Pattern Calculus

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Over time, basic research leads to specialization, with increasingly narrow topics addressed by focused communities publishing in confined workshops and conferences. The programming languages community has splintered into sub-communities tackling different aspects and paradigms, such as functional, imperative, relational, and object-oriented programming. Few individuals maintain a broader perspective, and even fewer step back to understand the fundamental principles, their interrelations, and their larger context. The pattern calculus emerges from a thorough re-examination of a 50-year development, aiming to unify different programming styles and paradigms under the concept that computation is essentially pattern matching. This work systematically presents and evaluates the power of pattern matching as a guiding paradigm for programming. Patterns are dynamically generated, discovered, passed, applied, and adapted through pattern matching and rewriting technology, allowing for elegant connections between functions and data structures. While pattern matching is not a novel concept—being foundational to term rewriting and incorporated in functional programming languages like Standard ML—it has not previously been explored as the basis for a unifying framework in programming.