An embedded geometrical language in Haskell : construction, visualisation, proof

Abstract

Geometric constructions based on compass and straight-edge have been thoroughly studied and explored. In this paper, we present a language embedded in Haskell, to describe, manipulate and analyse such constructions. The use of embedded languages has been explored in various specialised domains, and have been shown to be an excellent frontend to describe such specialised programs, enabling, for instance, the description of families of constructions as functions in the host language, which produce different specialised programs based on input parameters. In particular, we are interested, not only in providing a framework within which one may describe a construction and families of similar constructions in an algorithmic fashion, but also in providing facilities to both test and verify certain properties of constructions, such as equivalence of constructions, or equality of angles and distances in a construction.