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Simple easy terms
 Intersection Types and Related Systems, volume 70 of Electronic Notes in Computer Science
, 2002
"... Dipartimento di Informatica Universit`a di Venezia ..."
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Cited by 12 (4 self)
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Dipartimento di Informatica Universit`a di Venezia
Collapsing Partial Combinatory Algebras
 HigherOrder Algebra, Logic, and Term Rewriting
, 1996
"... Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We ..."
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Cited by 12 (2 self)
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Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We establish several facts concerning final collapses (maximal identification of elements). `En passant' we find another example of a pca that cannot be extended to a total one. 1
Meaningless Terms in Rewriting
, 1999
"... We present an axiomatic approach to the concept of meaninglessness in finite and transfinite term rewriting and lambda calculus. We justify our axioms in several ways. They can be intuitively justified from the viewpoint of rewriting as computation. They are shown to imply important properties of me ..."
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We present an axiomatic approach to the concept of meaninglessness in finite and transfinite term rewriting and lambda calculus. We justify our axioms in several ways. They can be intuitively justified from the viewpoint of rewriting as computation. They are shown to imply important properties of meaninglessness: genericity of the class of meaningless terms, confluence modulo equality of meaningless terms, the consistency of equating all meaningless terms, and the construction of Bohm trees and models of rewrite systems. Finally, we show that they can be easily verified for many existing notions of meaninglessness and easily refuted for some notions that are known not to be good characterizations of meaninglessness. 1 Introduction The concept of a meaningless term in a rewrite system originates with the lambda calculus [Bar84, Bar92]. There exist terms in the lambda calculus that, in certain precisely definable senses, cannot be distinguished from each other and cannot contribute info...
Problem 19
"... Abstract. A closed λterm M is easy if, for any other closed term N, the lambda theory generated by M = N is consistent, while it is simple easy if, given an arbitrary intersection type τ, one can find a suitable preorder on types which allows to derive τ for M. Simple easiness implies easiness. Th ..."
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Abstract. A closed λterm M is easy if, for any other closed term N, the lambda theory generated by M = N is consistent, while it is simple easy if, given an arbitrary intersection type τ, one can find a suitable preorder on types which allows to derive τ for M. Simple easiness implies easiness. The question whether easiness implies simple easiness constitutes Problem 19 in the TLCA list of open problems. In this paper we negatively answer the question providing a nonempty cor.e. (complement of a recursively enumerable) set of easy, but non simple easy, λterms. Key words: Lambda calculus, easy terms, simple easy terms, filter models 1