Explaining Algebraic Theory with Functional Programs

Abstract. 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.

• Type: Conference
• Year: 1995
• Where: FPLE
• Authors: Jeroen Fokker
• Keywords: Abstract Algebra, FPLE 1995, Gofer Class Definitions, Many Instance Declarations, Programming Languages