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Denotational semantics for a program logic of objects

Published online by Cambridge University Press:  17 May 2006

BERNHARD REUS  and
JAN SCHWINGHAMMER
BERNHARD REUS
Affiliation:
Department of Informatics, University of Sussex, Brighton BN1 9QH, U.K.
JAN SCHWINGHAMMER
Affiliation:
Programming Systems Lab, Saarland University, 66041 Saarbrücken, Germany
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Abstract

The object-calculus is an imperative and object-based programming language in which every object comes equipped with its own method suite. Consequently, methods need to reside in the store (‘higher-order store’), which complicates the semantics. Abadi and Leino defined a program logic for this language enriching object types by method specifications. We present a new soundness proof for their logic using denotational semantics. It turns out that denotations of store specifications are predicates defined by mixed-variant recursion. A benefit of our approach is that derivability and validity can be kept distinct. Moreover, it reveals which of the limitations of Abadi and Leino's logic are incidental design decisions and which follow inherently from the use of a higher-order store. We discuss the implications for the development of other, more expressive, program logics.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 16 , Issue 2 , April 2006 , pp. 313 - 358
Copyright
2006 Cambridge University Press

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Footnotes

This work was supported by the EPSRC under grant GR/R65190/01, ‘Programming Logics for Denotations of Recursive Objects’.