Proof Theory and Logic Programming by Dale Miller (.PDF)+

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Proof Theory and Logic Programming: Computation as Proof Search by Dale Miller
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Overview: This book offers a principled view of programming, showing how computation arises from logic. It explores different logical and proof-theoretic systems as foundations for programming, providing a deeper understanding for readers interested in the theoretical underpinnings of computation and the logic programming paradigm. Beyond theory, the book explores practical applications, including encoding security protocols, specifying operational semantics, and static analysis of Horn clauses, demonstrating the versatility and power of this proof-theoretic approach. We establish a proof-theoretic foundation using Gentzen’s sequent calculus for logic programming languages based on first-order and higher-order classical, intuitionistic, and linear logics. This approach provides the basis for the well-known languages Prolog (employing first-order Horn clauses in classical logic) and λProlog (utilizing higher-order hereditary Harrop formulas in intuitionistic logic), as well as the linear logic programming languages Lolli and Forum. As we will illustrate, these increasingly expressive logic programming languages enable the logic programming paradigm to capture essential aspects of modular programming, higher-order programming, abstract data-types, state encapsulation, and concurrency.
Genre: Non-Fiction > Tech & Devices

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