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ORDERED MODELS OF THE LAMBDA CALCULUS ∗
, 2013
"... Vol. 9(4:21)2013, pp. 1–29 www.lmcsonline.org ..."
An Invariant Cost Model for the Lambda Calculus
, 2005
"... We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties ..."
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We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial
KripkeStyle Models for Typed Lambda Calculus
 Annals of Pure and Applied Logic
, 1996
"... The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripkestyle models. In categorical terms, our Kripke ..."
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Cited by 50 (3 self)
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The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripkestyle models. In categorical terms, our Kripke
SetTheoretical and Other Elementary Models of the lambdacalculus
 Theoretical Computer Science
, 1993
"... Part 1 of this paper is the previously unpublished 1972 memorandum [43], with editorial changes and some minor corrections. Part 2 presents what happened next, together with some further development of the material. The first part begins with an elementary settheoretical model of the ficalculus. F ..."
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Cited by 45 (0 self)
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Part 1 of this paper is the previously unpublished 1972 memorandum [43], with editorial changes and some minor corrections. Part 2 presents what happened next, together with some further development of the material. The first part begins with an elementary settheoretical model of the ficalculus
Formalising a Model of the lambdacalculus in HOLST
, 1994
"... Most new theorem provers implement strong and complicated type theories which eliminate some of the limitations of simple type theories such as the HOL logic. A more accessible alternative might be to use a combination of set theory and simple type theory as in HOLST which is a version of the HOL s ..."
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Cited by 3 (0 self)
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system supporting a ZFlike set theory in addition to higher order logic. This paper presents a case study on the use of HOLST to build a model of the calculus by formalising the inverse limit construction of domain theory. This construction is not possible in the HOL system itself, or in simple type
A Syntactic Characterization of the Equality in some Models for the Lambda Calculus
 J. London Math. Soc
, 1976
"... An equality relation on the terms of the Acalculus is an equivalence relation closed under the (syntactical) operations of application and Aabstraction. We may distinguish between syntactic and semantic ways of introducing equality relations, /^equality is introduced syntactically; it is the leas ..."
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Cited by 52 (0 self)
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An equality relation on the terms of the Acalculus is an equivalence relation closed under the (syntactical) operations of application and Aabstraction. We may distinguish between syntactic and semantic ways of introducing equality relations, /^equality is introduced syntactically
Parallel Implementation Models for the lambdacalculus Using the Geometry of Interaction
"... An examination of Girard's execution formula suggests implementations of the Geometry of Interaction at the syntactic level. In this paper we limit our scope to groundtype terms and study the parallel aspects of such implementations, by introducing a family of abstract machines which can be dir ..."
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Cited by 6 (0 self)
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be directly implemented. These machines address all the important implementation issues such as the choice of an interthread communication model, and allow to incorporate specic strategies for dividing the computation of the execution path into smaller tasks. 1
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 applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model. 1 Introduction This paper
Optimality and Inefficiency : What Isn't a Cost Model of the Lambda Calculus?
 In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming
, 1996
"... We investigate the computational efficiency of the sharing graphs of Lamping [Lam90], Gonthier, Abadi, and L'evy [GAL92], and Asperti [Asp94], designed to effect socalled optimal evaluation, with the goal of reconciling optimality, efficiency, and the clarification of reasonable cost models f ..."
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Cited by 21 (2 self)
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for the calculus. Do these graphs suggest reasonable cost models for the calculus? If they are optimal, are they efficient? We present a brief survey of these optimal evaluators, identifying their common characteristics, as well as their shared failures. We give a lower bound on the efficiency of sharing graphs
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