Type Refinements for Equation-Based Languages

Describing a problem in terms of a system of equations is common to many branches of science and engineering. Due to their size and complexity, constructing and solving such systems often warrants the use of computers. A class of equation-based languages has grown out of the desire to describe equation systems using the wellunderstood and mature techniques from conventional programming language theory. Just as with many conventional programming language, the correctness of equation-based programs can be, to at least some degree, mechanically verified by ensuring certain simple invariants are upheld. The existence of certain structural properties related to solvability are of particular interest. In this report we present a preliminary investigation into the role types can play in equation-based languages. We also discuss ongoing work into a novel refinement type system that is able to capture a number of simple structural properties that might be indicative of problems in a modular system of equations.