García-Pérez, Á. and Nogueira, P. - No solvable lambda-value term left behind

lmcs:1644 - Logical Methods in Computer Science, June 30, 2016, Volume 12, Issue 2
No solvable lambda-value term left behind

Authors: García-Pérez, Á. and Nogueira, P.

In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated without loss of consistency. There is a definition of solvability for the lambda-value calculus, called v-solvability, but it is not synonymous with operational relevance, some lambda-value normal forms are unsolvable, and unsolvables cannot be consistently equated. We provide a definition of solvability for the lambda-value calculus that does capture operational relevance and such that a consistent proof-theory can be constructed where unsolvables are equated attending to the number of arguments they take (their "order" in the jargon). The intuition is that in lambda-value the different sequentialisations of a computation can be distinguished operationally. We prove a version of the Genericity Lemma stating that unsolvable terms are generic and can be replaced by arbitrary terms of equal or greater order.


Source : oai:arXiv.org:1604.08383
DOI : 10.2168/LMCS-12(2:12)2016
Volume: Volume 12, Issue 2
Published on: June 30, 2016
Submitted on: August 11, 2016
Keywords: Computer Science - Logic in Computer Science,F.4.1


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