Karl-Heinz Pennemann

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

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.

Constraints and Application Conditions: From Graphs to High-Level Structures

Graph constraints and application conditions are most important for graph grammars and transformation systems in a large variety of application areas. Although different approaches have been presented in the literature already there is no adequate theory up to now which can be applied to different kinds of graphs and high-level structures. In this paper, we introduce an improved notion of graph constraints and application conditions and show under what conditions the basic results can be extended from graph transformation to high-level replacement systems. In fact, we use the new framework of adhesive HLR categories recently introduced as combination of HLR systems and adhesive categories. Our main results are the transformation of graph constraints into right application conditions and the transformation from right to left application conditions in this new framework.

Nested constraints and application conditions for high-level structures

Constraints and application conditions are most important for transformation systems in a large variety of application areas. In this paper, we extend the notion of constraints and application conditions to nested ones and show that nested constraints can be successively transformed into nested right and left application conditions.

Weakest preconditions for high-level programs

In proof theory, a standard method for showing the correctness of a program w.r.t. given pre- and postconditions is to construct a weakest precondition and to show that the precondition implies the weakest precondition. In this paper, graph programs in the sense of Habel and Plump 2001 are extended to programs over high-level rules with application conditions, a formal definition of weakest preconditions for high-level programs in the sense of Dijkstra 1975 is given, and a construction of weakest preconditions is presented.

Development of Correct Graph Transformation Systems

A major goal of this thesis is the ability to determine the correctness of graphical specifications consisting of a graph precondition, a graph program and graph postcondition. According to Dijkstra, the correctness of program specifications can be shown by constructing a weakest precondition of the program relative to the postcondition and checking whether the precondition implies the weakest precondition. With the intention of tool support, we investigate the construction of weakest graph preconditions, consider fragments of graph conditions, for which the implication problem is decidable, and investigate an approximative solution of said problem in the general case. All research is done within the framework of adhesive high-level replacement categories. Therefore, the results will be applicable to different kinds of transformation systems and petri nets.

Resolution-Like Theorem Proving for High-Level Conditions

The tautology problem is the problem to prove the validity of statements. In this paper, we present a calculus for this undecidable problem on graphical conditions, prove its soundness, investigate the necessity of each deduction rule, and discuss practical aspects concerning an implementation. As we use the framework of weak adhesive HLR categories, the calculus is applicable to a number of replacement capable structures, such as Petri-Nets, graphs or hypergraphs.

Satisfiability of high-level conditions

In this paper, we consider high-level structures like graphs, Petri nets, and algebraic specifications and investigate two kinds of satisfiability of conditions and two kinds of rule matching over these structures. We show that, for weak adhesive HLR categories with class

An Algorithm for Approximating the Satisfiability Problem of High-level Conditions

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ENFORCe: A System for Ensuring Formal Correctness of High-level Programs

of all morphisms and a class

Type Checking C++ Template Instantiation by Graph Programs

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