Modularity is a key concern in programming. However, programming languages remain limited in terms of modularity and extensibility. Small canonical problems, such as the Expression Problem (EP), illustrate some of the basic issues: the dilemma between choosing one kind of extensibility over another one in most programming languages. Other problems, such as how to express dependencies in a modular way, add up to the basic issues and remain a significant challenge.

This paper presents a new statically typed modular programming style called Compositional Programming. In Compositional Programming, there is no EP: it is easy to get extensibility in multiple dimensions (i.e. it is easy to add new variants as well as new operations). Compositional Programming offers an alternative way to model data structures that differs from both algebraic datatypes in functional programming and conventional OOP class hierarchies. We introduce four key concepts for Compositional Programming: compositional interfaces, compositional traits, method patterns, and nested trait composition. Altogether these concepts allow us to naturally solve challenges such as the Expression Problem, model attribute-grammar-like programs, and generally deal with modular programs with complex dependencies. We present a language design, called CP, which is proved to be type-safe, together with several examples and three case studies.