Pattern calculus
Computing with Functions and Structures
Over time, basic research leads to specialization, with increasingly narrow topics addressed by focused communities that publish in confined workshops and conferences, discussing incremental contributions. The programming languages community, for instance, is divided into sub-communities focusing on different paradigms like functional, imperative, relational, and object-oriented programming. Few individuals maintain a broader perspective, and even fewer strive to understand the fundamental principles, their interrelations, and their larger context. The pattern calculus emerges from a deep re-examination of a 50-year development, aiming to unify disparate programming styles and paradigms under the notion that computation is essentially pattern matching. This work systematically presents and evaluates the power of pattern matching as a guiding paradigm in programming. Patterns are dynamically generated, discovered, passed, applied, and adapted through pattern matching and rewriting technology, allowing for elegant connections between seemingly unrelated concepts like functions and data structures. While pattern matching is not new and is foundational in term rewriting and functional programming languages like Standard ML, it has not been fully explored as a unifying framework for programming.
