Functional Logic Origami Programming with Open CFLP

Origami is a Japanese traditional art of paper folding. Recently, Origami became a topic of active research due to its relation to art, geometry, theorem proving, and declarative programming. It has been recognized that several interesting mathematical problems can be described in an elegant way by paper folds. In this paper we describe an origami programming methodology based on functional logic programming. We use two software components. The first one provides primitives to construct, manipulate and visualize paper folds. The second one, called Open CFLP, solves systems of equations whose operations are defined by conditional rewrite rules. We show that paper folding constructs can be expressed as systems of equations which are then solved by Open CFLP. Both components of our programming environment are implemented in Mathematica. We illustrate functional logic origami programming with some interesting examples.