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Richard Zippel

Senior Research Associate

PhD MIT, 1979

My research focuses on representing scientific knowledge and making these representations easy to manage and use. Recently, we developed tools that allow scientists and engineers to specify computations in terms of mathematical and geometric constraints and, using a toolkit of program transformations, convert the specifications into executable code. The constraints take the form of algebraic and differential equations, and the toolkit's transformations capture familiar mathematical techniques like the Runge-Kutta method for numerically solving initial value

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problems. This higher level approach to software development dramatically reduces the amount of code and time required developing a scientific computation, but it introduces a number of challenging and difficult problems in programming languages.

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 a number of new challenges to the language's type system as well as new opportunities for deductive reasoning, which we are pursuing in concert with B. Constable's Nuprl project.

We are combining all these tools using an interchange formalism called the MathBus. The MathBus tools allow one to represent a very wide range of mathematical objects and pass them freely between programs written in different languages. MathBus objects can be placed in mail messages, in databases, and on Web pages without losing their mathematical semantics. Thus, one can cut a MathBus equation from a Web page (where it has two-dimensional display) and paste it into a computer algebra system like Maple or Mathematica. This array of tools and technologies allows one to represent and manipulate scientific and engineering knowledge in a freer and semantic richer fashion than previously possible.

Professional Activities

  • Editorial Boards: J. Symbolic Computation; ACM Trans. Mathematical Software

  • Referee/Reviewer: NSF, Information and Computation

  • DARPA ISAT Complex Systems Study Group

  • INRIA Research Review Committee

  • A constraint based scientific programming language. Computer Science, Tel Aviv Univ., Tel Aviv, Israel, Feb. 1, 1998.

  • Problem solving with symbolic systems, Weiz_mann Inst. Science, Rehovot, Israel, June 23, 1998.


Zero testing of algebraic functions. IPL 61 (1997), 63-67.