Richard Zippel
Senior Research Associate
Ph.D. MIT, 1979

My research focuses on making mathematical descriptions easier to manage and easier to use. Recently we have developed tools that allow scientists and engineers to describe desired computations in terms of differential equations and geometries, and then, using a toolkit of program transformation, convert these specifications into executable code. The transformations in the toolkit correspond to familar mathematical techniques like Runge-Kutta methods. This alternative to expressing these techniques as subroutine libraries has made the techniques more widely useful, but has introduced a number of challenging and difficult programming language problems.

Another component of this toolkit is a computer algebra substrate, called Weyl, that extends the data structures available in Common Lisp to include objects like polynomials, matrices, rational functions, rings, vector spaces, and ideals. The introduction of these new objects into a programming language provides additional challenges to the language's type system and provides new opportunities for deductive reasoning, which we are pursuing in concert with Bob Constable's Nuprl project.

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