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1. First-order terms and representations of data; 2. First-order horn clauses; 3. First-order hereditary Harrop formulas; 4. Typed lambda terms and formulas; 5. Using quantification at higher-order types; 6. Mechanisms for structuring large programs; 7. Computations over -terms; 8. Unification of -terms; 9. Implementing proof systems; 10. Computations over functional programs; 11. Encoding a process calculus language; Appendix: the Teyjus system.
A programming language based on a higher-order logic provides a declarative approach to capturing computations involving types, proofs and other syntactic structures.
Dale Miller is currently Director of Research at INRIA-Saclay where he is the Scientific Leader of the Parsifal team. He has been a professor at the University of Pennsylvania, Pennsylvania State University and the Ecole Polytechnique, France. Miller is the Editor-in-Chief of the ACM Transactions on Computational Logic and has editorial duties on several other journals. He was awarded an ERC Advanced Investigators Grant in 2011 and is the recipient of the 2011 Test-of-Time award of the IEEE Symposium on Logic in Computer Science. He works on many topics in the general area of computational logic, including automated reasoning, logic programming, proof theory, unification theory, operational semantics and, most recently, proof certificates. Gopalan Nadathur is Professor of Computer Science at the University of Minnesota. He has previously held faculty appointments at Duke University, the University of Chicago and Loyola University Chicago. Nadathur's research interests span the areas of computational logic, programming languages and logic programming. His work has been regularly funded by the National Science Foundation and has appeared in publications such as the Journal of the Association of Computing Machinery, Information and Computation, Logic and Computation, the Journal of Automated Reasoning and Theory and Practice of Logic Programming.
'... I am impressed with the depth of the discussion and the clearly well-produced book. The authors have argued successfully for the power and versatility of the fundamental ideas underlying Prolog.' Sara Kalvala, Computing Reviews