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Infinitary Lambda Calculus
, 1995
"... In a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of infinitary rewriting, the Böhm model of the lambda calculus can be seen as an infinitary term mo ..."
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Cited by 5 (1 self)
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In a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of infinitary rewriting, the Böhm model of the lambda calculus can be seen as an infinitary term
An AlphaCorecursion Principle for the Infinitary Lambda Calculus
, 2012
"... Gabbay and Pitts proved that lambdaterms up to alphaequivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitary lambdacalculus form the final coalgebra for the same functor. This allows us to give a corecursion pri ..."
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Cited by 2 (2 self)
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Gabbay and Pitts proved that lambdaterms up to alphaequivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitary lambdacalculus form the final coalgebra for the same functor. This allows us to give a corecursion
Decomposing the Lattice of Meaningless Sets in the Infinitary Lambda Calculus
"... Abstract. The notion of a meaningless set has been defined for infinitary lambda calculus axiomatically. Standard examples of meaningless sets are sets of terms that have no head normal form, the set of terms without weak head normal form and the set of rootactive terms. The collection of meaningles ..."
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Abstract. The notion of a meaningless set has been defined for infinitary lambda calculus axiomatically. Standard examples of meaningless sets are sets of terms that have no head normal form, the set of terms without weak head normal form and the set of rootactive terms. The collection
Weakening the Axiom of Overlap in Infinitary Lambda Calculus
"... In this paper we present a set of necessary and sufficient conditions on a set of lambda terms to serve as the set of meaningless terms in an infinitary bottom extension of lambda calculus. So far only a set of sufficient conditions was known for choosing a suitable set of meaningless terms to make ..."
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Cited by 4 (4 self)
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In this paper we present a set of necessary and sufficient conditions on a set of lambda terms to serve as the set of meaningless terms in an infinitary bottom extension of lambda calculus. So far only a set of sufficient conditions was known for choosing a suitable set of meaningless terms to make
Infinitary Lambda Calculus and Discrimination of Berarducci Trees
, 2001
"... Introduction In this paper we will prove equivalent an operational and a denotational semantics for lambda calculus with the rule. Both semantics are based on the 1 This paper was made possible thanks to the hospitality ETL oered in March 1999 to both Mariangiola Dezani and Paula Severi. 2 Part ..."
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Cited by 8 (4 self)
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Introduction In this paper we will prove equivalent an operational and a denotational semantics for lambda calculus with the rule. Both semantics are based on the 1 This paper was made possible thanks to the hospitality ETL oered in March 1999 to both Mariangiola Dezani and Paula Severi. 2
Under consideration for publication in Math. Struct. in Comp. Science The Infinitary Lambda Calculus of the Infinite Eta Böhm
, 2013
"... In this paper we introduce a strong form of eta reduction called etabang that we use to construct a confluent and normalising infinitary lambda calculus, of which the normal forms correspond to Barendregt’s infinite eta Böhm trees. This new infinitary perspective on the set of infinite eta Böhm tr ..."
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In this paper we introduce a strong form of eta reduction called etabang that we use to construct a confluent and normalising infinitary lambda calculus, of which the normal forms correspond to Barendregt’s infinite eta Böhm trees. This new infinitary perspective on the set of infinite eta Böhm
Computational LambdaCalculus and Monads
, 1988
"... The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the ..."
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Cited by 505 (7 self)
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The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise
Continuity and Discontinuity in Lambda Calculus
"... Abstract. This paper studies continuity of the normal form and the context operators as functions in the infinitary lambda calculus. We consider the Scott topology on the cpo of the finite and infinite terms with the prefix relation. We prove that the only continuous parametric trees are Böhm and Lé ..."
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Abstract. This paper studies continuity of the normal form and the context operators as functions in the infinitary lambda calculus. We consider the Scott topology on the cpo of the finite and infinite terms with the prefix relation. We prove that the only continuous parametric trees are Böhm
A calculus for cryptographic protocols: The spi calculus
 Information and Computation
, 1999
"... We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the ..."
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Cited by 919 (55 self)
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We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols
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