type Path)
\i
(5) Type(; Data) = Y
(6) Type(; in s : open : Data) = y Y ]
(4)(5)+(Type Act)
(7) y Y ] Ta
(6)+(Type Amb)
(8) Type(; in a) =
(7)+(Type Co-in)
t
(9) Type(; open a) =
(7)+(Type Open),
t( Y t )
J Ta 4 9 t y Y ]
\i
(10) Type(; Collect) = Y
y Y yY
(11) Type(; open a : Collect) =
(9)(10)+(Type Act)
y Y yY
(12) Type(; in a : open a : Collect) =
(8)(11)+(Type Act)
(13) Type(; ! in a : open a : Collect) = !
(12)+(Type Repl)
(14) ! Ts
(13)+(Type Amb)
4
4
_
1
_
1
_
1
;
1
1
1
2
;
_
_
_
;
1
1
1
1
_
_
1
_
;
1
_
1
j
;
1
_
_
1
2
_
1 (
1j
_
2)
1 (
1j
2)
_
_
( (14) ni?K*Rt s cn]40Y;
7 ` e < P?ch % {GE _ L n] f$0Y;%( Q p % 7?h%7c EDB +0] LB c T | ED Z ETS-MT 0]+ ROAM ?7Fb y @. 6 TD cgK B ETS-MTY,j+c ( {Bn]rB?cY;%(p Q&] H%a g& #+ {B ]'B
LLb+T]t f? (Rt9 cfa~T] &Xj+ ETS-MT7gKF4 Y;Z
c0) %
B Lc-LjV3+*7 ROAM E fc c $~c T3n ]0 h ` m Y q$!u RtE f Z
k SA E f B Lc l @ 4`>< P ROAM ?cKQ % 7 o + N c l Y 5
U5@' MA 8;%h/-9HF fMP B open %#r] MA ;NP?AVm f? S&=D Amtoft 9@
m 33] 8 =1 / / - 9]* 87f Q < %? S- MA 8;% open A8 bUw f #+ Hdf h / %9% 1
" f w i;u &
5
30 ]
36
Dh Y$2VOL
} 7 & X1:;-
B Lb' d+N#$ c- s Zc &dL8 FT| X$ Y d labelled
transition semantics Z BQ ] ? 'n = cn % 4 X$ Y dL. Y
"&dch %
h RtE f X$ Y d c k 19, 16] $ ~c S commitment (
W, outcome c &dE $n T3X$ !*: X$ Y- #+? L n3 #
7W, concretion ">k 20] $~c 7$ hardening relation c&nm+T]
cZTX$Y-c4 ?:0; nYX$c] Q( c; @]Q rU&&
` ~y B L X$ Y d c s = r~6T &B L;h (`T L;h cB ~3 >k
20] MA ch % -L7 ROAM c s~G T>k 20] c / Tn ] Q0 /VV ;@c>7 ROAM c-LXqhN 7X$ Yd c{ d]k oI L?
(Q~`> harness c=~ ?h Z< PcI n3 ;h h [k $ Z4 +F) c RU?c
&Os=6N{dc wDZ c&O s=I) r~G c& (n /JZ +&Om
c=$, T -
=
U
.9% W
x4.1
RtE fc~B %?Y &c n3 n 6, 7v]Rt c; n &cQ n3' T]' Rt ?m!; nU$` RtE fc X$ Y d0 ~ ~ _ CCS ( E fc & (n'gK 4 + 7 ?; n n u &cz&? U63 MA h Z c
 -wDZ YT* ( P > (~p) P P (~p) P P 4 7W, ! P 4 P n ] ' 5 = cv ]n3 4 ? ? prime P 4 P #L \6 q5c n3 4 d/ residue &Om - ) ~p > / + P ( P r~
c&Om wDZ5 ? P *]zh?RtP 562c &?cvT] 'z
T]\ c wD - ` c \ ` )~Bc =~ %U L ?c = ~% TnL
?wDc ` h c \%h 3P ROAM c n m wD - C
cT*(k `
C : : = (~p) A:P Q
C??
(~p) nP] Q
<a??
20]
h
0
1
00
i
h
0
i
00
0
00
0
00
2 C
h
i
h
i
U&Om-) ~p r~Gc&(:!cW 23 Gc 4F )&R`> n'~ ~p
Z +&Om h- p , p , : : :, pk h- ~p 4 w wD - ) @ () P P { dwD cJ)m 5 Q fn((~p ) P P ) = (fn(P ) fn(P )) ~p A 8f(Pu?\K- 9p58%yF#] 8f p~ 8f-9>&Rsu \K%X,P -9>&-%uXJ
f
f
1
g
2
h
0
i
f g
00
4
h
0
1
6) p~ : T~ &
p
37
0
; f g
0
i
00
g
Ih #"m\d]
38
2 n m wDZ cxc > dwDZ @ T n 3Pq? P Y ; @ A:Q aR
t nQ] c ( Bnn' wD4 () hP i 0 "q? P Q cv T] n wD4 v wD - B!a~ P j Q QnwD4_c-3Th3 L- c x4 "- c x a~ P Q c8wDT" ! P n04 ! P P j ! P z ! P a~ P wD-cx n`$ ! P cw
D - "q P n wD4 C B (n)P cwD - n # Q n c&O #2h (n) 3]/ 7 C
c&Om-) \ax n3 `$ Ly @{ dc (n)C w$)'
wDZ cn 0 b ! ( D c{ d k `
4.1 7$U d}uP >
à1Q
(Harden Action)
A : P > () A : P 0
(Harden Amb)
nP] > () nP] 0
P C
h
i
h
i
P > (~p) P P
~p fn(Q) =
P Q > (~p) P (P Q)
Q > (~q) Q Q ~q fn(P ) =
(Harden Par 2)
P Q > (~q) Q (P Q )
P > (~p) P P
(Harden Repl)
!P > (~p) P (P !P)
P >C
(Harden Res)
(n)P > (n)C
P >C
(Harden Empty)
:P > C
M : (N : P ) > C
(Harden Path)
(M : N) : P > C
+}N& (n)C àL6 C = (~p) P P - n ~p (1). 1w n fn(P ) s (n)C = (~p) P (n)P "
(2). 1w n fn(P ) s (a) 1w P = mP ] m = n n fn(P ) s (n)C = (~p) m(n)P ] P "
(b) ls (n)C = (n~p) P P (Harden Par 1)
h
0
00
i
f g\
j
h
h
0
00
i
h
0
0
00
i
4
0
0
h
i
j
i
j
00
00
i
h
0
0
h
h
00
f g\
j
62
0
j
00
i
62 f g
00
i
0
2
0
0
6
1
4
00
62
h
0
i
4
h
0
1
i
00
00
3P ~K{ dh ~f k P > (~p) hP i P B P (~p)(P j P ) `> b U T -L
cdjn 4.4 0
x4.2
00
0
00
B1.9% W xY223!
B *7~ >wDZ c c $~ +* T | ROAM c X$ Y da 7 ` *dj!. >
qK ROAM &dch%
4.2 W09
ROAM \Hx;^la LTS
Label L]3nuP
+}\Hx{ Label nAf I: = Action I:]p(M;â& LhG=V (P , Q, ) LTS VL P Q LTS \à1Q
P P 4
2
f g
;!
!ed]##"m\d]('W
4.3
x
39
P > (~p) A:P P fn(A) ~p =
P A (~p)(P P )
P > (~p) nQ] R Q in m Q R > (~r) mS] R
S in n S
~r fn(nQ] ) =
~r ~p =
P (~p~r)(nmS ] Q ] R )
P > (~p) nQ] P Q > (~q) mR] S
R out n R
S out m S
n ~q
P (~p)((~q)(mR ] nS ] ) P )
P > (~p) nQ] R Q open Q R open n R
P (~p)(Q R )
P > (~p) nQ] P Q Q
P (~p)(nQ ] P )
(Trans Cap)
h
0
00
i
\f g
0
;!
(Trans In)
h
0
;!
i
j
0
;!
h
f g\
h
i
0
;!
0
h
0
;!
(Trans Open)
h
i
h
;!
i
0
j
0
;!
0
0
j
0
;!
0
j
0
;!
0
i
0
j
;!
(Trans Amb)
0
j
62 f g
0
;!
0
j
0
i
f g\f g
0
;!
(Trans Out)
00
0
A- Y P A Q Z +? P >7 T z&?ns !; @ A - Y P Q Z +? P
IT];n;@ 6n D4 Q `>~ fn() Z+ hc) m h-
B (Trans In) (Trans Out) ( (Trans Open) ~ ( t & B (Red In) (Red
Out) (Red Open) rs A- Y c n m D +U Bc n3 (Trans Amb) T
g +1 0 - Y 7 Rt ; n U Ts 3 aU G+ 5 o (Red Par) (Red Res) (
(Red Struct) sc X$ YB l47wDZ c{ d U B \ I h !u `
>n 4.7 4.9 ( 4.15 cdj ;!
x4.3
;!
+ !5Y223!x{J n
B * N) ' X$ Y d( 9( n mc & d jch % dj vu_9 h " gK+ r c? = ~ % Q$` `>]X$ Y d4c $? !c?h %< P-L
& dL '* B *c TZ /djn 34 & ]n3o Tn3 " ~n 4.4 4.5 dj & d6,X$ Y d p 4.6 o "n3 > d dj+ n 4.7 4.9 4.15 nX$ Y dL o _
(Red Par) (Red Res) ( (Red Struct) q1 0 c?; n &c X4dj+ X$ Y d6, & d p 4.16 9 6B *0 - p 4.6 4.16 `&| dr= hc-L
{ 4.17 r 4.3 1w P Q '# fn(P ) = fn(Q) * , -c{d?! }` d 4(J
r 4.4 1w P > (~p) P P s P (~p)(P P ) 0
h
i
00
0
j
* P > (~p) P P c-Y?!} (Harden Action)(Harden Amb) n'ni#'*
h
0
i
00
00
Ih #"m\d]
40
(Harden Par 1) 4 P = P Q P > (~p) P P P = P Q : ~p fn(Q) = }#i P (~p)(P P ) l 4 P = P Q (~p)(P P ) Q (~p)(P P ) !
o"7-s ~p fn(Q) = 9d #'*
(Harden Par 2) - (Harden Par 1) ni#'* (Harden Repl) 4 P =!P P > (~p) P P : P = P !P }#i P (~p)(P
P ) eX n 4.3 i fn(P ) = fn((~p)(P P )) l 4 ~p fn(P ) = 4" ~ (Struct
Res Par) ni P =!P P !P (~p)(P P ) !P (~p)(P (P !P )) = (~p)(P P ) #'*
(Harden Res) 4 P = (n)P P > (~p ) P P n ~p : (~p) P P =
(n)((~p ) P P ) }#i P (~p )(P P ) l 4 P = (n)P (n)(~p )(P
P ) (~p )(n)(P P ) ` e n ( P k P cZ3 @;{L (1). q n fn(P ) B (n)((~p ) P P ) = (~p ) P (n)P n p~ = ~p P = P :
P = (n)P % P (~p )(n)(P P ) (~p )(P (n)P ) = (~p)(P P ) #
'*
(2). q n fn(P ) B (a) q P = mP ] m = n n fn(P ) B (n)((~p ) P P ) = (~p ) m(n)P ] P
n ~p = p~ P = m(n)P ] : P = P % P (~p )(n)(P P )
j
1
0
1
00
j
j
1
h
1
1
0
1
1
1
1
1
j
1
j
1
0
h
1
h
1
00
1
0
1
j
f g \
j
1
0
0
1
1
1
00
j
62 f
00
j
j
1
0
1
1g
0
h
00
j
0
j
1
1
0
00
i
1
1
00
j
0
1
j
1
00
1
00
j
0
h
1
1
1
j
0
00
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00
i
1
1
1
1
00
j
0
0
62
j
00
f g\
00
1
00
00
1
1
1
00
00
1
1
0
0
1
j
0
00
i
00
1
00
i
0
1
00
0
h
1
1
1
00
1
1
1
00
i
j
1
1
f g\
00
0
h
1
1
1
00
i
0
1
1
0
1
1
00
j
0
1
0
1
j
00
0
2
0
0
1
2
6
00
62
0
1
1
1
0
00
0
h
1
00
i
00
2
1
1
1
0
h
0
1
1
00
j
00
i
2
1
1
(~p )(((n)P ) P ) = (~p )(((n)mP ] ) P ) (~p)(m(n)P ] P ) = (~p)(P
P ) #'* (b) : B (n)((~p ) P P ) = (n ~p ) P P n p~ = n ~p P = P :
P = P #n''* (Harden Empty) :P P ` i (Harden Path) M:(N:P) (M:N):P ì ] ~ qn@;c 3P ni -L'* 0
1
00
j
1
0
1
1
00
j
2
1
0
00
j
2
0
1
j
00
1
00
h
0
1
i
00
1
1
h
0
1
i
00
f
1
g 0
1
0
1
00
1
r 4.5 1w P
A
- fn(A) ~p = \f g
;!
Q sVq P P y ~p "* P
0
00
(~p)(A:P P ) Q = (~p)(P P )
0
j
00
0
j
00
* P A Q z B (Trans Cap) `$ l 4 P > (~p) A:P P Q = (~p)(P P ) : fn(A) ~p = n 4.4 i P (~p)(A:P P ) ;!
0
j
00
0
h
\f g
0
j
i
00
00
7n 4.4 4.5 cc$~X$Yd c{d `n3Tn O' rs c-s
Z? Tl $? TO4 & d qN Fc-sU La ,X$ Y d q`c - Y
Z `n`$ rs c & Z
4> 4.6 1w P P s P P * P P c-Y?!} ;!
0
;!
0
0
;!
(Trans In) 4 P > (~p) nQ] R Q in m Q R > (~r) mS] R S in n S ~r fn(nQ] ) =
~r
~p = : P = (~p ~r)(nmS ] Q ] R ) n 4.4 ni P (~p)(nQ] R) R (~r)(mS] R ) "5" ~n 4.5 n` Q (~q)(in m:Q Q ) Q (~q)(Q Q ) h
f g \f g
j
0
0
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q~ S (~s)(in n:S S ) S (~s)(S S ) n ~s ~q ~s ` 4 &O
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Par) c$ ~ ~r fn(nQ] ) = ~q fn(mS] ) = ~s fn(nQ] ) = 9d P
(~p)(n(~q)(in m:Q Q )] (~r)(m(~s)(in n:S S )] R ))
(~p~r)((~q~s)(n in m:Q Q ] min n:S S ] ) R )
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(~p~r)(n(~q)(Q Q ) m(~s)(S S )] ] R )
(~p~r)(nmS ] Q ] R )
= P
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Q
Q 2 n 4.4 i P (~p)(nQ] R) l 4 P (~p)(nQ] R)
(~p)(nQ ]
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;!
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(~p) A:P (P R) 5 (Trans Cap) ` P R A (~p)(P (P R)) Q R -L'
*
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` P R > (~r) mP ] (P R) 5 (Trans In) ` P R (~p~r)(nmP ] P ] (P
R)) Q R -L'* (Trans Out)(Trans Open) r~_ (Trans In) c &ni-L'* 4(J (Trans Amb) r~ _ (Trans Cap) c & ni-L'* 4(J ] ~ qn@;c 3P ni -L'* ;!
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(Trans Cap) 4 P > (~p) A:P P Q = (~p)(P P ) fn(A) ~p = : = A ~p 4&Om-)l4 h, n ~p ]`3&@;{L
(1). q n fn(A:P ) B (n)P > (n)((~p) A:P P ) = (~p) A:P (n)P " ~ (Trans
Cap) ` (n)P A (~p)(P (n)P ) (n)Q #'* "
(2). q n fn(A:P ) B (n)P > (n)((~p) A:P P ) = (n~p) A:P P n fn()
"~ (Trans Cap) ` (n)P A (n ~p)(P P ) (n)Q #'*
(Trans In) 4 P > (~p) n P ] P P in m P P > (~r) mP ] P P in n P ~r fn(n P ] ) = ~r ~p = Q = (~p~r)(n mP ] P ] P ) : = Lh, n ~p ~r ]`3 @;{L (1). q n fn(n P ] ) B (n)P > (~p) n P ] (n)P 3 @;{L (a) q n fn(mP ] ) B (n)P > (~r) mP ] (n)P (Trans In) ` (n)P (~p~r)(n mP ] P ] (n)P ) (n)Q -s N~ $ n 4.8 #'* "
(b) q n fn(mP ] ) n = m : n fn(P ) B (n)P > (~r) m(n)P ] P }
#i (n)P in n P (n)P (Trans In) ` (n)P (~p~r)(n mP ]
P ] P ) (n)Q - s N~ $ n 4.8 #'* "
(c) : B (n)P > (n ~r) mP ] P n'" ~ (Trans In) n` (n)P (~p n~r)
(n mP ] P ] P ) (n)Q #'* "
(2). q n fn(n P ] n = n : n fn(P ) B (n)P > (~p) n (n)P ] P _@;
(1).(b) ni (n)P (n)Q #'* (3). : B (n)P > (n~p) n P ] P _@; (1).(c) ni (n)P (n)Q #'* (Trans Out)(Trans Open) r~_ (Trans In) c &` i#'* 4(J
(Trans Amb) r~_ (Trans Cap) c &` i#'* 4(J ] ~ qn@;c 3P ni -L'* 0
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Cap) n` P A (~r)(P P ) 7 P = (~r)(P P ) ` i P Q #'* (Trans In) 4 Q > (~r ) nQ ] Q Q in m Q Q > (~r ) mQ ] Q Q in n Q ~r fn(nQ ] ) = ~r
~r = = : Q = (~r ~r )(nmQ ] Q ] Q ) n 4.14 i >7 P P $` P > (~r ) nP ] P P Q : P Q e X }#i >
7 P $` P in m P : P Q ni>7 P P ( P $` P > (~r ) mP ] P P Q P Q P in n P : P Q n 4.3 i fn(nP ] ) = fn(nQ ] ) l 4
~r fn(nP ] ) = 7 P = (~r ~r )(nmP ] P ] P ) ` i P Q (Trans In)
i P P #'*
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i>7 P P $` P > (~r) nP ] P P Q : P Q 5}#i>7 P
$` P P : P Q 7 P = (~r)(nP ] P ) ` i P Q % (Trans Amb)
n` P P l4#'*
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(Red Res) 4 P = (n)P P = (n)P : P
P }#i P P n >
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P }#i P P n >7
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P }#i P P n >7
Q $` P Q : Q P " ~n 4.7 n` P P Q P % Q P P P q] P P P P #'*
(Red Struct) 4 P P P
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X$ Y d { d 7 wDZ j~ l 4 >dN3P cT3 H(P ) nc wD - +
C
;!
;!
r 5.14 1w H(P ) > (~p) P P '#_Qw]Q
(1). H > (~p) nH ] P - P = nH (P)] "
(2). H > (~p) P H - P = H (P) "
(3). P > (~p) P P H
R P P R - ~p fn(R) = h
0
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* H(P) > (~p) P P c-Y? ! }
(Harden Action) 4 H(P ) = A : Q A Action : (~p) P P = () A : Q 0 Q
~ `> c{ d ni H(P ) = A : Q zn H = P = A : Q `$ 3 P = A : Q >
() A : Q 0 7 R = 0 ot@;'* (Harden Amb) 4 H(P ) = nQ] : (~p) P P = () nQ] 0 H(P) = nQ] zn) `
/@;
H = : P = nQ] 4 P > (~p) P P J R = 0 n ot@;'* H = nH ] : Q = H P ] 4 H > () nH ] 0 : P = nQ] = nH (P)] J P = 0
n o T @;'* (Harden Par 1) 4 H(P ) = Q Q Q > (~p) P P P = P Q : ~p fn(Q ) = Q~`>c{d ni H(P ) = Q Q zn)` /@;
H = : P = Q Q 4 P > (~p) P P J R = 0 n ot@;'* H = H Q : Q = H (P ) 4 H (P) > (~p) P P }#i L ` /
@;jT'* h
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49
{ H > (~p) nH ] P : P = nH (P)] 4 ~p fn(Q ) = ni H >
(~p) nH ] (P Q ) n H > (~p) nH ] P J H = H n -Lco T
@;'*
{ H > (~p) P H : P = H (P) 4 ~p fn(Q ) = ni H > (~p) P (H
Q ) : P = P Q = H (P) Q J H = H Q n -Lco " @;'* { P > (~p) P P H =
R P = P R : ~p fn(R ) = 4
H =H Q =
R Q P = P Q = P R Q : ~p fn(R Q ) = J R = R R n-Lcot@;'* H = Q H : Q = H (P) 4 ~p fn(Q ) = ni ~p fn(H ) = $
~ (Harden Par 1) n` H > (~p) P (P H ) : P = P Q = P H (P) 7
H = P H n -Lco " @;'* (Harden Par 2) r~_ (Harden Par 2) c3P nd 4(J
(Harden Res) 4 H(P ) = (m)Q Q > (~q) Q Q : (~p) P P = (m)(~q) Q Q > d H(P ) = (m)Q ni m fn(H(P )) % fn(P ) fn(H(P)) l 4 m fn(P) E _gD H(P) = (m)Q c> f Vk H = BJ R = 0 niot@;'* ":
B H = (m)H : Q = H (P) èeX C = (m)(~q) Q Q 7h@;`cJt
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m 62 fn(Q ) 4 C = (~
q) hQ i (m)Q = (~p) hP i P l 4 p~ = ~q P = Q :
P = (m)Q 4 H (P ) = Q > (~p) hP i Q }#ni L ]` @;j T
'*
{ H > (~p) hnH ]i Q : nH (P)] = P 4 m 62 fn(Q ) = fn(P ) =
fn(nH (P )] ) l 4 H = (m)H > (m)(~p) hnH ]i Q = (~p) hnH ]i (m)Q =
(~p) hnH ]i P 5 e X P = nH (P )] 7 H = H ni-Lco T @;'* { H > (~p) hP i H : Q = H (P ) 4 H > (m)(~p) hP i H = (~p) hP i (m)H
: P = (m)Q = (m)H (P) 7 H = (m)H n-Lco"@;'* { P > (~p) hP i P H ; j R Q = P j R : f~pg \ fn(R ) = e X
m 62 fn(P ) f~pg ]k P > (~p) hP i P ni m 62 fn(P ) l 4 P = (m)Q (m)(P j R ) P j (m)R 2 H = (m)H (m)( ; j R ) ; j (m)R :
f~
pg \ fn((m)R ) = l 4J R = (m)R ni -Lcot@;'* Q = m Q ] m 2 fn(Q ) m 6= m : m 62 fn(Q ) 4 C = (~
q) hm (m)Q ]i Q =
(~p) hP i P l4 ~p = ~q P = m (m)Q ] : P = Q 4 H (P) = Q >
(~q) hQ i Q = (~p) hm Q ]i P }#ni L ]` @;j T '* { H > (~p) hnH ]i P : nH (P)] = m Q ] 4 n = m : Q = H (P ) m 2 fn(Q ) m 62 fn(P) ni m 2 fn(H ) 3 a $ m 62 fn(Q ) = fn(P )
( m 6= m = n l 4 H = (m)H > (m)(~p) hnH ]i P = (~p) hn(m)H ]i P :
P = m (m)Q ] = n(m)H (P)] 7 H = (m)H ni-Lco T @;'* { H > (~p) hm Q ]i H : P = H (P) m 62 fn(Q ) = fn(P ) = fn(H (P))
ni m 62 fn(H ) l 4 H > (m)(~p) hm Q ]i H = (~p) hm (m)Q ]i H =
(~p) hP i H 5 e X P = H (P ) 7 H = H n -Lco " @;'* 1
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Nh ('W@
50
R P = P R : ~p fn(R ) = e X
m fn(Q ) m = m ( m ~p ni m fn((~p) m Q ] P ) = fn(P ) U \
i m fn(P ) TAz4L@; h n !u@;n m fn(Q ) : (a) m fn(Q ), (b) Q h3RtaT (c) Q 3Rt
: Q cm+4 m 4 C = (~q m) Q Q = (~p) P P l4 ~p = ~q m P = Q
: P = Q 4 H (P) = Q > (~q) P P }#ni L ]` @;jT '
*
{ H > (~q) nH ] P : nH (P )] = P 4 H = (m)H > (m)(~q) nH ] P 7@; (a) '* m fn(P ) 2 m fn(P ) ( m fn(P ) = fn(nH (P)] )
ni m fn(nH ] ) " Q = nH (P)] @; (b) h'*"k @; (c) '*
B m = n l 47qn@; `# (m)(~q) nH ] P = (~q m) nH ] P =
(~p) nH ] P 5 e X P = nH (P )] 7 H = H ni-Lco T @;'* { H > (~q) P H : P = H (P) 4 (a) m fn(P ) m fn(P ) ni
m fn(H ) " (b) P h 3 T]Rt" (c) P 4Rt :m+ 4 m 5 ~ ~ m fn(P )
ni G L , @; # H > (m)(~q) P H = (~p) P H : P = H (P) 7
H = H n-Lco " @;'* { P > (~q) P P H
R P = P R : ~p fn(R ) = e X m fn(P )
( m ~q ni m fn((~q) P P ) = fn(P) U \ i m fn(P ) T Az 4 L @; h n (Harden Repl)(Harden Empty)(Harden Path) _ (Harden Action) c3P niot@
;'*4(J ] ~ qn@;c 3P ni -L'* { P > (~p) m Q ] P H
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7n 5.14 cc$~è3P H(P ) R c`n@; ?Q~`>c=&(!*>d$ ~ ) H P R Z+U =&(cv
T 7 MA r 9 h c =& (6 [ kB m 9 "c 2 7 ROAM =& (E ~ $ ]` c 11 ;!
5.15 H P R
(Inter In) H (~r)H (m
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(Inter Open) H (~r)H ( nR ] ) P open n P R open R - R (~r)H (P R )
(Inter Co-in) H (~r)H (mR ] n R ] ) P in m P R in n R - R (~r)H (nmR ]
P R ])
(Inter Co-out) H (~r)H (nmR ]
R ] ) P out m P R out n R - R (~r)H (mR ]
P R)
(Inter Co-open) H (~r)H (n R ] R ) P open P R open n R - R (~r)H (P R
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51
R)
2
(Inter Amb In) P > (~p) nQ] P Q in m Q H (~r)H ( mR ] ) R in n R ~p fn(mR ] ) = - R (~r)H ((~p)(mnQ ] R ] P ))
(Inter Amb Co-in) P > (~p) nQ] P Q in m Q H (~r)H ( mR ] ) R in n R ~p fn(mR ] ) = - R (~r)H ((~p)(nmR ] Q ] P ))
(Inter Amb Out 1) P > (~p) nQ] P Q out m Q H (~r)H (m R ] ) R out n R ~p fn(mR ] ) = - R (~r)H ((~p)(nQ ] mP R ] ))
(Inter Amb Out 2) P > (~p) nQ] P Q out m Q P out n P H (~r)H (m R ] ) ~p fn(mR ] ) = - R (~r)H ((~p)(nQ ] mP R ] ))
(Inter Amb Co-open) P > (~p) nQ] P Q open Q H (~r)H ( R ) R open n R ~p fn(R ) = - R (~r)H ((~p)(Q P R ))
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B *c N a K 3dja a Q~ `> H ( a a ? P c =& (z~K H P R {
d b c 11 { 5.20 ` e> db dj +N~ $c T n r 5.16 1w H(P ) > (~p) nP ] P '#_Qw]Q (1). H > (~p) nH ] P - P = H (P ) "
(2). H > (~p) nP ] H - P = H (P ) "
(3). P > (~p) nP ] P H
R P P R - ~p fn(R) = h
0
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r 5.17 1w H(P )
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(2). H
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* (Trans Cap) "~n 5.14 h~dj4(J r 5.18 1w P Q A R s_Qw]Q
(1). P A P - R P Q "
(2). Q A Q - R P Q j
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* (Trans Cap) c{dh~dj 4(J
` e> de X X$ Y d c{ d( ~K p]n c-Ldj? ( Q~ `> = cn
%n 5.19 5 e X X$ Y d( & d ch %b 9+cQ~ `> h{ &
{ 5.20 r 5.19 1w H(P ) R '#_Qw]Q
(1). P
P - R H(P ) "
(2). H H - R H (P) "
;!
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(3). H P R 0
0
Nh ('W@
52
* H(P) R c-Y?!} (Trans In) 4 H(P) > (~q) nQ ] Q Q in m Q Q > (~r) mQ ] Q Q in n Q ~r fn(nQ ] ) = ~r
~p = : R = (~q~r)(nmQ ] Q ] Q ) e X H(P) >
(~q) nQ ] Q n 5.16 i L ]` @;j T '* H (~q)(nH ] Q ) : Q = H (P) 4 H (P ) in m Q e X n 5.17 ni L
]`@;j T'* { H (~s)(in m : R H ) Q (~s)(R H (P)) : ~s ( m fn(P )) =
4 ~s 4&Om h-h, ~s ( n~r q~ fn(Q )) = 7 H =
(~q~r~s)(nmQ ] R H ] Q ) Q > (~r) mQ ] Q : Q in n Q i H = (~q)(n(~s)(in m : R H )] Q )
H : R H (P) -Lco " @;
'*
{H
R P in m P : Q P R \ i Q > (~r) mQ ] Q " ~n 4.4 ni Q (~r)(mQ ] Q ) 5 ~r fn(nQ ] ) = H = (~q)(n
R ] Q ) (~q~r)(n R ] mQ ] Q ) 6 'E _ P in m P Q in n Q :
R (~q~r)(nmQ ] P R ] Q ) (Inter Co-in) i H P R ot@;
'*
H (~q)(nQ ] H ) : Q = H (P) 4 H (P ) > (~r) nQ ] Q e X n 5.16
niL]`@;jT '* { H (~r)(mH ] Q ) : Q = H (P ) 4 H (P) in n Q e X n 5.17 n
iL]`@;jT'*
(1). H (~s)(in n : R H ) Q (~s)(R H (P )) : ~s ( n fn(P)) = 4 ~s 4&Omh-h, ~s ( m ~q~r fn(Q ) fn(Q )) = 7 H = (~q ~r~s)(nmR H ] Q ] Q ) Q in m Q i H = (~q)(nQ ]
(~r)(m(~s)(in n : R H )] Q ))
H : R H (P) -Lco " @;
'*
(2). H
R P in n P : Q P R 4 H = (~q)(nQ ] (~r)(m
R ] Q )) (~q ~r)(nQ ] m R ] Q ) 6 'E _ P in n P Q in m Q
: R (~q~r)(nmP R ] Q ] Q ) (Inter In) i H P R ot
@;'*
{ H (~r)(mQ ] H ) : Q = H (P ) 47 H = (~q~r)(nmQ ] Q ] H ) H : R H (P) Q in m Q in n Q i H = (~q)(nQ ] (~r)(mQ ] H ))
-Lco"@;'*
{ P > (~r) mQ ] P H
R Q P R : ~r fn(R ) = 4 }
q E _ P > (~r) mQ ] P Q in n Q H (~q)(nQ ]
R) in m
Q ~r fn(nQ ] ) = (h, # ~r 4 &Om) : R (~q ~r)(nmQ ]
Q
Q ] P R ) (Inter Amb In) i H P R ot@;'* P > (~q) nQ ] P H
R Q P R : ~q fn(R ) = 4> d " ~
n 4.4 i P (~q)(nQ ] P ) !7 P R Q : Q > (~r) mQ ] Q " ~n 4.14 ni >7 Q Q R4 Q Q Q Q : P R > (~r) mQ ] Q w
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)-EPM('&B@
53
DZ c{d` i P j R > (~r) hmQ ]i Q L. $ ~]` Bj T `$ (Harden Par 1) 4 P > (~r) hmQ ]i Q Q = Q j R : f~rg \ fn(R ) = 4
0 -\ i "~ (Trans In) n` P ;! (~q~r)(nmQ ] j Q ] j Q ) 7~(
Jn4 P ni H(P ) = (~q ~r)(nmQ ] j Q ] j Q ) j R R oT@;'*
(Harden Par 2) 4 R > (~r) hmQ ]i Q Q = P j Q : f~rg \ fn(P ) = 4
f~qg \ fn(R ) ni f~rg \ fn(mQ ] ) = 0-\i P > (~q) hnQ ]i P Q in;!m Q H (~r)(Q j ; j mQ ] ) Q ;in!n Q Q Q : R (~q~r)(nmQ ] j Q ] j P j Q ) (Inter Amb Co-in) i H P R ot@
;'*
open n
(Trans Open) 4 H(P) > (~q) hnQ ]i Q Q ;open
! Q Q
;! Q : R = (~
q)(Q j Q ) e X H(P ) > (~q) hnQ ]i Q n 5.16 i L ]` @;j T '* ! Q e X n 5.17 ni L
H (~
q)(nH ] j Q ) : Q = H (P) 4 H (P ) ;open
]`@;jT'* { H (~r)(open:R j H ) Q (~r)(R j H (P)) : f~rg \ fn(P) = 4 ~r 4 &Omh-h, f~rg \ fn(Q ) = 7 H = (~q)(~r)(R j H j Q ) n
Q open
;! Q i H = (~
q)(n(~r)(open : R j H )] j Q ) ;! H : R H (P) Lco"@;'*
{ H ; j R P ;open
! P : Q P j R 4 H = (~
q)(n ; j R ] j Q ) open
open n
P ;! P Q ;! Q : R (~q)(P j R j Q ) (Inter Co-open) i
H P R ot@;'* n
H (~
q)(nQ ] j H ) : Q = H (P) 4 H (P ) open
;! Q e X n 5.17 ni L
]`@;jT'* { H (~r)(open n : R j H ) Q (~r)(R j H (P)) : f~rg \ (fng fn(P)) = 4
~r 4&Omh-h, f~rg \ fn(Q ) = 7 H = (~q)(~r)(Q j R j H ) Q ;open
! Q i H = (~
q)(nQ ] j (~r)(open n : R j H )) ;! H : R H (P) -Lco"@;'* ! P : Q P j R 4 H = (~
q)(nQ ] j ; j R ) { H ; j R P ;open
open
open
P ;! P Q ;! Q : R (~q)(Q j P j R ) (Inter Open) i H P R ot@;'*
P > (~
q) hnQ ]i P H ; j R Q P j R : f~qg \ fn(R ) = 4> d "
n
~n 4.4 i P (~q)(nQ ] j P ) !7 Q open
;! Q " ~n 4.15 i>7 Q
R4
open n
P j R ;! Q : Q Q n 5.18 ni L ]` @;j T '* n
{ P open
;! P : Q P j R 4 P ;! (~
q)(Q j P ) 7 P = (~q)(Q j P ) n
i R (~q)(Q j Q ) (~q)(Q j P j R ) (~q)(Q j P ) j R H(P ) l4-L
coT@;'* n
{ R open
;! R
: Q P j R 4 }q E _ P > (~q) hnQ ]i P open
n
Q ;! Q H ; j R R open
;! R f~
qg \ fn(R ) = : R (~q)(Q j Q ) (~q)(Q j P j R ) (Inter Amb Co-open) i H P R ot@;'* (Trans Out)(Trans Amb) r~_c 3P nd 4(J 0
1
00
3
4
00
1
0
00
0
0
0
3
1
0
0
0
3
1
5
0
5
00
5
3
0
5
4
0
00
0
00
5
3
1
4
5
1
00
1
3
0
1
5
1
000
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1
1
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000
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3
3
3
3
2
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1
2
1
1
0
1
1
0
2
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1
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
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1
0
0
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2
1
2
2
1
0
1
0
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0
2
2
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2
2
0
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2
2
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00
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1
2
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1
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0
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1
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0
0
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0
1
1
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2
2
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1
0
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1
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1
1
2
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00
0
2
0
2
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0
1
1
1
1
1
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2
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2
2
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5
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Nh ('W@
54
] ~ qn@;c 3P ni -L'* "~]~-E_n] `$B LcoT]-L activity lemma 1
r 5.20 (Activity) H(P ) R Y-$Y
(Act Proc) P P - R H(P ) .t
(Act Har) H H - R H (P) .t
(Act Inter) H P R ;!
0
;!
0
;!
0
0
* 9J$<cdj T % I) ' 9<$Jcdj n 5.19 ( { 4.17 cLn]n'`$ x7{J% W Mxw W
x5.3
9{ 5.20 n]fQ~`>hc{i~Qn!B*bBLco"] -L
n Q~ `> h Z( ~ `> h Z 3 T]Z { 5.39 U L ?c~ `> h Z
B Tn ] D4 ?cQ~ `>h Z? % Q~ `> hc{ &~] 0] >dE_TZ /cpp 5.21 5.22 5.23 5.25 5.30 ( 5.35 6'Q
~ `> h Z % p 5.36 cdj j 6h ` `&h Z {~ 4T Z
{ 5.39 4> 5.21
'# P Q uP P Q (]]uP/"C(+g dPyU^\0J 1w P Q '
'
* Q~`>hc{dìu3ThZo"]-L#{ P Q BgDa
a H ( n c % 7ni H(P) H(Q) 5" ~n 5.6 n` H(P ) n
H(Q) n l4 P Q +
()
+
'
4> 5.22 1w P P '# P
* a a H ( n s = H
'
H (P ) n n H(P Q) n
0
0
+
j
+
0
()
j
Q P Q
'
j
= H(
Q) P P ni n H (P) n
H(P Q) n l 4 P Q P Q 0
0
;
j
j
+
0
j
'
0
+
+
()
*
+
0
+
m
+
'
()
0
'
0
+
()
0
P m
+
, =) - (n)P +m c - Y ? ! } ` d P +m 4(J kWW activity lemma 5B 6 }:" j f %U@'?#! m%-af}: A - 6 activity "lemma"
6%D@DV-WV ;&
1
()
j
P ni m H (P ) m
H(nP ] ) n l 4 nP ] nP ] ;
r 5.24 1w m = n '# (n)P
6
0
0
0
'
0
H (P ) m n H(nP ] ) m
0
'
4> 5.23 1w P P '# nP ] nP ] * a a H ( m s = H = H(n ] ) P
'
0
0
20]
&m
5.3
x
6k('O(5O
55
, (= - P +m c - Y ? ! } ` d (n)P +m 4(J 4> 5.25 1w P P '# (n)P (n)P * a a H ( m P P ni H(P)
0
'
0
'
H(P ) m 7 (n)P k
(n)P n 4 &Om l 4 h, n = m : n fn(H) n 5.24 n` (n)H(P) m
(n)H(P ) m n H((n)P ) n
H((n)P ) n l 4 (n)P (n)P 0
'
0
6
0
+
+
m
+
0
()
+
62
0
()
+
+
()
0
'
Q~ `> h W 2; @c %n P P = M : P M : P p 5.30 cdj +
N +*7 ` ec n 5.26 $ n 5.29 c c $j~ 0
'
)
0
'
r 5.26 P n Y-$YVq ~p A P P y P "* P > (~p) nP ] P P
A BarbedAction - (fn(A) n ) ~p = #
0
1
2
f
g \f g
h
2
1
i
1
2
1
A
;!
P 0
1
*
, =) - 4 P #n { d ni >7 ~r A R R ( R R4 A 2 BarbedAction (fn(A) fng) \ f~rg = : P (~r)(nA : R j R ] j R ) h- f~rg (fn(R ) fn(R ) fn(R )) 7 ~p = ~r : B n7 ~p = f~rg \ (fn(R ) fn(R ) fn(R )) " ~ (Harden Amb) (Harden Par 1) ( (Harden Res) ni (~r)(nA : R j R ] j R ) > (~p) hnA : R j R ]i R 5n 4.14 n`>7 Q P R4 P > (~p) hQ i P : Q nA : R j R ] P R f V Q = nP ] : P A : R j R 5 A : R j R ;A! R j R ( P A : R j R " ~
n 4.15 ni>7 P R4 P ;A! P : P R j R 0 - ~K-Lni-L'* , (= - P > (~p) hnP ]i P " ~n 4.4 ni P (~p)(nP ] j P ) P ;A! P " ~n 4.5 ni P (~q)(A : R j R ) : fn(A) \ f~qg = h, f~qg \ (fng fn(P )) = 3
P (~p ~q)(nA : R j R ] j P ) (fn(A)fng)\f~p g = ` i (fn(A)fng)\f~p ~qg = 5 A 2 BarbedAction i P #n 1
1
3
2
2
3
3
1
1
2
3
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
0
3
2
1
0
2
1
1
2
1
1
2
2
1
1
2
3
2
1
3
2
0
1
00
00
2
2
2
1
0
1
2
1
2
2
r 5.27 1w M : P A P '#_Qw]Q (1). M > A : N - P N : P "
(2). M = - P A P ;!
0
;!
0
0
* n 4.11 ( (Trans Cap) `d4(J
r 5.28 1w H(P ) n s_Qw]Q (1). d0` Q H(Q) n "
(2). P n -d0` Q n h H(Q) n "
(3). P A P A BarbedAction -d0` Q
#
#
#
#
;!
0
H(Q) n #
2
#
A
0
;!
Q -A
0
0
2
BarbedAction h
Nh ('W@
56
* n 5.26 H(P ) n a:$>7 ~p A P P ( P R4 H(P ) > (~p) nP ] P A
P
P A BarbedAction : (fn(A) n ) ~p = " ~n 5.16 ni L ]` j T
'*
(1). H > (~p) nH ] P : P = H (P) 4 H (P ) A P " ~n 5.17 ni L ]` j
T '* (a) H (~r)(A : R H ) P (~r)(R H (P)) : ~r fn(A) = ` io T @;'
*
(b) H
R P A P : P P R ` iot@;'* (2). H > (~p) nP ] H : P = H (P ) 4 ` io T @;'* (3). P > (~p) nP ] P H
R P P R : ~p fn(R) = 4 ` io " @;'
*
] ~ qn@;c 3P ni -L'* #
1
;!
0
2
1
f
0
h
0
0
i
2
j
; j
h
1
h
1
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1
0
; j
2
0
;!
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f g\
j
j
f g\
'# H(M : P ) +n n
0
0
2
r 5.29 1w P P - H(M : P )
'
i
00
j
1
0
2
0
i
1
;!
i
0
h
2
1
g \f g
0
1
0
1
0
+
* H(M : P ) n c-Y? ! } (Conv Exb) 4 H(M : P ) n n 5.28 ni]`j T '*
(1). a a Q # H(Q) n 4*r-L H(M : P ) n (2). M : P n : a a Q n H(Q) n M : P n " ~n 5.26 ni M : P >
(~r) nR ] R R A R A BarbedAction : (fn(A) n ) ~r = 5" ~
n 4.11 n` M = l 4 P P ( H( : P) n ` i H( : P ) n (3). M : P A P A BarbedAction : a a Q A Q : A BarbedAction H(Q) n " ~n 5.27 _n ] dj H(M : P ) n (Conv Red) 4 H(M : P ) R : R n { 5.20 ni]`jT '* (Act Proc) 4 M : P R : R H(R ) ì M = : P R l4 H(M : P)
H(P) q ] H(P) n " ~ P P ni H(P ) n V % H(M : P ) H(P ) l 4
+
#
0
#
#
#
0
h
00
i
0
#
000
;!
#
2
f
0
'
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2
0
;!
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#
;!
g
0
0
0
;!
+
0
\f g
+
2
+
+
0
;!
0
+
;!
0
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0
0
0
+
0
H(M : P ) n (Act Har) 4 H H : R H (M : P ) R n " ~n 5.6 ni H (M : P) n :!
- Y R n c - Y r$ ~ }#ni H (M : P ) n % H(M : P )
H (M : P ) l 4 H(M : P ) n (Act Inter) 4>7 H ~r R4 ~r fn(M : P) = : * @;'* UE_ ]
(Inter In) T @; 4 bdj !u@;cdj & _ (Inter In) 4 H (~r)H (m R ] nR ] ) M : P in n P R in m R :
R (~r)H (nmP R ] R ] ) n 5.27 ni ]` j T '* (1). M > in n : N : P
N : P 4 M : P in n N : P l 4 H(M : P ) (~r)H (nmN : P R ] R ] ) R n (n 5.6 ni (~r)H (nmN : P
R ] R ] ) n :! - Y R n c - Y r$~ }#ni
(~r)H (nmN : P R ] R ] ) n n H(M : P ) n (2). M = : P in n P 4 H(M : P) H(P) H(M : P ) H(P ) 5
P P n` H(M : P ) n 0
+
0
;!
0
0
+
0
+
0
0
0
f g\
0
0
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j
1
0
0
1
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0
j
2
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2
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2
2
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+
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5.3
x
57
] ~ qn@;c 3P ni -L'* 4> 5.30 1w P P '# M : P M : P * aa H ( m P P "~n 5.29 ni H(M : P)
0
'
0
'
0
'
4 M :P M :P n ()
+
H(M : P ) n l
0
+
0
'
` e3 Q~ `> h F . s = % cdj p 5.35 > d+N dj T s J n
]`$~ P k KZ k ]j=c P a2!r{ d k` P = 0, P k = P j P k 0
r 5.31 1w H( ! P)
n
+
4
+1
4
'#Vqv@ k 97 H(P k ) +n * Bncdju K B 3 r 5.32 1w H(0)
n
+
'# H(P) +n * H(0) n c-Y?! } (Conv Exb) 4 H(0) n n 5.28 nit@;zo T '* n a a Q `
H(Q) n 4n' H(P) n (Conv Red) 4 H(0) Q : Q n { 5.20 ( 0 G &c0niL H H
: Q H (0) " ~n 5.6 ni H (0) n :! - Y Q n c - Y r$ ~
}#ni H (P) n 5 H H ni H(P ) H (P) q] H(P) n +
#
#
+
;!
+
;!
0
0
0
+
+
+
0
;!
0
0
'
0
;!
r 5.33 1w P P - Q Q '# P P
'
0
j
0
'
+
Q Q 0
j
* E_dja a H ( n k H(P Q) n zW H(P Q ) n )Oc
& ndj-Lc6 T0
J H = H( Q) H(P Q) n n H (P) n P P i H (P ) n n H(P Q) n 5J H = H(P ) n` H(P Q ) n j
0
00
; j
0
j
0
j ;
r 5.34 1w H(P )
* 7 H = H(P
0
n
+
j ;
Q) n +
0
+
0
j
+
0
'
0
0
j
0
+
0
+
j
+
+
'# H(P j Q) +n ) B H (0) = H(P) n n 5.32 ni H (Q) n n H(P
0
0
0
+
4> 5.35 1w P P '# ! P ! P * E_dja a H ( n k H( ! P )
'
0
+
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+
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0
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+
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0
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H( ! P) n " ~n 5.31 ni>7 k R4 H(P k) n % P P " ~n 5.33 n`
P k P k l 4 H(P k ) n 5 ! P P k ! P " ~n 5.34 n` H( ! P ) n +
'
0
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+
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0-~Kpc-L niQ~ `>h3 T Z
4> 5.36
1w P P '# (P )
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' C
(P ) 0
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+
58
Nh ('W@
* 0-p 5.22 5.23 5.25 5.30 ( 5.35 c-L
] 4 4c $ h ` dj ` ec& ] p 4> 5.37 1w P P '# P P * a a ~ `> ( n P P " ~ p 5.36 ni
0
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(P) n
+
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4> 5.38
* 0
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(P)
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+
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( ' c{ d n'n` ]` 3 B Lco "] -L n ~ `> h Z( Q~ `> h Z 3 TZ context
lemma r 5.39 (Context) P P Y-$Y P P 0
* 0-p 5.38 ( 5.37 c-L
'
0
R' d Y
B L ( ~ T Lc;h cB ~3 >k 20] MA ?h %< Pc-L7 ROAM c
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6 djQ~ `> h Z iT* c~ `> h Z 3 TZ
T3B> ROAM ?h%c k 20] cl@2h> d ROAM c
; @ (u Q n . bX$ Y d c{ d J+ i* c F 4 %>k 16] $ ~ + c ( - c &< P+Y ; @c SA E fc X$ Y dB>c wDZ Y ;@c RtE
fX$Yd< PL 3>7!7;@c>7 ROAM ?(Q~`> c =
i~G*7 hnm Bm 9 "c0 ROAM EfT 11 j*96>k 20] ?h % c 6 e" ~ U
-L a - -ED Z c k 20] B> c l
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}{& zI m 9 8
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Q c ZT3U {Gc n . 9 d+
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T \R| +*w\W({e\ / r`]pq ; }WL T \R P Vq ;H "*
;H ; H(P ) : T `
0
6.2 R P Q PL (;=T) WX4QN] 1w ; P : T ; Q : T -d0
` (;=T) WX4QNH h H(P ) n
H(Q) n -& ; . P Q : T YW T K~
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+
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Current(T)
H ~J T cV. (") F uture(T )
H ~J T IT7ED6c
U:Z, U:Y
JT]"c Y;%apQ3 ) T hreads(; n) Current(Type(; n)):Y k T ype(; n) 0 : BY ad
T hreads(; P) Current(Type(; P)):Y k Type(; P ) 0 : BY ad
Mobility(; n) Current(Type(; n)):Z k Type(; n) 0 : BY ad
Mobility(; P ) Current(Type(; P)):Z k T ype(; P) 0 : BY ad
Stable(; n)
4 True, k T ype(; n) = U : U:Z = ": B 4 False ! Stable(; n) ~%+Rt n 7JK ; `3:4A{c n u40Y;:h ?
Fb4QA {c Rt 7 & '+>7: ~ |{r !q7cHRt%
A! dr V >k 16] c Z + h Y;Qh ? Fbc # o U
T
_
h
59
7h ('W:
60
r 6.3 T hreads(; P ) = 0 Y-$Y Type(; P ) = * 9J|<n'{ d n` "9<|J f cQ 3P`d _
0
3P f ni k v?c 4 _ B!zn3Jy? Rta 3 Rt c a
~hfa, z ;@ l 4` ec -L'*
0
F: 6.4
1w Threads(; P) = 0 sK)h P A P r 6.5 1w ; nP] : T s Threads(; P ) T hreads(; n) * fc )>% { `d r 6.6 1w ; A : P Q : T - Current(T ):Y = 1 s Threads(; Q) = 0 * ; A : P Q : T " ~ { 3.11 ni Type(; A : P Q) = T T 5 (Type
Par) ni T ype(; A : P ) t Type(; Q) = T l 4 Threads(; A : P) y Threads(; Q) 1 %3P f ni 1 Threads(; A : P ) l 4 L T :Y = 1 Threads(; A : P) = 1 :
0
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=$ g ~ k (~p)(P P ) VF4 (~p : T~p )(P P ) (~p) P P VF4
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Qw]Q
(1). P
P - R nA : P P ] "
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c-s
(Inter Amb Out 1) 4ì-Lco " @;'* (Inter Amb Out 2) 4N P > (~p : T~p ) mR ] R R out m R : m ~p f V
Threads((; ~p : T~p ) R ) 1 l 4 T hreads(; P ) 1 % Threads(; n) = 1 " ~
n 6.5 n 6.6 (-L 6.4 ni T hreads(; P ) = 0 l 4 L @; h n'* 1
2
j ;
0
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sFh_Qw]Q
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P - R P nA : Q Q ] "
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: nA : Q Q ] R l4 R = P R o"@;'*
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c-s
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'*
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4 . c r 6.11 (ST Out) ; . n out m : P P m out n : Q Q ] ] nP P ] mQ
Q ] 1w Threads(; n) = 1 Threads(; m) = 1 ; n out m : P P m out n : Q Q ] ] : T
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h a a (;=T ) Q~ `>H (Rtm h H(P) h
H(Q) h P
Q
H(Q) h= H(P ) h z+5d H(P) h= H(Q) h nn H(P ) h c - Y }k `
(Conv Exb) 4 H(P ) h e X n 5.28 b ct@;ni 7o T @; ` n'
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]`@;jT '* (1). P m out n : Q Q ]
R : P n out m : P R ] 45" ~n 6.9 ni
L ]` @;j T'* "
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m out n : Q Q ] ] l 4 R H(n out m : P P m out n : Q Q ] ] ) h "~}#n` H(nP P ] mQ Q ] ) h % P
P ni H(Q)
H(nP P ] mQ Q ] ) l 4 H(Q) h (b) m out n : Q Q ]
R : R P R 4 n 6.7 nizn
Q
Q : R P m out n : Q Q ] 5" ~ R h _o T @;ni
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n` H(Q) h (Act Inter) 43P` @; P cN Fni 9 * z 6 5 @;'*%\ i
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x
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] ~ qnc 3P ni -L'* r 6.12 (ST Open 1) ; . n open m : P P m open : Q Q ] ] nP P Q
Q ] 1w Threads(; n) = 1 Threads(; m) = 1 ; n open m : P P m open : Q Q ] ] : T
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n ] b 4 Ya , G ]?; n c!u & hX U ; @c &> S Z{G Rt cQ
p %9 d+ a ~c? P ( Q hXS Z & ; @ca? !k #L? Z B(c P
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2
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0* @; `?ch %L. +*7 T {c~ `> j `B *{L& ~ `> cQp{G>d { dT ~`>c&O 6.13
(1). A @ H (. P )
H A H (. P A P ) / A KSRq H (. P ) \,8Mk (2). n A @ H (. P )
di H (. P ) }\0`%9L+g% n \;T nH ](. nP ]) b
h A @ H (. A @ P ) (3). A n A H (. P )
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H (. P
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h VisibleAction ~ Z +~ `> n h c ; @ % DeepAction ~ Z +& Rt n
f cz ; @ ` ec T h % {G +Nn .~ `>1 0 h c; @ nh 1 0 v ]n
;@h- L ca,c h 7~ `> w L H(a P ) k a a L # H(a P ) n {~ `> h h L cn ; @ 6'n Qs @ rs c&O 6v
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6.14 P Ln
P (~p : T~p )(nA : Q Q ] Q ) A BarbedAction (fn(A)
n ) ~p = - n A L L
(Conv Ctx Exb) P L= P L
(Conv Ctx Red) P PP L P n
n
n
n
!aa VisibleAction c{dk`
#
f
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n open = open n
m in n = n in m
m out n = n out m
n = n open
n in m = m in n
n out m = m out n
open
]
]
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k7 P = m in n : Q] L = n in m B P m T P Lm 7&Oc'n c $~ ~`>n .c (;=T ) Q~`> h{ dk `
f
6.15 ; L . P
f
H(P ) +Ln ()
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(1). d0` Q H(Q) Ln "
(2). P Ln -d0` Q Ln h H(Q) Ln "
(3). P A P A BarbedAction n A L -d0` Q
- n A L h H(Q) Ln #
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` e b & n {~ `> 1 0 h; @cQ p h % {G {G (ST In) v & ] Q
p Rt c Y m & ; @7;:~`> h hS Z LY m ; @c s = &. 6 ?3h
cn?!un3ctf hXv}LYm; @cW" &{G (ST Open 2) b+
Fby@_c- r 6.17 (ST In) ; n in m m in n . n in m : P P ] m in n : Q Q ] nP P
mQ Q ] ] 1w Threads(; n) = 1 T hreads(; m) = 1 - ; n in m : P P ] m in n : Q
f
1
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mQ Q ] ] B"p h a a (;=T ) Q~ `>H (Rt m h k L H zW
H(P ) Lh
H(Q) Lh P
Q H(Q) Lh = H(P ) Lh z + 5d H(P) Lh = H(Q) Lh
nn
H(P ) Lh c - Y }k `
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a m cQ~ `>#L. i S L h- cvc l 4 L @; h n hot@; N F
P A P ih n h
(Conv Ctx Red) 4 H(P ) R : R Lh { 5.20 ni L ]` @;j T'* (Act Proc) 4 P
P : R H(P ) h Threads(; n in m : P P ] ) = 0 (
Threads(; m) = 1 " ~n 6.9 ni L ]` @;j T '* (1). n in m : P P ] R 45" ~n 6.7 nizn ]`T @;'* "
f
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65
(a) P
P : R n in m : P P ] 4 P n in m : P P ] m in n : Q
Q ] q ] H(P ) R Lh " ~ }#n` H(nP P mQ Q ] ] ) Lh % P
P ni H(Q)
H(nP P mQ Q ] ] ) l 4 H(Q) Lh 6'&@; hn'*
(2). m in n : Q Q ] R 4_o T @;" ~n 6.7 ni H(Q) Lh (3). n P
Q : R H(Q) h (4). 4@; h=- A = in n c h n'* (Act Har) 4 H H : R H (P) Lh }#i H (Q) Lh H(Q) H (Q)
n` H(Q) Lh (Act Inter) 4 3P`@; P c NFni 9 * z6 5 @;'* %\ i
T hreads(; n) = 1 9 d+U 5 @;z (Inter Amb In) ( (Inter Amb Co-in)
n'*T?Tl3Pn ]hU&@; H cNF`hR4b{ L H c
Lhn'* ] ~ qnc 3P ni -L'* 2
0
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; @ca & ~K n .7 u Y m ; @c& ]Rt# Ya ,9< c@; `q 3 L. c k
U& ]Rt T] cm+ h4' 5 J Kqi a T& ]Rt# (76 'T]Rt ; % 7U
] 6 ' c Rt v9 d7 Y;y @ . Y!uc RtXS Z Y m y @cW"? !B~
K~`>n .Tn] J *` ec - L2-+Up @; F: 6.18 (ST Aux In)
r`G: Threads(; n) = T hreads(; m) = 1 Q$\]Yu
PQ
(1). ; . (n : Tn )(n in m : P P ] m in n : Q Q ] ) (n : Tn )(nP P mQ Q ] ] )
(2). ; . (m : Tm )(n in m : P P ] m in n : Q Q ] ) (m : Tm )(nP P mQ Q ] ] )
(3). ; . hn in m : P P ] m in n : Q Q ] A : R] hnP P mQ Q ] ] A : R] u
A _L&p out . open a&
1
j
j
1
1
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2
2
2
j
1
j
j
1
1
r 6.19 (ST Open 2) ;
Q 1w Threads(; n) = 1 - ;
j
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2
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2
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n n open . open n : P n open : Q Q ]
open n : P n open : Q Q ] : T fopen
2
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1
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1
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2
* 7 L = open n n open P = open n : P n open : Q Q ] Q = P Q Q B"p
h a a (;=T ) Q~ `>H (Rt m h k L H zW H(P) Lh
H(Q) Lh P Q H(Q) Lh = H(P) Lh z+5d H(P ) Lh= H(Q) Lh nn
H(P ) Lh c - Y }k `
(Conv Ctx Exb) 4 H(P) Lh e Xn 6.16 ct@;ni zo T @;n'* n H(Q) Lh o " @; 3P P c s =ni h zn3 n T4 $ n c
Q~ `>L. i S L h- c open n l 4 L @; h n hot@; N F P A P
: h A L P 3Tcz ;@ 4 open n QhR4N F
(Conv Ctx Red) 4 H(P) R : R Lh { 5.20 ni L ]` @;jT '* f
]
g
1
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(Act Proc) 4 P P : R H(P ) h 3P P c s = Threads(; n) = 1 ni
L ]` &@;j T '* (1). Q
Q : P open n : P n open : Q Q ] 4 H(P ) R Lh " ~ }
#n` H(P Q Q ) Lh % Q
Q ni H(Q)
H(P Q Q ) l
4 H(Q) Lh (2). P Q 4 R H(Q) h (Act Har) 4 H H : R H (P) Lh }#i H (Q) Lh H(Q) H (Q)
n` H(Q) Lh (Act Inter) 4 Threads(; n) = 1 3P` @; P c N Fni 9 * z
(Inter Open) ( (Inter Amb Co-open) n'*T? Tl3Pn ]hU&
@; H cNF`hR4b { L H cLhn'* ] ~ qnc 3P ni -L'* 0
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6v
L (ST Open 2) k J * ~ `> _ - L 6:18 c-L F: 6.20 (ST Aux Open)
r`G: Threads(; n) = 1 Q$\]YuPQ (1). ; . (n : Tn )(open n : P n open : Q Q ] ) (n : Tn )(P Q Q )
(2). ; . h open n : P n open : Q Q ] A : R] hP Q Q A : R] u A _(&
p out a&.(]p open n a& u n = n 1
1
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a ? kU {Gc P Q h S Z ; @c &a? !k h 1 0 U a ?c>
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2
2
r 6.21 _QR]Y`=Q (UT Res In 1)
(n)(n in m : P] m in n : Q] ) (n)nP mQ] ]
(UT Res In 2)
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0
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(esc Red Output)
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(esc Red Input)
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x=M
(esc Red Comm)
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0
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0
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0
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000
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s c ^ (esc Red Comm) ~ ) ' ^;Em ( E?c 99 $Èm?c
X 8 n3?T] cK Z + T ) O c f ( T ) s =q&O U L7 esc f ( ^ s =
" E fc T 7 9; @ B34& ]l (>d " >7 ^~EmaE c?P$a
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3t Ef_c- Y B 6.Zg
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in m=n
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in
Q
n
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P in
P Q in
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i
(esc Pres Repl) !PP i nn
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i
P in
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:P i n
i
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in
(esc Pres Var) (x :PM)P
(esc Pres Channel) n S: S]i m m
i
in
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i
+
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6
+
j
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+
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j
+
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0
0
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+
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P in
(x) : P i n
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m+&Os=;|*z hT]L&Omsc f( ^s= { P : OK c-YBk`
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P : OK P n
(n)P : OK
6+2
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`
0 : OK
P : OK
Q : OK
P Q : OK
P : OK n Name P
! P : OK
P : OK n Name P
M M : P : OK
P : OK n Name P
M(x) : P : OK
S : OK
n : S] : OK
P : OK
(x : M)P : OK
`
`
(esc OK Repl)
`
j
8
2
6+1
n
2
6+1
n
6+1
n
2
6+1
n
2
6+1
n
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`
8
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(esc OK Input)
`
0
h
8
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2
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`
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`
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(esc OK Eps)
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(esc OK Abs)
`
: OK
S : OK
S : OK
S S : OK
P : OK n Name P
M : P : OK
P : OK n Name P
(x) : P : OK
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(esc OK Out Abs)
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0
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0
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(esc Valid)
P : V alid
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8
2
6+2
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esc Q
;!
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`
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cl((n)P) = (n)(n : ] cl(P )) k P
4
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(n)cl(P)
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4
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nk : ] cl(P)
j
nk = (fn(P) fn() pr(P )) g
n
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Q cl (P ) P P : V alid - fv(P ) = '#Vq esc R P
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f
g ;!
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0
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0
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esc
v:xX]
B * b + esc E f h4 ROAM c T &%a " ~\ c ROAM ?h % {G b h&%y @ T } % cdj -g
7èchJm+ enter c r r r w w Name Var >dE_{d k`c
T ) server a : P = ! enter in a : open : P]
request n
= in n : in enter : open enter
request x
= in x : in enter : out x : open enter
fwd M
= server r : request M server w : request M
allowIO
= ! in r ! out r ! in w ! out w
x7.3.1
1
2
1
62
1
4
4
4
4
4
j
j
j
j
'}f 8f request ;%[ w T5 = _o b= _ V * %/ 9Yjs+%W2 ( kW j1A$%U (S
- fwd f}f%<&bb@f2jk ;pH&Z D%M/9&;W ]MJ -%NP5 A8iF%gbj :_ &
1
Ah YJ=^
84
U )N~ )' client/server r(cBF;h("W - k xserver agent : P ] agentrequest x Q]
j
j
;!
+
xserver agent : P] agentP Q]
j
(7.1)
j
7( esc c/?()?3]!h4 rrequest M ] ( wrequest M ] ! M 4EmEy@q7cxX^f(T)s= (x : M ) !h-4 xfwd M
allowIO] Bk/? a) ?cx X^ 4T ) x B` ec &n$x X ^ T
4f + T ) x ct M j j 0
xfwd M allowIO] rrequest x
xfwd M allowIO] wrequest x
j
]
]
j
j
j
j j ;!
+
+
;!
0
xfwd M allowIO] rrequest M
xfwd M allowIO] wrequest M
j
j
j
j
j
] (7.2)
] (7.3)
j j f ( ^ s = n : S] E _! h4T] m 4 n c ?KRt!;h 34| {c ?K
n3 server r : Pr j server w : Pw j allowIO ( :>ct ?n3 S c h - U L V '
n c /) ?BF ^ n c ?K nserver r : Pr server w : Pw allowIO
j
+
;!
j
nserver r : Pr server w : Pw allowIO
j
j
nserver r : Pr server w : Pw allowIO
j
+
;!
j
nserver r : Pr server w : Pw allowIO
j
j
] rrequest n
j j
rPr
j j
]]
(7.4)
j ] wrequest n
j j
j j
]
j wPw
]
j ]]
(7.5)
j 3a7 request c{dVu Q4T)6,2 ?K* Rt c;@ %uQ 4 ^m
Bh6,2 ;@ 7 ` ec h KQ f ( ^c Pr ( Pw { 4 X Rt rPr ] ( wPw ] ? !
= r7 / ? () ?7 ^;c 9a 7 = c > &-rsc h K
QULT)'+~ ROAM r7 esc Efy@dcxc ` e E _" ~] ~ )b a , esc ? P 7 b {cvN O ` cY h&%
P c P S n ( j hh
ii
hh
ii
0
hh
!P
=
4
ii
h
4
i
M(x) : P
ii
ii
= (n : ! ) P
ii
0
hh
ii
_
ii
hh
ii
= wrequest M c out r : open : P ]
4
j
j
hh
ii
Q
ii j hh
! P
4
M M :P
hh
P
hh
=
ii
(n)P
hh
hh
4
P Q
j
ii
= 0
hh ii
hh
hh
j hh
ii
w in r : open : (fwd M allowIO)] ]
1
0
1
j
= rrequest M (x : ! )(c out r : open : P ] r in w : in x : open]
4
j
j
_
hh
ii j
1
x in r : out r : open r : open w r out x : open] ] )]
1
2
1
1
j
2
1
7.3
x
esc YJ=^
85
j
n : S]
hh
c
open
open
j
c
j
open
r
= nallowIO server w : in r : open
4
ii
j
j
j
server r : in w : out n : out c : open w : out c : open r : open S n ]
j hh
2
(open c
j
c
open
j
open
ii
r)k
(U k 4 S / ?c ] Q)
hh
(x : M)P
ii
n
S S n
M :P n
hh ii
hh
0
j
hhh
ii
i
ii
= (x : ! )(xfwd M allowIO] P )
4
(x) : P n
4
=
S n S n
= w in r : open c out r : open : P ]
4
hh
1
1
ii
hh
ii
w in r : open : (fwd M allowIO)] ]
1
0
1
j
4
2
=
]]
(x : ! )(c out r : open : P ] r in w : in x : open]
hh
_
ii j
1
1
x in r : out r : open r : open w r out x : open] ] )]
1
4
ii
M =x
0
j hh
j
j
hh
ii
4
j
P
ii
= r in w : out n : out c : open w : out c : open r : open
ii
hh
j hh
= 0
j
hh
j
_
hh
P
ii j hh
Mk =xk
2
1
j
1
ii
= x fwd M allowIO]
4
ii
2
1
1
j
j j
xk fwd Mk allowIO]
j
oh\I
~K h&% >k 18] c h&% c9I h3 Y;?cQ p %#+ ^Rt(
T ) Rt ! 0Y;%!c? 4*p '!u Rtk ? # YQ p ~ %UT$`
h - aS % cdjn ]) O" ~. > c?h{G ) ' 4 +" ~c Q p ch % {G E _ b h c T] Q p &%7 x7.3.2
;SY S = enter : y y ] ] r : y 4
1
w :y 1
_
1
0
_
0
1
_
0
] r : y 1
1
] w : y ! ] c : y ]
1
1
1
_
_
_
0
] r : y ]
2
1
_
0
0
7 Env()
Env(P )
Env( P )
=
=
=
4
4
4
x : ! x dom()
M : ! M fn(P) fv(P)
Env() Env(P)
f
_
f
j
_
2
j
g
2
g
4ècp9d+ h - c 7 ;SY S qbcQp&%` 3-c 4> 7.5
d0` esc R P y??FO 1w P : V alid cl (P) P - fv(P)
dom() s Env( P ) ;SY S
`
P :
` hh
ii
!
_
86
Ah YJ=^
* P cs'?!} eX P c{d"~ B T% I` d
hh
x7.3.3
ii
Zg^:] XvyH l
h aS % cdj& ,d> dh - n ] r7"?cq & ; @n
: P ;!esc Q =) hh P ii ;! R : R ( hh Qii h "!7 h - ca , & ; @ L.
s v"?c & ; @n hh P ii ;! R =) : P ;! Q : R ( hh Qii h 7U , R ( hh Qii h -ch %+N +*7vh % {c c $~ c cQ~ `>
h%jV3T ~ c&%T3 esc ?chkr~ Uh %{@4c$ BNFhc-qc)m( )T )6 dom() cT)#L. &O&:B"
esc ?c-%( T)cO tcaS %TG`$9 dk#h- P
>7Rt n ~KZT] esc cf(^ esc ?c-%h -B6h n>
7&]m4 n cRtT3V (? P /$aac~`> ~ `> Tn>76T]m n
c RtU L " ^c 3T% T ? ) I &n> a{h $c- ?ch%G `
$h
~K BT 0] & 379+c h - 'n~ ~q) ^m ( ) T )c&
O s = 9 d ' 5 hX >7j mcRtTU LT h - L+!6 -%7djT
hR $ ~ } + c ~K" l7 `>h - aS % cdj { d + T] ?~Bch %
Z?7 hJ K ` ch %>dE _{ dT ? u_ L. 3v ]h - c6' n3
7.6 :]>Zg ROAM R P PL]pfb~>@R 1wVqX4
QN H ??FO y esc R R "* R
H(P) -L PTC P hh
ii ;!
`
hJ K&? P &I J K ;SY S $! 6, P K Z ^c) Rt m B74
&IcJ K` P Y-c4 4{d Y P q>c&I J Kk`
Env (P ) = fn : _ ! j n 2 fn(P )nfenter r r r w w cgg
4
1
2
1
r 7.7 1w PTC P '# Env (P) ;SY S P : T `
`
* PTC P c{dni>7 H ( R R4 R
H(P) J ; = Env( R) !
p 7.5 ni ; ;SY S R : 5 R
H(P) " ~ { 3.9 n` ; ;SY S
!
H(P ) : l 4 L ; ;SY S P : T f V Env (P) ; : fn(P) dom(Env (P) ;SY S ) l 4$ ~ ; ;SY S P : T ) O r c- Y l ( n n`$ Env (P) ;SY S P : T `
hh
` hh
_
ii
_
hh
ii ;!
`
ii ;!
`
`
`
c hJ K&?c{ dE _ n {h % $ ~ c~ `>{ d ?7 hJ
K`ch% k`
7.8 ROAM Rq fb~>Q\] PTC . P Q
H y;T% n 1w PTC H(P) '# H(P) n
H(Q) n '
`
+
()
+
~Kh%f V6,7.> { dcYn{ch Z ()
PTC P J-d0`
`
7.3
x
esc YJ=^
4> 7.9 1w PTC P - Env(P ) ;SY S . P Q : T '# PTC . P Q * a a H (Rt m n R4 PTC H(P ) n 7.7 ni Env (H(P)) ;SY S
`
'
87
'
`
`
H(P ) : T % Env (P ) Env (H(P)) ni H 4 (Env (P ) ;SY S =T) Q~ `>" ~
Env(P ) ;SY S . P Q : T ni H(P) n
H(Q) n l 4 PTC . P Q 0
'
+
()
+
'
~KpXjo)Lch% {GL6 ~ hJK`ch %
x7.3.4
\Iv)1l* &R F )( 0 /{ d k ` )
wHead
wTail(M P)
rHead
rTail(x P )
=
=
=
=
r : open
c out r : open : P ] w in r : open : (fwd M allowIO)]
in w : out n : out c : open w : out c : open r : open
(x : ! )(c out r : open : P ] r in w : in x : open]
x in r : out r : open r : open w r out x : open] ] )]
allowIO server w : wHead server r : rHead
4
in
4
hh
4
1
j
1
2
4
hh
_
j
Channel
ii j
=
4
1
2
ii j
1
1
1
j
1
j
2
j
` e n ch % - Z j+ h - 7 & hX > a' c- 7U h % - cdjq[k ? 4h- &? PTC ` P UTs0h`h&%`7
djn'@ 4\ i $~
r 7.10
(Enter Input)
(1). PTC . nChannel
nChannel
(2). PTC . nChannel
nChannel
(Enter Output)
(1). PTC . nChannel
nChannel
(2). PTC . nChannel
nChannel
'
'
'
'
j
j
j
j
j
j
j
j
r in enter : open enter rTail(x P )] ]
r open enter enter open : rHead] rTail(x P )] ]
r open enter enter open : rHead] rTail(x P )] ]
rrHead rTail(x P )] ]
j
j
j
j
j
j
w in enter : open enter wTail(M P)] ]
w open enter enter open : wHead] wTail(M P)] ]
w open enter enter open : wHead] wTail(M P)] ]
wwHead wTail(M P)] ]
j
j
j
j
j
j
* ] (Enter Input) 4 (Enter Output) nd
>dg- (2) 7 P = nChannel r open enter enter open : rHead] rTail(x P )] ] PTC P i (ST Open 1) q + cq 6 Env(P ) ;SY S P : T r enter
enter
4 Q p `nR4 : rTail(x P ) =
l 4n'$ ~ (ST Open 1) n` - (1) N 3%+h % {G (Rec In) c6 ~%7 P = nChannel
r in enter : open enter rTail(x P )] ] PTC P iqc 6 Env(P) ;SY S
j
j
`
j
`
open]
6
)
j
j
`
`
Ah YJ=^
88
P : T n 40Y;( r 4 Q p `nR4 h 7 &3 9 d a ab {R4 PTC H(P) c
H ` hX 7 n > S Z enter ?m r c 5' c enter in r ? 7 hJ K `g n n h cz& Rte Xh&% cY Bni a,f (
^ n s c Rt z&( F . s = ` c enter Rt(s EmE y @c Rt r ( w a : r ( w 7 n z3 X enter ?m ( X w ?m r c Y;y @ hX? Fb QhX 7 / c enter Rt] ~ 3P ni a ,f ( ^c F . s = enter in r : open : rHead] 7a
,hJ K&?Y{s'~ %l 4n s~ {G (Rec In) `$-L `
]
r 7.11
(Subst Input)
(1). PTC . xfwd M allowIO r in enter : out x : open enter rTail(y P)] ]
xfwd M allowIO
r out x : open enter enter open : request M] rTail(y P)] ]
(2). PTC . xfwd M allowIO
r out x : open enter enter open : request M] rTail(y P)] ]
xfwd M allowIO] r open enter enter open : request M] rTail(y P)]
(3). PTC . r open enter enter open : request M] rTail(y P)]
wrequest M rTail(y P )]
(Subst Output)
(1). PTC . xfwd M allowIO w in enter : out x : open enter wTail(M P)] ]
xfwd M allowIO
w out x : open enter enter open : request M] wTail(M P )] ]
(2). PTC . xfwd M allowIO
w out x : open enter enter open : request M] wTail(M P )] ]
xfwd M allowIO] w open enter enter open : request M] wTail(M P)]
(3). PTC . w open enter enter open : request M] wTail(M P)]
wrequest M wTail(M P)]
j
'
j
j
j
j
j
j
j
j
j
j
'
j
j
j
j
j
'
j
j
j
'
j
0
j
j
j
j
j
j
j
0
j
j
'
j
j
j
j
j
'
0
0
0
j
0
j
* ] (Subst Input) 4-L (1) (3) cdj_ n 7.10 -L (2) n]$
~ (Rec Co-out) L {Gc s~ N ~s3 ; @ x out r 7a ,hJ K&?{s'~ %
c9d3PRt x ;ns!c;@ni x )6nfcz; @z& in ( out Y open ; @c>7 q ] x 7 & Qh n n ma , cz; @ Qnh n
hc out r : P SZ" ! out r c&l4~Kc{s' n ]?9 d
]
r 7.12
(Communicate)
(1). PTC . nChannel S r out n : out c : open w : out c : open r : open
w open wTail(M P )] rTail(x P )] ]
nChannel S ] r out c : open w : out c : open r : open
w open wTail(M P )] rTail(x P )]
j hh
j
j
'
j
2
1
j hh
j
ii j
j
2
ii j
2
1
j
2
7.3
x
esc YJ=^
89
(2). PTC . r out c : open w : out c : open r : open w open wTail(M P )] rTail(x P )]
(x : ! )(r open w : out c : open r : open w open wTail(M P )]
r in w : in x : open]
x in r : out r : open r : open w r out x : open] ] ]
c open : P ] )
(3). PTC . r open w : out c : open r : open w open wTail(M P )]
r in w : in x : open] x in r : out r : open r : open w r out x : open] ] ]
r out c : open r : open wTail(M P ) r in w : in x : open]
x in r : out r : open r : open w r out x : open] ] ]
(4). PTC . r out c : open r : open wTail(M P ) r in w : in x : open]
x in r : out r : open r : open w r out x : open] ] ]
r open r : open w in r : open : (fwd M allowIO)]
r in w : in x : open] x in r : out r : open r : open w r out x : open] ] ]
c open : P ]
(5). PTC . r open r : open w in r : open : (fwd M allowIO)]
r in w : in x : open] x in r : out r : open r : open w r out x : open] ] ]
r open r : open r in x : open w open : (fwd M allowIO)] ]
x in r : out r : open r : open w r out x : open] ] ]
(6). PTC . r open r : open r in x : open w open : (fwd M allowIO)] ]
x in r : out r : open r : open w r out x : open] ] ]
r open r : open x out r : open r : open w
r open w open : (fwd M allowIO)] ] r out x : open] ] ]
(7). PTC . r open r : open x out r : open r : open w
r open w open : (fwd M allowIO)] ] r out x : open] ] ]
r open r : open r open]
x open r : open w r open w open : (fwd M allowIO)] ] ] ]
(8). PTC . r open r : open r open]
x open r : open w r open w open : (fwd M allowIO)] ] ] ]
r open x open r : open w r open w open : (fwd M allowIO)] ] ] ]
(9). PTC . open r r open x open r : open w r open w open : (fwd M allowIO)] ] ] ]
x open r : open w r open w open : (fwd M allowIO)] ] ]
(10). PTC . x open r : open w r open w open : (fwd M allowIO)] ] ]
x open w w open : (fwd M allowIO)] ]
(11). PTC . x open w w open : (fwd M allowIO)] ]
xfwd M allowIO]
(12). PTC . open c c open : P
P
j
2
'
_
j
1
2
hh
1
1
1
1
2
1
'
1
j
' hh
2
j
2
j
2
1
1
j
2
1
j
2
1
j
2
2
1
j
j
1
j
1
j
j
1
j
1
j
2
1
1
1
j
j
j
1
1
1
j
j
1
1
j
1
1
1
j
1
j
1
j
1
1
j
1
j
1
j
1
j
1
j
1
j
1
j
j
j
2
j
j
j
'
1
1
j
'
j
1
1
1
'
j
j
2
'
j
1
1
1
j
1
1
j
2
j
2
1
1
j
'
1
j
j
1
1
1
2
j
2
2
j
2
1
j
1
j
1
1
j
j
1
2
2
j
1
1
2
1
1
j
2
'
1
1
j
j
1
j
2
j
1
1
2
j
1
j
j
2
1
1
1
1
1 ii
2
'
j
1
j
hh
1
1
1
j
1
2
j
1
j
1
1
2
2
j
j
2
j
1
2
j
j
2
j
2
2 ii
'
j
j
1
2
j
j
j
1
j
j
1
j
2
1
j
j
hh
ii
ii
* dj_ n 7.10 7.11 Q3Pk`
j
Ah YJ=^
90
$~ (Rec Co-out) _n 7.11 c-L (2) "
$~ (ST Out) "
$~ (ST Open 1) "
$~ (ST Out) "
$~ (ST In) fV r hXho"] w a r Rt"
$~ (ST Aux In) ot@;"
$~ (ST Out) "
$~ (ST Open 1) "
$~ (Rec Open) 7hJK open r ;@zn] open r : 0 c&(h79 '
l 4n ] f@3 T ~Bcn] Qc{s'@;: ?Kc ] Q:9 ht ?
c]Q4'hX !u (c open r h"
(10). $ ~ (ST Open 1) "
(11). $ ~ (ST Open 1) "
(12). $ ~ (Rec Open) _@; 9 (1).
(2).
(3).
(4).
(5).
(6).
(7).
(8).
(9).
1
1
7~Kncc $~ ècp 7.13 7.14 Xj+~K ROAM Ef esc Efh&%
cy@T}% operational correspondence 4> 7.13 1w : P esc Q '# P
* : P esc Q c-Y?! } ;!
hh
ii ;!
R-R
Q hh
ii
;!
(esc Red Subst Out) 4 P = x M : P Q = M M : P : x = M x = M ni
= M=x l 4 P = wrequest x wTail(M P )] xfwd M
allowIO] wrequest x wTail(M P )]
xfwd M allowIO] wrequest M
wTail(M P )] Q (esc Red Subst In) _ (esc Red Subst Out) nd (esc Red Output) 4 P = n : S] n M : P : Q = n : S M : P ] B P = nallowIO server w : wHead server r : rHead S ] (open c open c open r)k
wrequest n wTail(M P )](! k 4 S / ?c ] Q) q ] P
nallowIO server w : wHead server r : rHead S wwHead wTail(M P )] ]
(open c open c open r)k Q 96Tl+N 4 cg S M : P / ?
c]Qc4 k) (esc Red Input) _ (esc Red Output) nd (esc Red Comm) 4 P = n : S M : P (x) : P ] : Q = n : S] P (x : M)P B P = nallowIO server w : wHead server r : rHead S wwHead
wTail(M P )] rrHead rTail(x P )] ] (open c open c open r)k
nallowIO
!
server w : wHead server r : rHead S ] P (x : )(xfwd M allowIO] P )
0
h
f
0
g ]
hh
j
ii
hh
hh
1
j
hh
0
h
i
j h
j hh
hh
hh
ii
j
i
j hh
i
1
j
j
j hh
1
Q
hh
ii
j
ii
j
j hh
1 ii
j
_
ii j
j
ii ;!
j
1
j hh
j
hh
j
j
j
2
j
(open c j open c j open r)k;
ii j
2
ii
j
j h
j
(esc Red Var) `d j
j
hh
1
ii
ii j
j
ii j
j
hh
j h
1
j
1
j
j
0
hh
1
1
j
ii
0
ii j
j
j
hh
1
ii
j
j
i
j
;!
1
0
h
1
ii j
0
j
0
i
;!
j
hh
i
hh
ii j
1
j
1
j
2
ii j
j
ii j
j
j hh
2 ii
j
esc YJ=^
7.3
x
91
(esc Red Res) `d (esc Red Par) `d (esc Red Struct) c P
4> 7.14
1w P
hh
Q
esc Q =) hh
ii ;!
Q ` d ii hh
ii
Q sVq esc R R "* : P
;!
esc R - PTC . hh
R
ii '
* P cs'?! }
P = 0 4 0
h n5? ! & P = (n)P 4 (n)P = (n : ! ) P
(n : ! )( P )=
!
!
(n : )( P )
Q l 4 L P
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; ` (n : Tn )P : T Uz (ET Sub) ( (ET Res) `$ : ; n : Tn ` P : T :
T T P Q " ~ }# (1) ni ; n : Tn ` Q : T 5" ~ (ET Res) ( (ET
Sub) n` ; ` (n : Tn )Q : T # (1) '* # (2) cdj # (1) 4(
J
(Struct Par) 4# (1) P = P j R Q = Q j R : P Q #{ ; ` P j R : T Uz (ET Sub) ]k (ET Par) `$: ; ` P : T ; ` R : T : T jt T T P Q "~ }# (1) ni ; ` Q : T 5" ~ (ET Par) ( (ET Sub) n`
; ` Q j R : T # (1) '* # (2) cdj # (1) 4(J (Struct Repl) 4 # (1) P = ! P Q = ! Q : P Q #{ ; ` ! P : T Uz
(ET Sub) ( (ET Repl) `$ : ; ` P : T : T jt T T P Q " ~ }
# (1) ni ; ` Q : T 5"~ (ET Repl) ( (ET Sub) n` ; ` ! Q : T l4# (1)
'*# (2) cdj# (1) 4(J
(Struct Amb) 4# (1) P = nP ] Q = nQ ] : P Q #{ ; ` nP ] : T Uz
(ET Sub) ( (ET Amb) `$ : ; ` n : T ; ` P : T : _ T P Q
" ~ }# (1) ni ; ` Q : T 5" ~ (ET Amb) ( (ET Sub) n` ; ` nQ ] : T l 4# (1) '* # (2) cdj # (1) 4(J (Struct Act) 4 # (1) P = M : P Q = M : Q : P Q #{ ; ` M : P : T Uz (ET Sub) ( (ET Act) `$ : ; ` M : W ; ` P : T : W (T ) T P Q " ~ }# (1) ni ; ` Q : T 5" ~ (ET Act) ( (ET Sub) n`
; ` M : Q : T # (1) '* # (2) cdj # (1) 4(J (Struct Par Zero) 4 P = Q j 0 # (1) #{ ; ` Q j 0 : T Uz (ET Sub)
( (ET Par) `$ : ; ` Q : T ; ` 0 : _ : T jt _ T 5 % 7 3.2 c (Par
1
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_9 1 _3 3.8 #3 3.9 i<
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Zero T ) n` T T "~ (ET Sub) n` ; Q : T # (1) '* # (2) #{
; Q : T n 3.5 n` ;
" ~ (ET Inact) ; 0 : 5" ~ (ET Par) n
` ; Q 0 : T t n ; Q 0 : T # (2) '*
(Struct Par Comm) 4 P = P Q : Q = Q P # (1) #{ ; P Q : T Uz (ET Sub) ( (ET Par) `$ : ; P : T ; Q : T : T t T T (ET Par) ni ; Q P : T t T % % 7 3.2 c (Par Symm T ) ni
T t T = T t T l 4" ~ (ET Sub) n` ; Q P : T # (1) '* # (2) cd
j# (1) 4(J
(Struct Par Assoc) 4 P = (P Q ) R : Q = P (Q R) # (1) #{
; (P Q ) R : T Uz (ET Sub) ( (ET Par) `$ : ; P Q : T ; R : T : T t T T % .T Q z (ET Sub) ( (ET Par) `$ : ; P : T ; Q : T : T t T T " ~ &7 (ET Par) n` ; P (Q R) : T t (T t T ) % 7 3.2 c (Par Assoc T ) i T t (T t T ) = (T t T ) t T l 4"~ (ET Sub) n`
; P (Q R) : T # (1) '* # (2) cdj # (1) 4(J (Struct Res Zero) 4 P = (n : Tn )0 : Q = 0 # (1) #{ ; (n : Tn)0 : T U
z (ET Sub) ( (ET Res) `$ : ; n : Tn 0 : T : T T n fn(0) e
Xn 3.6 ni ; 0 : T 5"~ (ET Sub) n` ; 0 : T # (1) '*# (2) #{ ; 0 : T &Om O mn 9 d n dom(;) " ~n 3.7 ni ; n : Tn 0 : T 5"~ (ET Res) n` ; (n : Tn)0 : T # (2) '*
(Struct Res Res) 4 P = (n : Tn )(m : Tm )R : Q = (m : Tm )(n : Tn )R #
(1) #{ ; (n : Tn )(m : Tm )R : T Uz (ET Sub) ( (ET Res) `$ :
; n : Tn (m : Tm )R : T : T T L Uz (ET Sub) ( (ET Res) `$ :
; n : Tn m : Tm R : T : T T J K 4Th- ni !c ~ Gl 4"
~ &7 (ET Res) ( (ET Sub) n` ; (m : Tm )(n : Tn )R : T # (1) '* # (2)
cdj# (1) 4(J
(Struct Res Par) 4 P = (n : Tn)(P Q ) Q = P (n : Tn)Q : n fn(P ) # (1) #{ ; (n : Tn)(P Q ) : T Uz (ET Sub) ( (ET Res) `$ :
; n : Tn P Q : T : T T L Uz (ET Sub) ( (ET Par) `$ :
; n : Tn P : T ; n : Tn Q : T : T t T T n fn(P) e X n 3.6 ni
; P : T 2 (ET Res) i ; (n : Tn )Q : T " ~ (ET Par) ( (ET Sub) n`
; P (n : Tn )Q : T # (1) '* # (2) cdj # (1) r!a $ ~ +
n 3.7 4(J (Struct Res Amb) 4 P = (n : Tn)mR] Q = m(n : Tn )R] : n = m # (1) #
{ ; (n : Tn)mR] : T Uz (ET Sub) ( (ET Res) `$: ; n : Tn mR] : T
: T T L Uz (ET Sub) ( (ET Amb) `$ : ; n : Tn m : Tm ; n : Tn R : Tm :
T n = m e X n 3.6 ni ; m : Tm 2 (ET Res) i
; (n : Tn )R : Tm " ~ (ET Amb) ( (ET Sub) n` ; m(n : Tn)R] : T l 4#
(1) '* # (2) cdj # (1) r!a $ ~ + n 3.7 4(J 1
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105
(Struct Repl Par) 4 P = ! R : Q = R ! R # (1) #{ ; ! R : T U
z (ET Sub) ( (ET Repl) `$ : ; R : T : T T T " ~ (ET
Par) ni ; R ! R : T t (T t T ) t c{ d ni T = Z Y 5 t c{ d n`
Z Y t Z Y = Z Y t (Z Y t Z Y ) " ~ (ET Sub) n` ; R ! R : T # (1) '* # (2) #{ ; R ! R : T Uz (ET Sub) ( (ET Par) : ; R : T ; ! R : T : T t T T 5 (ET Repl) ni T = Z Y . l 4n" ~% 7 3.2 c (Par
Zero T ) ( (Par Strict T ) `$ T T 9 6 "~ (ET Sub) n` ; ! R : T # (2)
'*
(Struct Repl Zero) 4 P = ! 0 : Q = 0 # (1) #{ ; ! 0 : T Uz (ET
Sub) ( (ET Repl) `$ : ; 0 : T : T t T T t c{d i T = Z Y l 4n
" ~% 7 3.2 c (Par Zero T ) ( (Par Strict T ) `$ T T t T " ~ (ET Sub) n
` ; 0 : T # (1) '*# (2) #{ ; 0 : T Uz (ET Sub) ( (ET
Inact) `$: ; 0 : :
T " ~ (ET Repl) ( (ET Sub) n` ; 0 : T # (2) '*
(Struct Empty) 4 P = : Q # (1) #{ ; : Q : T Uz (ET Sub)
( (ET Act) `$ : ; : W ; Q : T : W (T ) T % (ET Empty) i
W = l 4 W (T ) = T "~ (ET Sub) n` ; Q : T # (1) '* #
(2) #{ ; Q : T " ~n 3.5 i ;
5 (ET Empty) n` ; : l 4" ~
(ET Act) n` ; : Q : (T ) n ; : Q : T # (2) '* (Struct Path) 4 P = (M : M ) : R : Q = M : (M : R) # (1) #{ ; (M : M ) : R :
T Uz (ET Sub) ( (ET Act) `$ : ; M : M : W ; R : T :
W (T ) T % .Tz (ET Path) `$ : ; M : W ; M : W :
W = W (W ) " ~ &7 (ET Act) ni ; M : (M : R) : W (W (T )) % W (W (T )) =
(W (W ))(T ) = W (T ) l 4" ~ (ET Sub) ; M : (M : R) : T # (1) '* #
(2) cdj # (1) cB _ 4(J ] ~ qn@;c 3P ni -L'* _
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r A.1 ` ; A : Z Y t _Q)p*!Q (1). 1w ; A : P : T '# ; P : T - T T "
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3.1 ni T Z Y t T n T T (2). ; A : P Q : T L V (ET Sub) ( (ET Par) `$ : ; A : P : T ; Q : T : T t T T -L (1) i ; P : T : T T 7 T = T T , " ~
(ET Par) n` ; P Q : T : T T `
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_9 1 _3 3.8 #3 3.9 i<
106
r 3.9 (Subject reduction) 1w ; P : T - P Q '# ; Q : T - T T * P Q c-Y? ! &
(Red In) n\i ; m in n : P P ] n in m : Q Q ] : T N d ; nmP P ] Q Q ] : T
: T T djk`
\i
(1)
; m in n : P P ] n in m : Q Q ] : T
(2.1) ; m in n : P P ] : T
(1),!$ ~(ET Sub)
(2.2) ; n in m : Q Q ] : T
+(ET Par)
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0
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1
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1
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2
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(3.1)
(3.2)
(3.3)
(4.1)
(4.2)
(4.3)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
j
1
j
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(2.1)
(2.2)
(2.3)
(3.1)
(3.2)
(3.3)
(4.1)
2
2
2
T tT T
; m : Tm
; in n : P P : Tm
T
; n : Tn
; in m : Q Q : Tn
T
; in n : y t
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; in m :
t
; Q Q : Tn
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t Tn
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T
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2
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+(ET Amb)
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2
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(3.1)(6)+(ET Amb)
(3.1)+(ET Cap Imm)
(4.2)(8)+n A.1.(2)~(ET Sub)
(7)(9)+(ET Par)
(10)+% 73.2
(4.1)(11)+(ET Amb)
(2.3)(3.3)(4.3)+% 73.2
(12)(13), J T =
;
2
1
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2
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j
1
1
j
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2
1
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(Red Out) n\ i ; nm out n : P P ]
Q ] : T : T T dj k `
2
j
1
j
2
j
out
0
1
j
2
; nm out n : P P ] out m : Q Q ] : T
; n : Tn
; m out n : P P ] out m : Q Q : Tn
T
; m out n : P P ] : T
; out m : Q Q : T
T t T Tn
; m : Tm
1
j
2
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`
1
`
j
2
1
j
2
j
1
j
2
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1
j
2
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`
j
1
0
m : Q Q ] : T N d ; mP P ] nQ
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1
2
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2
1
2
(2.2),!$ ~(ET Sub)
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(3.1),!$ ~(ET Sub)
1
j
107
(4.2)
(4.3)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
;
`
0
_
2
1
T
; out m : Q Q : Tn
; out m :
t
; Q Q : Tn
; nQ Q ] :
; out n : y t
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; mP P ] :
; mP P ] nQ Q ] :
-L'* 2
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j
1
1
_
`
`
j
1
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j
j
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0
;
2
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1
j
2
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1
j
2
`
_
1
1
2
2
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`
(4.3)(3.3)+% 73.2
(3.2)(5)+(ET Sub)
(4.1)+(ET Cap Imm)
(6)(7)+n A.1.(2)~(ET Sub)
(2.1)(8)+(ET Amb)
(2.1)+(ET Cap Mbl)
(4.2)(10)+n A.1.(2)~(ET Sub)
(4.1)(11)+(ET Amb)
(12)(9)+(ET Par)
(13)(2.3), J T =
2
1
(Red Open) n\ i ;
djk`
(1)
(2.1)
(2.2)
(2.3)
(3.1)
(3.2)
(3.3)
(4)
(5.1)
(5.2)
(5.3)
(6.1)
(6.2)
(6.3)
(7)
(8)
(9)
(10.1)
(10.2)
(11)
(12)
j
1
T
Tn
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n : P P : Tm
out
open
0
_
j
1
j
_
2
0
0
n : P n open : Q Q ] : T N d ; P Q Q : T : T
j
1
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1
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1
2
2
2
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1
1
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2
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1
2
1
2
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1
1
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1
1
1
2
0
0
\i
(1),!$ ~(ET Sub)
+(ET Par)
(2.2),!$ ~(ET Sub)
+(ET Amb)
1
j
;
j
1
2
2
j
2
(3.3)(2.3)+% 73.2
(3.2),!$ ~(ET Sub)
+(ET Par)
(5.1),!$ ~(ET Sub)
+(ET Act)
1
1
j
2
0
1
j
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`
1
2
`
2
j
0
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0
j
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2
; open n : P n open : Q Q ] : T
; open n : P : T
; n open : Q Q ] : T
T tT T
; n : Tn
; open : Q Q : Tn
T
T T
; open : Q : Tn
; Q : Tq
Tn t Tq Tn
; open : W
; Q : Tq
W(Tq ) Tn
W= ]
Tq ] t Tq Tn
t Tq Tq t Tq ] Tn
Tn = Z Y Tn ]
Tq t Tq Tn
; Q Q : Tq t Tq
; Q Q : Tn
j
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1
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2
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1
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(7)(6.3)(5.3)+% 73.2
(8)+ t c{ d
(9)+ c{ d
j
0
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0
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2
(6.2)(5.2)+(ET Par)
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T
_9 1 _3 3.8 #3 3.9 i<
108
(13)
(14.1)
(14.2)
(15)
(16)
(17)
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0
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0
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0
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0
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T dj k `
1
1
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2
0
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P N d ; (n : Tn )P : T : T
0
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`
; nP] : T
; n : Tn
; P : Tn
T
P
P
; P : Tn
Tn Tn
`
`
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0
0
T dj
;!
0
0
0
1
P N d ; nP ] : T : T
\i
(1),!$ ~(ET Sub)
+(ET Amb)
;!
0
`
0
(4.1)(4.2)+(ET Res)(ET Sub)
(5)(2.2), J T = T
1
`
0
`
1
`
0
j
\i
(1),!$ ~(ET Sub)
+(ET Res)
\i
(2.1)(3)+ }#
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0
0
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(5)(2.3), J T = Tp t Tq
j
; (n : Tn )P : T
; n : Tn P : T
T T
P
P
; n : Tn P : T
T T
; (n : Tn )P : T
-L'* _
0
j
0
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(1)
(2.1)
(2.2)
(2.3)
(3)
(4.1)
(4.2)
0
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j
\i
(2.1)(3)+ }#
0
(Red Res) n\i ; (n : Tn)P : T : P
k `
(1)
(2.1)
(2.2)
(3)
(4.1)
(4.2)
(5)
(6)
0
;!
0
0
(Red Par) n\ i ; P Q : T : P
(1)
(2.1)
(2.2)
(2.3)
(3)
(4.1)
(4.2)
(5)
(6)
(10.1)+(ET Open)
(2.1),!$ ~(ET Sub)
+(ET Act)
(14.1)(12)+(ET Par)
(14.2)(4)+% 73.2, 3.1
(15)(16), J T = Tp Tn
; open n :
t (Tn t )
; P : Tp
t (Tn t Tp ) T
; P Q Q : T p Tn
Tp Tn T
-L'* \i
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0
0
0
T dj k `
109
(5)
(6)
0
`
_
0
(Red Struct) n\ i ; P : T P
T T dj k `
`
0
(1)
(2)
(3)
(4)
(5.1)
(5.2)
(6)
(7)
(8)
(4.1)(4.2)+(ET Sub)(ET Amb)
(5)(2.3), J T =
; nP ] :
-L'* ; P :T
P P
; P :T
P
P
; P :T
T T
P P
; P :T
-L'* `
0
0
`
0
;!
00
`
1
00
1
0
P P
0
0
;!
_
P :P
00
\i
\i
(1)(2)+n 3.8
\i
(3)(4)+ }#
00
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000
000
1
\i
(5)(6)+n 3.8
(7)(5.2), J T = T
0
] ~ qn@;c 3P ni -L'* _
0
1
00
P N d ; P : T :
000
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0
110
_9 1 _3 3.8 #3 3.9 i<
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(1). q n fn(P ) n B.2.(4) (n 4.3 i n fn(Q ) l 4 (n)C = (~r) P (n)P
(~r) Q (n)Q = (n)D -L'* (2). q n fn(P ) B 3]` &@; (a) q P = mP ] m = n : n fn(P ) B (n)C = (~r) m(n)P ] P % P b Q
c{di Q = mQ ] : P Q 5"~ P Q eXn 4.3 n` n fn(Q ) l 4 (n)D = (~r) m(n)Q ] Q ` i (n)C (n)D -L'* (b) : B ` i (n)C = (n~r) P P : (n)D = (n ~r) Q Q -L'* ] ~ qn@;c 3P ni -L'* 00
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(2). q Q > D B>7 C R4 P > C : C D (Struct Re) 4 P = Q ì#'* (Struct Symm) 4 Q P # (1) n }# (2) `$ # (2) n }# (1) `
$
(Struct Trans) 4 P R : R Q # (1) #{ P > (~p) P P }# (1)
i R > (~r) R R P b R : P R 5}# (1) i Q > (~q) Q Q R b Q : R Q b ( c,r % n` P b Q : P Q # (1) '* #
(2) cdj # (1) 4(J (Struct Res) 4 P = (n)P Q = (n)Q : P Q # (1) #{ (n)P > C UzB (Harden Res) `$n P > C : C = (n)C }# (1) i>
7 D' R4 Q > D : C D " ~ (Harden Res) n` Q = (n)Q > (n)D n B.4 i (n)C (n)D # (1) '* # (2) cdj # (1) 4(J (Struct Par) 4 P = P R Q = Q R : P Q # (1) #{ P R >
(~r) P P L- L {) ]` & Bj T
(Harden Par 1) 4 P > (~r) P P P = P R : ~r fn(R) = }#
(1) i Q > (~r) Q Q P b Q : P Q " ~ (Harden Par 1) `
Q R > (~r) Q (Q R) P R Q R i # (1) '* (Harden Par 2) 4 R > (~r) P P P = P P : ~r fn(P ) = n
4.3 i fn(P ) = fn(Q ) l 4 ~r fn(Q ) = " ~ (Harden Par 1) `
Q R > (~r) P (Q P ) P P
Q P i # (1) '* # (2) cdj# (1) 4(J
(Struct Repl) 4 P =!P Q =!Q : P Q # (1) #{ !P > (~r) P P Uz (Harden Repl) `$ n P > (~r) P P : P = P !P }#
(1) i Q > (~r) Q Q P b Q : P
Q " ~ (Harden Repl) ` !Q > (~r) Q (Q !Q ) P !P Q !Q i # (1) '* # (2) cdj # (1) 4(J
(Struct Amb) 4 P = nP ] Q = nQ ] : P Q # (1) #{ nP ] >
(~r) P P Uz (Harden Amb) `$ n P = nP ] ~r = : P = 0 %
"~ (Harden Amb) nQ ] > () nQ ] 0 \i P Q i nP ] b nQ ] l4
# (1) '*# (2) cdj# (1) 4(J
(Struct Action) 4 P = M:P Q = M:Q : P Q # (1) #{ M:P > C n 4.11 z>7]`&@; (1). M > A:N C = () A:P 0 : P N:P 4 n 4.12 i M:Q > () A:Q 0
: Q N:Q P Q n` P N:P N:Q Q l4 A:P b A:Q # (1)
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(2). M = : P > C 4 e X }# (1) >7 D R4 Q > D : C D n 4.13
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(Struct Par Zero) 4 P = Q 0 # (1) #{ P > C Uz ]` j T `$ (Harden Par 1) 4 Q > (~q) Q Q : C = (~q) Q (Q 0) Q 0 Q i #
(1) '*
(Harden Par 2) 4 L. B$` 0 > C '* TU f V3 h n~ a ,wD B`$
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# (2) #{ Q > (~q) Q Q B" ~ (Harden Par 1) ` Q 0 > (~q) Q (Q 0) Q 0 Q i# (2) '*
(Struct Par Comm) 4 P = R R : Q = R R # (1) #{ P = R R > C Uz]` jT `$
(Harden Par 1) 4 R > (~r) R R C = (~r) R (R R ) : ~r fn(R ) = " ~ (Harden Par 2) n` Q = R R > (~r) R (R R ) R R R R
i# (1) '*
(Harden Par 2) dj (Harden Par 1) 4(J # (2) cdj# (1) 4(J
(Struct Par Assoc) 4 P = (R R ) R : Q = R (R R ) # (1) #{
P = (R R ) R > C Uz ]` j T `$ (Harden Par 1) 4 (R R ) > (~r) R R C = (~r) R (R R ) : ~r fn(R ) =
% (R R ) > (~r) R R L z ]` j T `$ (Harden Par 1) 4 R > (~r) R R R = (R R ) : ~r fn(R ) = - - ~r fn(R ) = ni ~r fn(R R ) = " ~ (Harden Par 1) R > (~r) R R n` Q = R (R R ) > (~r) R (R (R R )) %
R R = (R R ) R R (R R ) l 4# (1) '* (Harden Par 2) 4 R > (~r) R R R = (R R ) : ~r fn(R ) = " ~ (Harden Par 1) ~r fn(R ) = ( R > (~r) R R n` R R >
(~r) R (R R ) 5 e X ~r fn(R ) = " ~ (Harden Par 1) n`
Q = R (R R ) > (~r) R (R (R R )) % R R = (R R ) R R
(R R ) l 4# (1) '* (Harden Par 2) dj (Harden Par 1) 4(J # (2) cdj# (1) 4(J
(Struct Res Zero) 4 P = (n)0 : Q = 0 h >7 P > C ( Q > D l 4# (1) (2) n''* (Struct Res Res) 4 P = (n)(m)R : Q = (m)(n)R U#{ n = m : B# f V
'*# (1) #{ P > C Uz$~&7 (Harden Res) `$: R > C
: C = (n)(m)C $ ~ &7 (Harden Res) n` Q > (m)(n)C e X n B.5 i
(n)(m)C (m)(n)C l 4# (1) '* # (2) cdj # (1) 4(
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(Struct Res Par) 4 P = (n)(R R ) Q = R (n)R : n fn(R ) # (1) #{ P > C Uz (Harden Res) `$ : C = (n)C : R R > C U
C = (~r) R R ~r 4 &Om - ) l 4n n ~r ` e 3 @;{L (n)C cY {d
q n fn(R ) B R R > (~r) R R L{]` jT `$ (Harden Par 1) 4 R > (~r) R R R = R R : ~r fn(R ) = n 4.4 ni R (~r)(R R ) l 4 fn(R ) = (fn(R ) fn(R )) ~r n fn(R )
( n ~r n` n fn(R ) U \ i T Al 4 L @; h n (Harden Par 2) 4 R > (~r) R R R = R R : ~r fn(R ) = 4
3 (a) (b) &@;{L (a) k R = mRm] m = n : n fn(R ) n n fn(R ) fn(R ) : C = (~r) m(n)Rm ] (R R ) B (Harden Res)
ni (n)R > (~r) m(n)Rm] R 5 (Harden Par 2) n` R (n)R >
(~r) m(n)Rm] (R R ) l 4# (1) '* (b) : B C = (n~r) R R (Harden Res) ni (n)R > (n~r) R R 5 n fn(R ) "~ (Harden
Par 2) n` R (n)R > (n~r) R (R R ) l 4# (1) '* q n fn(R ) B C = (~r) R (n)R : R R > (~r) R R L { ]` j T `
$
(Harden Par 1) 4 R > (~r) R R R = R R : ~r fn(R ) = ~r fn(R ) = i ~r fn((n)R ) = l 4" ~ (Harden Par 1) n
` R (n)R > (~r) R (R (n)R ) n 4.4 ni R (~r)(R R ) l 4 fn(R ) = (fn(R ) fn(R )) ~r e X \ i n fn(R ) ( n ~r n`
n fn(R ) l 4 (n)R = (n)(R R ) R (n)R # (1) '* (Harden Par 2) 4 R > (~r) R R R = R R : ~r fn(R ) = n ~r fn(R ) "~ (Harden Res) ni (n)R > (~r) R (n)R 5
~r fn(R ) = " ~ (Harden Par 2) n` R (n)R > (~r) R (R (n)R ) %\ i n fn(R ) 9 d+ (n)R = (n)(R R ) R (n)R l 4# (1) '
*
# (2) cdj# (1) _4(J
(Struct Res Amb) 4 P = (n)mR] Q = m(n)R] : n = m # (1) #{
P > C Uz (Harden Res) `$ : mR] > C : C = (n)C % .Tz (Harden Amb) `$ : C = () mR] 0 U L C = (n)() mR] 0 e X n 3 : H
fn(R) 3]`&@;{L q n fn(R) B C = () m(n)R] 0 (Harden Amb) ni Q > () m(n)R] 0 # (1) '*
q n fn(R) B C = () mR] (n)0 (Harden Amb) ni Q > () m(n)R] 0 V % n fn(R) ` i R (n)R l 4 mR] b m(n)R] 2 (Struct Res Zero)
i (n)0 0 l4# (1) '*
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(Struct Empty) 4 P = :Q # (1) #{ P = :Q > C Uz (Harden Empty)
`$: Q > C l4# (1) '*# (2) #{ Q > C "~ (Harden Empty)
n` P = :Q > C # (2) '*
(Struct Path) 4 P = (M:M ):R : Q = M:(M :R) # (1) #{ P = (M:M ):R > C Uz (Harden Path) `$ :
M:(M :R) > C n Q > C l4# (1) '* # (2) #{ Q = M:(M :R) > D n'" ~ (Harden Path) n ` P = (M:M ):R >
D # (1) '* (Struct Repl Par) 4 P =!R : Q = R !R # (1) #{ P =!R > (~r) R R Uz (Harden Repl) `$ :
R > (~r) R R : R = R !R n 4.4 ni !R (~r)(R R ) 5" ~n 4.3 n
` fn(!R) = (fn(R ) fn(R )) ~r l 4 ~r fn(!R) = " ~ (Harden Par 1) n`
Q = R !R > (~r) R (R !R) = (~r) R R l 4# (1) '* # (2) #{ Q = R !R > (~r) R R Uz ]` j T `$ (Harden Par 1) 4 R > (~r) R R R = R !R : ~r fn(!R) = (Harden
Repl) n` !R > (~r) R R !R = (~r) R R # (2) '* (Harden Par 1) 4 !R > (~r) R R R = R R : ~r fn(R) = % !R >
(~r) R R z (Harden Repl) `$ : R > (~r) R R : R = R !R l 4
R = R !R R !R R R R R # (2) '* (Struct Repl Zero) 4 P =!0 : Q = 0 h >7 P > C ( Q > D l 4# (1) (2)
n''*
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(~p) Q P : R = P ! P n 4.3 (n 4.4 ni fn(P) = fn((~p)(Q P ) l 4 ~p fn(P) =
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(Trans Amb) 4 ! P > (~p) nP ] P P P : Q = (~p)(nP ] P ) ! P >
(~p) nP ] P "~n C.1 ni>7 R R4 P > (~p) nP ] R P = R ! P : fn(P)
~p = 5"~ (Harden Par 1) n` P P > (~p) nP ] (R P ) 5 (Trans Amb) n
i P P R U R = (~p)(nP ] R P) 2 Q = (~p)(nP ] P ) = (~p)(nP ] R
! P) (~p)(nP ] R P ) ! P = R ! P l 4 -L'* (Trans In) 4 ! P > (~p) nP ] P P in m P P > (~r) mP ] P P in n P ~r fn(nP ] ) = ~r ~p = : Q = (~p~r)(nmP ] P ] P ) ! P > (~p) nP ] P
" ~n C.1 ni>7 R $` P > (~p) nP ] R P R ! P : ~p fn(P ) = P > (~r) mP ] P ( P R ! P " ~n 4.14 ni>7 R ! P > (~r) mP ] P :
P P P P V %z ]` &@;n ]- Y R ! P > (~r) mP ] P (Harden Par 1) 4 R > (~r) mP ] P P = P ! P : ~r fn( ! P ) = (1) P > (~p) nP ] R ( ~p fn(P ) = "~ (Harden Par 1) ni P P > (~p) nP ] (R
P) (2) 5 R > (~r) mP ] P ( ~r fn(P ) = ~r fn( ! P) = "~ (Harden
Par 1) n` R P > (~r) mP ] (P P ) (3) 5 P P ( P in n P " ~n 4.15 ni>7 P $` P in n P : P P 0 - (1),(2),(3) (\ i P in m P ~r fn(nP ] ) = ~r
~p = "~ (Trans In) n` P P (~p~r)(nmP ]
P ] P P) = R % fn(P) ~p ~r = ` i Q = (~p ~r)(nmP ] P ] P )
(~p~r)(nmP ] P ] P ) (~p~r)(nmP ] P ] P ! P ) R ! P l 4-L'* (Harden Par 2) 4 ! P > (~r) mP ] P P = R P : ~r fn(R ) = ! P > (~r) mP ] P "~n C.1 ni>7 R $` P > (~r) mP ] R P = R ! P
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118
: ~p fn(P ) = (1) P > (~p) nP ] R ( ~p fn(P) = "~ (Harden Par
1) ni P P > (~p) nP ] (R P) (2) 5 P > (~r) mP ] R ( ~r fn(R ) =
" ~ (Harden Par 2) n` R P > (~r) mP ] (R R ) (3) 5 P P (
P in n P " ~n 4.15 ni>7 P $` P in n P : P
P 0 - (1),(2),(3)
in m
(\ i P
P ~r fn(nP ] ) = ~r
~p = "~ (Trans In) n
`P P
(~p~r)(nmP ] P ] R R ) = R % fn(P ) ~p ~r = ` i
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Q = (~p~r)(nmP ] P ] P ) (~p ~r)(nmP ] P ] P ) (~p~r)(nmP ] P ] R
P ) (~p~r)(nmP ] P ] R R ! P) R ! P l 4-L'* (Trans Out)(Trans Open) r~_ (Trans In) c &` i#'* 4(J
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] ~ qn@;c 3P ni -L'* r C.4 1w H( ! P)
H(P k )
+2
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Q $` P P
Q : P Q ! P 7 H = H(Q ) R H(Q ! P ) = H ( ! P ) 6 'a a0I _Q k P P P k Q P k l 4 H(P k ) H(Q P k) n
H(P k ) H (P k ) -L'* (Act Har) 4 H
H : R H ( ! P) 7 H = H (P P
) B R H (P P
k
k
! P) = H ( ! P) : a a0I _Q k H(P ) H (P ) = H (P k ) -L'* (Act Inter) 4 >7 H ( ~r R4 ~r fn(P) = : ]` jT'* (Inter In) 4 H (~r)H (m R ] nR ] ) ! P in n P R in m R : R
(~r)H (nmP R ] R ] ) n C.2 ni>7 Q R4 P in n Q : P Q ! P 7 H = (~r)H (nm P Q R ] R ] ) B R (~r)H (nmQ ! P R ] R ] )
(~r)H (nm ! P P Q R ] R ] ) = H ( ! P ) : a a0I _Q k H(P k )
(~r)H (mP k P P R ] nR ] )
(~r)H (nmP k P Q R ] R ] ) = H (P k ) L'*
(Inter Out) 4 H (~r)H (nm
R ] R ] ) ! P out n P R out m R :
R (~r)H (mP R ] nR ] ) n C.2 ni>7 Q R4 P out n Q : P Q ! P 7 H = (~r)H (m P Q R ] nR ] ) B R (~r)H (mQ ! P R ] nR ] )
(~r)H (m ! P P Q R ] nR ] ) = H ( ! P ) : a a0I _Q k H(P k )
(~r)H (nmP k P P R ] R ] )
(~r)H (mP k P Q R ] nR ] ) = H (P k ) L'*
(Inter Open) 4 H (~r)H ( nR ] ) ! P open n P R open R : R (~r)H (P
R ) n C.2 ni>7 Q R4 P open n Q : P Q ! P 7 H = (~r)H ( P Q
R ) B R (~r)H (Q ! P R ) (~r)H ( ! P P Q R ) = H ( ! P ) : a a0I _
Q k H(P k ) (~r)H (P k P P nR ] ) (~r)H (P k P Q R ) = H (P k) L'*
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(~r)H (mR ] n
R ] ) ! P in m P R in n R :
R (~r)H (nmR ] P R ] ) n C.2 ni>7 Q R4 P in m Q : P Q ! P 7 H = (~r)H (nmR ]
P Q R ] ) B R (~r)H (nmR ] Q ! P R ] )
(~r)H (nmR ] ! P P Q R ] ) = H ( ! P) : a a0I _Q k H(P k )
(~r)H (mR ] nP k P P R ] )
(~r)H (nmR ] P k P Q R ] ) = H (P k ) L'*
(Inter Co-out) 4 H (~r)H (nmR ]
R ] ) ! P out m P R out n R :
R (~r)H (mR ] nP R ] ) n C.2 ni>7 Q R4 P out m Q : P Q ! P 7 H = (~r)H (mR ] n P Q R ] ) B R (~r)H (mR ] nQ ! P R ] )
(~r)H (mR ] n ! P P Q R ] ) = H ( ! P) : a a0I _Q k H(P k )
(~r)H (nmR ] P k P P R ] )
(~r)H (mR ] nP k P Q R ] ) = H (P k ) L'*
(Inter Co-open) 4 H (~r)H (n R ] R ) ! P open P R open n R :
R (~r)H (P R R ) n C.2 ni>7 Q R4 P open Q : P Q ! P 7
H = (~r)H ( P Q R R ) B R (~r)H (Q ! P R R ) (~r)H ( ! P P
Q R R ) = H ( ! P) : a a0I _Q k H(P k ) (~r)H (nP k P P R ]
R ) (~r)H (P k P Q R R ) = H (P k ) -L'* (Inter Amb In) 4 !P > (~p) nQ] P Q in m Q H (~r)H ( mR ] ) R in n
R ~p fn(mR ] ) = : R (~r)H ((~p)(mnQ ] R ] P )) !P > (~p) nQ] P
"~n C.1 ni>7 P R4 P > (~p) nQ] P P = P ! P : ~p fn(P) = 7 H = (~r)H ( P (~p)(mnQ ] R ] P )) B R (~r)H ((~p)(mnQ ] R ]
P ! P)) (~r)H ( ! P P (~p)(mnQ ] R ] P )) = H ( ! P ) : a a0I _Q k H(P K ) (~r)H (P k P P mR ] )
(~r)H (P k P (~p)(mnQ ] R ] P )) =
H (P k ) -L'* (Inter Amb Co-in) 4 !P > (~p) nQ] P Q in m Q H (~r)H ( mR ] ) R in n R ~p fn(mR ] ) = : R (~r)H ((~p)(nmR ] Q ] P )) !P >
(~p) nQ] P " ~n C.1 ni>7 P R4 P > (~p) nQ] P P = P ! P
: ~p fn(P) = 7 H = (~r)H ( P (~p)(nmR ] Q ] P )) B R
(~r)H ((~p)(nmR ] Q ] P ! P)) (~r)H ( ! P P (~p)(nmR ] Q ] P )) =
H ( ! P ) : a a0I _Q k H(P K ) (~r)H (P k P P mR ] )
(~r)H (P k
P (~p)(nmR ] Q ] P )) = H (P k ) -L'* (Inter Amb Out 1) 4 !P > (~p) nQ] P Q out m Q H (~r)H (m R ] ) R out n R ~p fn(mR ] ) = : R (~r)H ((~p)(nQ ] mP R ] )) !P >
(~p) nQ] P " ~n C.1 ni>7 P R4 P > (~p) nQ] P P = P ! P : ~p
fn(P) = 7 H = (~r)H ((~p)(nQ ] m P P R ] )) B R (~r)H ((~p)(nQ ]
mP ! P R ] )) (~r)H ((~p)(nQ ] m ! P P P R ] )) = H ( ! P) : a a0I _
Q k H(P K ) (~r)H (mP k P P R ] ) (~r)H ((~p)(nQ ] mP k P P
R ] )) = H (P k ) -L'* (Inter Co-in) 4 H
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_9 3 _3 5.31 i<
120
(Inter Amb Out 2) 4 !P > (~p) nQ] P Q out m Q P out n P H (~r)H (m
R ] ) ~p fn(mR ] ) = : R (~r)H ((~p)(nQ ] mP R ] )) !P >
(~p) nQ] P " ~n C.1 ni>7 P R4 P > (~p) nQ] P P = P ! P :
~p fn(P) = P = P ! P out n P " ~n 5.18 ni L ]` @;j T '* P out n P : P P ! P 47 H = (~r)H ((~p)(nQ ] m P P R ] )) B R (~r)H ((~p)(nQ ] mP ! P R ] )) (~r)H ((~p)(nQ ] m ! P P P
R ] )) = H ( ! P ) : a a0I _Q k H(P K ) (~r)H (mP k P P R ] )
(~r)H ((~p)(nQ ] mP k P P R ] )) = H (P k ) -L'* ! P out n P : P
P P 4 e X n C.2 ni>7 P R4 P out n
P :P
P ! P 7 H = (~r)H ((~p)(nQ ] m
P P R ] )) B
R (~r)H ((~p)(nQ ] mP P ! P R ] )) H ( ! P ) : a a0I_Q k h
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H(P K ) (~r)H (mP k P P R ] )
(~r)H ((~p)(nQ ] mP k P P
R ] )) = H (P k ) -L'* (Inter Amb Co-open) 4 !P > (~p) nQ] P Q open Q H (~r)H ( R ) R open n R ~p fn(mR ] ) = : R (~r)H ((~p)(Q P R )) !P >
(~p) nQ] P " ~n C.1 ni>7 P R4 P > (~p) nQ] P P = P ! P :
~p fn(P ) = 7 H = (~r)H ( P (~p)(Q P R )) B R (~r)H ((~p)(Q
P ! P R )) (~r)H ( ! P P (~p)(Q P R )) = H ( ! P ) : a a0I _Q k H(P K ) (~r)H (P k P P R )
(~r)H (P k P (~p)(Q P R )) = H (P k ) -L'*
] ~ qn@;c 3P ni -L'* +2
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r 5.31 1w H( ! P) n '#Vqv@ k 97 H(P k) n * H( ! P) n c-Y? ! }
(Conv Exb) 4 H( ! P) n n 5.28 ni ]` j T'*"
(1). a a Q H(Q) n 4J k = 1 n H(P ) n (2). ! P n : a a Q n H(Q) n 4 n 5.26 ni>7 ~p P ( P $`
! P > (nP ]) P : n ~p n C.1 n`>7 P R4 P > (~p) nP ] P P = P ! P : ~p fn(P) = 5 n 5.26 n` P n J k = 1 n H(P ) n (3). ! P A P A BarbedAction : a a Q A Q A BarbedAction H(Q) n n C.2 ni>7 R R4 P A R l 4J k = 1 n H(P ) n (Conv Red) 4 H( ! P) Q : Q n n C.4 ni>7 H R4 Q H ( ! P) : a a
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H (P j ) Q n : Q H ( ! P ) " ~n 5.6 ni H ( ! ) n :L-n Q n Lc-Y`$ }#i>7_Q k $` H (P k) n 5\i H(P k ) H (P k) "~ (Conv Red) ni H(P k ) n ] ~ qn@;c 3P ni -L'* +
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(2). Xudong Guan, Yiling Yang, Jinyuan You. Typing evolving ambients. Info. Proc. Letters.
80(5):265-270, 2001, Elsevier.
(3). Xudong Guan, Yiling Yang, Jinyuan You. Making ambients more robust. In Proc. Int'l. Conf.
on Software: Theory and Practice, pp.377-384, Beijing, China, Aug. 2000.
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