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Computation, Proof, Machine by Marion Roman, Pierre Guillot, Gilles Dowek

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Chapter Ten Automated Theorem Proving

IN THE EARLY SEVENTIES, when word of Martin-Löf’s type theory and subsequent research on the subject had not yet reached computer scientists, the idea that a proof is not built solely with axioms and inference rules but also with computation rules developed in computer science – especially in a branch called “automated theorem proving.” Thus, work on type theory and work on automated theorem proving were pursued contemporaneously by two distinct schools that ignored each other – admittedly, an improvement on the behavior of the schools that developed, respectively, the theory of computability and the theory of constructivity, which abused each other. It was not until much later that the links between these ...

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