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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 pc ..."
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Cited by 17 (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
Filter Models and Easy Terms
, 2001
"... We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by n ..."
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Cited by 14 (3 self)
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We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by nonextensional lter models.
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 13 (3 self)
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Dipartimento di Informatica Universit`a di Venezia
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
SN Combinators and Partial Combinatory Algebras
"... . We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable iff it is sn. We then prove the soundness and completeness for the class of partial combinatory algebras. Let F be the class of nonempty filters which consist of types. Then F is an ..."
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. We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable iff it is sn. We then prove the soundness and completeness for the class of partial combinatory algebras. Let F be the class of nonempty filters which consist of types. Then F is an extensional nontotal partial combinatory algebra. Furthermore, it validates the strongest consistent equality of the set of sn terms of combinatory logic. By F , we can solve BethkeKlop's question; "find a suitable representation of the finally collapsed partial combinatory algebra of P ". Here, P is a partial combinatory algebra, and is the set of closed sn terms of combinatory logic modulo the inherent equality. Our solution is the following: the finally collapsed partial combinatory algebra of P is representable in F . To be more precise, it is isomorphically embeddable into F . 1 Introduction Combinatory logic (cl, for short) is a simple rewriting system where the terms (clterms, fo...