Evident logic
نویسنده
چکیده
Many logical systems justify their consistency via proofs of cut elimination or normalization. However, these metatheoretic proofs inevitably use a transfinite induction which cannot be proved wellfounded within the system itself. We present evident logic, a logical system with a normalization proof which does not require any induction that is stronger than what is available within the logical system itself. Via the Curry-Howard correspondence, this system may also be viewed a programming language for very efficient computations. We provide a typechecker and normalizer within Coq; all programs normalize in time constant with respect to their length. We discuss the potential advantages of working with weak foundations.
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