Basic proof theory
Information and Computation
A Symmetric Lambda Calculus for "Classical" Program Extraction
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
On equivalence and canonical forms in the LF type theory
ACM Transactions on Computational Logic (TOCL)
Alpha-structural recursion and induction
Journal of the ACM (JACM)
Strong Normalisation of Cut-Elimination in Classical Logic
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Mechanizing the Metatheory of LF
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Barendregt's Variable Convention in Rule Inductions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
The language X: circuits, computations and classical logic
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
A recursion combinator for nominal datatypes implemented in Isabelle/HOL
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Mechanizing the metatheory of LF
ACM Transactions on Computational Logic (TOCL)
Quotients revisited for Isabelle/HOL
Proceedings of the 2011 ACM Symposium on Applied Computing
General bindings and alpha-equivalence in nominal Isabelle
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
A new foundation for nominal isabelle
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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Powerful proof techniques, such as logical relation arguments, have been developed for establishing the strong normalisation property of term- rewriting systems. The first author used such a logical relation argument to establish strong normalising for a cut-elimination procedure in classical logic. He presented a rather complicated, but informal, proof establishing this property. The difficulties in this proof arise from a quite subtle substitution operation, which implements proof transformation that permute cuts over other inference rules. We have formalised this proof in the theorem prover Isabelle/HOL using the Nominal Datatype Package, closely following the informal proof given by the first author in his PhD-thesis. In the process, we identified and resolved a gap in one central lemma and a number of smaller problems in others. We also needed to make one informal definition rigorous. We thus show that the original proof is indeed a proof and that present automated proving technology is adequate for formalising such difficult proofs.