Third International Workshop on Variability Modelling of Software-Intensive Systems, Seville, Spain, January 28-30, 2009. Proceedings

Transformation-based program synthesis is a hallmark of automated program development. Some time ago, we discovered that the design of a program could be expressed as a matrix of transformations, where both rows and columns represented features. The technique was called Origami, as the matrix was folded in precise ways (thereby composing transformations) until a scalar was produced. This scalar defined an expression (a composition of transformations) that, when evaluated, synthesized the program. Origami generalized to n-dimensional matrices, where each axis defined a dimension of variability. But we never quite understood why Origami worked. Our research seeks principles of automated construction that can be appreciated by practitioners and that are expressed in terms of simple mathematics. This talk explains Origami by an interesting integration of diverse topics: data cubes (database technology), basic ideas from tensors and categories (mathematics), extensibility problem (programming languages), and feature interactions (software design). VaMoS'09