Anytime, Anywhere: Modal Logics for Mobile Ambients

38 Pages·1999·0.16 MB·English

Anytime, Anywhere 1
Anytime, Anywhere:
Modal Logics for
Mobile Ambients
Luca Cardelli
Andy Gordon
Anytime, Anywhere 2
Orientation: Ambients
An ambient is a named, bounded place where computation happens;
it is both a unit of mobility and a security perimeter.
A capability represents a right to move into or out of an ambient, or to
dissolve its boundary.
Ambient security rests on the controlled distribution of capabilities; the
right to enter an ambient does not imply the right to exit it.
We are investigating a process calculus based on ambients, with the
goal of developing a flexible, secure, and typeful model for mobile
computation.
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Mobile Ambients: a packet from to
a b
Machine Machine
a b
out in open
z }| { z }| {
a[m[ a: b:hMi]] j b[ m:(x):P]
receive ;
| {z } | {z }
a b : M x P
Ambients may mo!del both machines and packets
(cid:15)
Ambients are mobile: moves out of and into
(cid:15) m[(cid:1) (cid:1) (cid:1)] a b
You need capability out to exit ; capability in to enter ; and
(cid:15) a a b b
capability open to dissolve
m m
There is an ether local to each ambient for message exchange
(cid:15)
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Ambient Behaviour, By Example
There are four basic reduction rules in the calculus:
out in open
a[m[ a: b:hMi]] j b[ m:(x):P]
in open
a[] j m[ b:hMi] j b[ m:(x):P]
! open
a[] j b[m[hMi] j m:(x):P]
!
a[] j b[hMi j (x):P]
!
a[] j b[Pfx Mg]
!
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The Restriction-Free Ambient Calculus
Expressions and Processes:
::= expressions ::= processes
M; N P;Q; R
name 0 inactivity
n
in can enter composition
M M P j Q
out can exit replication
M M !P
open can open ambient
M M M[P]
null action
(cid:15) M:P
path input
0
M:M (n):P
output
hMi
Reduction:
in
n[P j m:Q] j m[R] ! m[n[P j Q] j R] P ! Q ) P j R ! Q j R
out
m[n[P j m:Q] j R] ! n[P j Q] j m[R] P ! Q ) n[P] ! n[Q]
open
0
n[P] j n:Q ! P j Q P (cid:17) P;P ! Q;
0 0 0
hMi j (n):P ! Pfn Mg Q (cid:17) Q ) P ! Q
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A Vexing Problem
A recurring issue is how to state behavioural properties of ambients.
We have tools for establishing equational properties.
But many properties cannot easily be formulated as equations.
For example, type systems for ambients guarantee certain properties,
such as that some ambients are immobile, some are persistent.
It’s hard to write down equations for immobility or persistence!
Our solution: invent a modal logic for ambients.
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A Modal Logic
for Mobile Ambients
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Modal Formulas
In a modal logic, the truth of a formula is relative to a state.
In our case, formulas such as the following are true relative to an
ambient calculus process:
(1) “there’s an ambient here”
p
(2) “somewhere there’s an ambient ”
p
(3) “if (2) then forever (2)”
(4) “somewhere there’s an ambient with a child ”
p q
(5) “if (4) then forever (4)”
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A Logic of Spacetime
To talk about time, we use standard temporal operators.
To talk about space, we introduce spatial operators:
Process Formula
0 0 (there is nothing here)
(there is one thing here)
n[P] n[A]
(there are two things here)
P j Q A j B
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Syntax of the Logic
Logical Formulas:
a name or a variable
(cid:17) n x
formula
A; B ::=
T true
negation
:A
disjunction
A _ B
0 inaction
ambient match
(cid:17)[A]
composition match
A j B
universal quantification
8x:A
sometime modality (temporal)
(cid:6)GA
somewhere modality (spatial)
A
@ location adjunct
A (cid:17)
composition adjunct
.
A B