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Correctness of high-level transformation systems relative to nested conditions†

Published online by Cambridge University Press:  01 April 2009

ANNEGRET HABEL  and
KARL-HEINZ PENNEMANN
ANNEGRET HABEL
Affiliation:
Computing Science, D-26111 Oldenburg, Germany Email: [email protected]; [email protected]
KARL-HEINZ PENNEMANN
Affiliation:
Computing Science, D-26111 Oldenburg, Germany Email: [email protected]; [email protected]
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Abstract

In this paper we introduce the notions of nested constraints and application conditions, short nested conditions. For a category associated with a graphical representation such as graphs, conditions are a graphical and intuitive, yet precise, formalism that is well suited to describing structural properties. We show that nested graph conditions are expressively equivalent to first-order graph formulas. A part of the proof includes transformations between two satisfiability notions of conditions, namely -satisfiability and -satisfiability. We consider a number of transformations on conditions that can be composed to construct constraint-guaranteeing and constraint-preserving application conditions, weakest preconditions and strongest postconditions. The restriction of rule applications by conditions can be used to correct transformation systems by pruning transitions leading to states violating given constraints. Weakest preconditions and strongest postconditions can be used to verify the correctness of transformation systems with respect to pre- and postconditions.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Issue 2 , April 2009 , pp. 245 - 296
Copyright
Copyright © Cambridge University Press 2009

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