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Static Balance Checking for First-Class Modular Systems of Equations

  • John Capper
  • Henrik Nilsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6546)

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, current approaches to modular balance checking have a number 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 paper is developed in the context of Functional Hybrid Modelling (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.

Keywords

Systems of equations equation-based non-causal modelling first-class components equation-variable balance structural analysis linear constraints refinement types 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • John Capper
    • 1
  • Henrik Nilsson
    • 1
  1. 1.Functional Programming Laboratory, School of Computer ScienceUniversity of NottinghamUnited Kingdom

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