Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of comonad yield two expressive metalanguages for higher-order processes, both arising from canonical constructions in the model. Their denotational semantics are fully abstract with respect to contextual equivalence. One language, called HOPLA for Higher-Order Process LAnguage, derives from an exponential of linear logic. It can be viewed as an extension of the simply-typed lambda calculus with CCS-like nondeterministic sum and prefix operations, in which types express the form of computation path of which a process is capable. HOPLA can directly encode calculi like CCS,
|
2782
|
Communication and Concurrency
– Milner
- 1989
|
|
1763
|
clocks, and the ordering of events in a distributed system
– LAMPORT
- 1978
|
|
1080
|
A Calculus of Communicating Systems
– Milner
- 1980
|
|
547
|
Concurrency and automata on infinite sequences
– Park
- 1981
|
|
473
|
The semantics of a simple language for parallel programming
– Kahn
- 1974
|
|
404
|
Algebraic laws for nondeterminism and concurrency
– Hennessy, Milner
- 1985
|
|
327
|
Communicating and Mobile Systems: The π-calculus
– Milner
- 1999
|
|
248
|
Domains for denotational semantics
– Scott
- 1994
|
|
244
|
The linear time - branching time spectrum II; the semantics of sequential systems with silent moves. Preliminary version available from boole.stanford.edu. Extended abstract
– Glabbeek
- 1993
|
|
234
|
Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms
– Sangiorgi
- 1992
|
|
232
|
Models for concurrency
– Winskel, Nielsen
- 1997
|
|
231
|
The π-Calculus: A Theory of Mobile Processes
– Sangiorgi, Walker
- 2001
|
|
224
|
Event structures
– Winskel
- 1987
|
|
212
|
Computational interpretations of Linear Logic
– Abramsky
- 1993
|
|
207
|
The lazy lambda calculus
– Abramsky
- 1990
|
|
173
|
A calculus of mobile processes, parts
– Milner, Parrow, et al.
- 1992
|
|
170
|
A powerdomain construction
– Plotkin
- 1976
|
|
164
|
The Formal Semantics of Programming Languages: An Introduction
– Winskel
- 1993
|
|
156
|
Lectures on a mathematical theory of Computation
– Scott
- 1981
|
|
135
|
Anytime, anywhere: Modal logics for mobile ambients
– Cardelli, Gordon
|
|
130
|
Fundamental concepts in programming languages. Unpublished lecture notes
– Strachey
- 1967
|
|
127
|
Petri nets, event structures and domains
– Nielsen, Plotkin, et al.
- 1981
|
|
126
|
J.H.: Lambda-Calculus Models of Programming Languages
– Morris
- 1968
|
|
110
|
Bisimulation fromopen maps
– Joyal, Nielsen, et al.
- 1996
|
|
106
|
Communicating and Mobile Systems: the -Calculus
– Milner
- 1999
|
|
102
|
spaces: Why is a security protocol correct
– Strand
- 1998
|
|
98
|
Scenarios: a model of non-determinate computation
– Brock, Ackerman
|
|
92
|
Linear logic, *-autonomous categories and cofree algebras
– Seely
|
|
91
|
Towords a mathematical semantics for computer languages
– Scott, Strachey
- 1971
|
|
88
|
Full abstraction for a simple parallel programming language
– Hennessy, Plotkin
- 1979
|
|
84
|
A mixed linear and non-linear logic: Proofs, terms and models
– Benton
- 1995
|
|
71
|
Strand spaces: why is a security protocol correct
– Thayer, Herzog, et al.
- 1998
|
|
60
|
Events in computation
– Winskel
- 1980
|
|
53
|
Semantics of weakening and contraction
– Jacobs
- 1994
|
|
49
|
Petri nets, event structures and domains, part 1
– Nielsen, Plotkin, et al.
- 1981
|
|
47
|
Presheaf Models for Concurrency
– Cattani
- 1999
|
|
47
|
A fully abstract denotational model for higher-order processes
– Hennessy
- 1994
|
|
44
|
Concurrent machines
– Shields
- 1985
|
|
44
|
Using information systems to solve recursive domain equations
– Larsen, Winskel
- 1991
|
|
43
|
Bisimulation for higher-order process calculi
– Sangiorgi
- 1996
|
|
43
|
Events in security protocols
– Crazzolara, Winskel
- 2001
|
|
39
|
A presheaf semantics of value-passing processes (extended abstract
– Winskel
- 1996
|
|
34
|
Mod`eles compl`etement ad'equats et stables des lambda-calculs typ'es. Th`ese de Doctorat d'Etat, Universit'e Paris VII
– Berry
- 1979
|
|
33
|
Categories for the Working Mathematician. second edn. Volume 5 of Graduate Texts in Mathematics
– Lane
- 1998
|
|
27
|
A calculus of higher-order communicating systems
– Thomsen
|
|
27
|
An Axiomatic Approach to Adequacy
– Brauner
- 1996
|
|
24
|
A relational model of non-deterministic dataflow
– Hildebrandt, Panangaden, et al.
|
|
23
|
Practical Foundations of Mathematics
– Taylor
- 1999
|
|
22
|
Categorical models of linear logic revisited
– Melli`es
- 2002
|
|
18
|
Doctrinal adjunction
– Kelly
- 1974
|
|
