Modular Design of Domain-Specific Languages Using Splittings of Catamorphisms

Abstract

Language oriented programming is an approach to software composition based on domain specific languages (DSL) dedicated to specific aspects of an application domain. In order to combine such languages we embed them into a host language (namely Haskell, a strongly typed higher-order lazy functional language). A DSL is then given by an algebraic type, whose operators are the constructors of abstract syntax trees. Such a multi-sorted signature is associated to a polynomial functor. An algebra for this functor tells us how to interpret the programs. Using Bekić's Theorem we define a modular decomposition of algebras that leads to a class of parametric multi-sorted signatures, associated with regular functors, allowing for the modular design of DSLs.