Basic proof theory
Term rewriting and all that
Proving termination with multiset orderings
Communications of the ACM
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Weak Orthogonality Implies Confluence: The Higher Order Case
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
LJQ: a strongly focused calculus for intuitionistic logic
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
The ILTP library: benchmarking automated theorem provers for intuitionistic logic
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with terms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which gave different arguments for Cut-admissibility suggesting weakly normalising procedures for Cut-elimination, our main reduction system and all its variations are strongly normalising, with the variations corresponding to different optimisations, some of them with good properties such as confluence.