Embedded languages for origami-based geometry

Abstract

Embedded languages have been used to support compositional descriptions for various domains. In this paper, we look at the domain of paper folding, or Origami-based geometry, in which sequences of paper folding are used to describe points and lines on the plane. Based on seven basic origami axioms, we design and develop an embedded domain specific language for the descriptions of such constructions in Haskell. We argue that the embedded language approach, that is composing a model using the basic constructors in the domain specific language, gives a compositional and concise way to describe Origami models. We look into analysis, manipulation and generation of origami models using this approach, including textual explanations of models, analysis of models to discover inherent preconditions (or constraints) in a description and basic animation of the folding of a model. Finally, we look into the tagging of blocks within a construction, enabling different evaluations at various levels of abstraction according to the user’s knowledge of Origami.