Commutation, transformation, and termination
Proc. of the 8th international conference on Automated deduction
Proofs and types
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Combining algebraic rewriting, extensional lambda calculi, and fixpoints
ICALP '94 Selected papers from the 21st international colloquium on Automata, languages and programming
Term rewriting and all that
On the Power of Simple Diagrams
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Rewriting with Extensional Polymorphic Lambda-Calculus
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Isomorphisms of simple inductive types through extensional rewriting
Mathematical Structures in Computer Science
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A common way to show the termination of the union of two abstract reduction systems, provided both systems terminate, is to prove that they enjoy a specific property (some sort of ‘commutation’ for instance). This specific property is actually used to show that, for the union not to terminate, one of the systems must itself be non-terminating, which leads to a contradiction. Unfortunately, the property may be impossible to prove because some of the objects that are reduced do not enjoy an adequate form. Hence the purpose of this paper is threefold: –First, it introduces an operator enabling us to insert a reduction step on such an object, and therefore to change its shape, while still preserving the ability to use the property. Of course, some new properties will need to be verified.–Second, as an instance of our technique, the operator is applied to relax a well-known lemma stating the termination of the union of two termination abstract reduction systems.–Finally, this lemma is applied in a peculiar and then in a more general way to show the termination of some lambda calculi with inductive types augmented with specific reductions dealing with:(i)copies of inductive types;(ii)the representation of symmetric groups.