Restructuring a concurrent refinement algebra
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In order to allow specifications to be combined, the algebra...
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| creator | Hayes, Ian J Meinicke, Larissa A Evangelou-Oost, Naso |
| description | The concurrent refinement algebra has been developed to support
rely/guarantee reasoning about concurrent programs. The algebra supports atomic
commands and defines parallel composition as a synchronous operation, as in
Milner's SCCS. In order to allow specifications to be combined, the algebra
also provides a weak conjunction operation, which is also a synchronous
operation that shares many properties with parallel composition. The three main
operations, sequential composition, parallel composition and weak conjunction,
all respect a (weak) quantale structure over a lattice of commands. Further
structure involves combinations of pairs of these operations:
sequential/parallel, sequential/weak conjunction and parallel/weak conjunction,
each pair satisfying a weak interchange law similar to Concurrent Kleene
Algebra. Each of these pairs satisfies a common biquantale structure.
Additional structure is added via compatible sets of commands, including tests,
atomic commands and pseudo-atomic commands. These allow stronger (equality)
interchange and distributive laws. This paper describes the result of
restructuring the algebra to better exploit these commonalities. The algebra is
implemented in Isabelle/HOL. |
| doi_str_mv | 10.48550/arxiv.2405.05690 |
| format | Article |
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rely/guarantee reasoning about concurrent programs. The algebra supports atomic
commands and defines parallel composition as a synchronous operation, as in
Milner's SCCS. In order to allow specifications to be combined, the algebra
also provides a weak conjunction operation, which is also a synchronous
operation that shares many properties with parallel composition. The three main
operations, sequential composition, parallel composition and weak conjunction,
all respect a (weak) quantale structure over a lattice of commands. Further
structure involves combinations of pairs of these operations:
sequential/parallel, sequential/weak conjunction and parallel/weak conjunction,
each pair satisfying a weak interchange law similar to Concurrent Kleene
Algebra. Each of these pairs satisfies a common biquantale structure.
Additional structure is added via compatible sets of commands, including tests,
atomic commands and pseudo-atomic commands. These allow stronger (equality)
interchange and distributive laws. This paper describes the result of
restructuring the algebra to better exploit these commonalities. The algebra is
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rely/guarantee reasoning about concurrent programs. The algebra supports atomic
commands and defines parallel composition as a synchronous operation, as in
Milner's SCCS. In order to allow specifications to be combined, the algebra
also provides a weak conjunction operation, which is also a synchronous
operation that shares many properties with parallel composition. The three main
operations, sequential composition, parallel composition and weak conjunction,
all respect a (weak) quantale structure over a lattice of commands. Further
structure involves combinations of pairs of these operations:
sequential/parallel, sequential/weak conjunction and parallel/weak conjunction,
each pair satisfying a weak interchange law similar to Concurrent Kleene
Algebra. Each of these pairs satisfies a common biquantale structure.
Additional structure is added via compatible sets of commands, including tests,
atomic commands and pseudo-atomic commands. These allow stronger (equality)
interchange and distributive laws. This paper describes the result of
restructuring the algebra to better exploit these commonalities. The algebra is
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rely/guarantee reasoning about concurrent programs. The algebra supports atomic
commands and defines parallel composition as a synchronous operation, as in
Milner's SCCS. In order to allow specifications to be combined, the algebra
also provides a weak conjunction operation, which is also a synchronous
operation that shares many properties with parallel composition. The three main
operations, sequential composition, parallel composition and weak conjunction,
all respect a (weak) quantale structure over a lattice of commands. Further
structure involves combinations of pairs of these operations:
sequential/parallel, sequential/weak conjunction and parallel/weak conjunction,
each pair satisfying a weak interchange law similar to Concurrent Kleene
Algebra. Each of these pairs satisfies a common biquantale structure.
Additional structure is added via compatible sets of commands, including tests,
atomic commands and pseudo-atomic commands. These allow stronger (equality)
interchange and distributive laws. This paper describes the result of
restructuring the algebra to better exploit these commonalities. The algebra is
implemented in Isabelle/HOL.</abstract><doi>10.48550/arxiv.2405.05690</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Logic in Computer Science |
| title | Restructuring a concurrent refinement algebra |
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