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Recurrent Construction of MacWilliams and Chebyshev Matrices

Gogin N., Hirvensalo M.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

93-110

We give two recursive expressions for both MacWilliams and Chebyshev matrices. The expressions give rise to simple recursive algorithms for constructing the matrices. In order to derive the second recursion for the Chebyshev matrices we find out the Krawtchouk coefficients of the discrete Chebyshev polynomials, a task interesting on its own.

Proof Methods for Corecursive Programs

Gibbons J., Hutton G.

Fundamenta Informaticae

2005

Vol. 66, nr 4

353--366

Recursion is a well-known and powerful programming technique, with a wide variety of applications. The dual technique of corecursion is less well-known, but is increasingly proving to be just as useful. This article is a tutorial on the four main methods for proving properties of corecursive programs: fixpoint induction, the approximation (or take) lemma, coinduction, and fusion.

UPSILON: Universal Programming System with Incomplete Lazy Object Notation

Postow B., Regan K., Smith C.H.

Fundamenta Informaticae

2002

Vol. 50, nr 3,4

325-359

This paper presents a new model of computation that differs from prior models in that it emphasizes data over flow control, has no named variables and has an object-oriented flavor. We prove that this model is a complete and confluent acceptable programming system and has a usable type theory. A new data synchronization primitive is introduced in order to achieve the above properties. Subtle variations of the model are shown to fall short of having all these necessary properties.