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Static Balance Checking for First-Class Modular Systems of Equations

By Henrik Nilsson

Abstract

Abstract. Characterising a problem in terms of a system of equations is common to many branches of science and engineering. Due to their size, such systems are often described in a modular fashion by composition of individual equation system fragments. Checking the balance between the number of variables (unknowns) and equations is a common approach to early detection of mistakes that might render such a system unsolvable. However, currentapproaches tomodular balance checkinghaveanumber of limitations. This paper investigates a more flexible approach that in particular makes it possible to treat equation system fragments as true first-class entities. The central idea is to record balance information in the type of an equation fragment. This information can then be used to determine if individual fragments are well formed, and if composing fragments preserves this property. The type system presented in this paperisdevelopedinthecontextofFunctionalHybridModelling (FHM). However, the key ideas are in no way specific to FHM, but should be applicable to any language featuring a notion of modular systems of equations. Key words: Systems of equations; equation-based, non-causal modelling; first-class components; equation-variable balance; structural analysis

Topics: linear constraints, refinement
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.363.8157
Provided by: CiteSeerX
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