PLDI '91 Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Types and programming languages
Types and programming languages
PADL '03 Proceedings of the 5th International Symposium on Practical Aspects of Declarative Languages
A Debugging Scheme for Declarative Equation Based Modeling Languages
PADL '02 Proceedings of the 4th International Symposium on Practical Aspects of Declarative Languages
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Determining over- and under-constrained systems of equations using structural constraint delta
Proceedings of the 5th international conference on Generative programming and component engineering
Towards a formal semantics for a structurally dynamic noncausal modelling language
TLDI '12 Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation
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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.