Explaining algebraic theory with functional programs


Jeroen Fokker, Explaining Algebraic Theory with Functional Programs.
In: Functional Programming Languages in Education, Proceedings of the first international symposium FPLE'95 in Nijmegen, the Netherlands, december 1995. (Pieter Hartel and Rinus Plasmeijer, eds).


A hierarchy of six important structures from abstract algebra (groups, rings, fields etc.) is introduced as Gofer class definitions and laws about them. Many instance declarations are provided, explaining the algebraic construction of integers, quotients, adding $i$, function spaces, polynomials, and matrices. The definitions include generalized implementations of polynomial division and matrix inversion. Monadic parsers are provided for all constructs discussed. As an application, a one-line program is given for calculating the eigenvalue equation of a matrix.

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