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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
The Algebraic LambdaCalculus
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2009
"... We introduce an extension of the pure lambdacalculus by endowing the set of terms with a structure of vector space, or more generally of module, over a fixed set of scalars. Terms are moreover subject to identities similar to usual pointwise definition of linear combinations of functions with value ..."
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Cited by 18 (2 self)
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with values in a vector space. We then study a natural extension of betareduction in this setting: we prove it is confluent, then discuss consistency and conservativity over the ordinary lambdacalculus. We also provide normalization results for a simple type system.
Confluence of the Coinductive LambdaCalculus
, 2001
"... The coinductive calculus co arises by a coinductive interpretation of the grammar of the standard calculus and contains nonwellfounded terms. An appropriate notion of reduction is analyzed and proven to be conuent by means of a detailed analysis of the usual Tait/MartinL of style developme ..."
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Cited by 4 (2 self)
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development argument. This yields bounds for the lengths of those joining reduction sequences that are guaranteed to exist by conuence. These bounds also apply to the wellfounded calculus.
Confluence of the Coinductive LambdaCalculus
, 2003
"... Abstract The coinductive *calculus \Lambda co arises by a coinductive interpretation of the grammar of the standard *calculus \Lambda and contains nonwellfounded *terms. An appropriate notion of reduction is analyzed and proven to be confluent by means of a detailed analysis of the usual Tait/Ma ..."
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/MartinL"of style development argument. This yields bounds for the lengths of those joining reduction sequences that are guaranteed to exist by confluence. These bounds also apply to the wellfounded *calculus, thus adding quantitative information to the classic result. Introduction Coinductive structures provide a
Twolevel Lambdacalculus
 Electron. Notes Theor. Comput. Sci
, 2009
"... Twolevel lambdacalculus is designed to provide a mathematical model of capturing substitution, also called instantiation. Instantiation is a feature of the ‘informal metalevel’; it appears pervasively in specifications of the syntax and semantics of formal languages. The twolevel lambdacalculus ..."
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Cited by 3 (2 self)
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level. In this paper we lay down the syntax of the twolevel lambdacalculus; we develop theories of freshness, alphaequivalence, and betareduction; and we prove confluence. In doing this we give nominal terms unknowns — which are level 2 variables and appear in several previous papers — a functional meaning
The LambdaCalculus with Multiplicities
, 1993
"... We introduce a refinement of the λcalculus, where the argument of a function is a bag of resources, that is a multiset of terms, whose multiplicities indicate how many copies of them are available. We show that this "λcalculus with multiplicities" has a natural functionality theory, simi ..."
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Cited by 19 (2 self)
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, similar to Coppo and Dezani's intersection type discipline. In our functionality theory the conjunction is managed in a "multiplicative" manner, according to Girard's terminology. We show that this provides an adequate interpretation of the calculus, by establishing that a term
An Illative LambdaCalculus
"... This is an approach to illative lambdacalculi via construction of an infinitary calculus in a wellfounded set theory. Created 2010/09/07 ..."
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This is an approach to illative lambdacalculi via construction of an infinitary calculus in a wellfounded set theory. Created 2010/09/07
Expressibility in the LambdaCalculus with Letrec
, 2012
"... We investigate the relationship between finite terms in λletrec, the lambda calculus with letrec, and the infinite lambda terms they express. As there are easy examples of infinite λterms that, intuitively, are not unfoldings of terms in λletrec, we consider the question: How can those infinite lam ..."
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Cited by 3 (2 self)
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We investigate the relationship between finite terms in λletrec, the lambda calculus with letrec, and the infinite lambda terms they express. As there are easy examples of infinite λterms that, intuitively, are not unfoldings of terms in λletrec, we consider the question: How can those infinite
..., Constructive Reals and lambdaCalculus
, 1999
"... Contents 0 Introduction 5 1 HA # and constructive reals 7 1.1 HA # (9.1.1  9.1.14) . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 #terms in HA # . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.2 The theories E HA # , I HA # . . . . . . . . . . . . . . . 12 1.1.3 Em ..."
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Contents 0 Introduction 5 1 HA # and constructive reals 7 1.1 HA # (9.1.1  9.1.14) . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 #terms in HA # . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.2 The theories E HA # , I HA # . . . . . . . . . . . . . . . 12 1.1.3 Embedding of HA in HA # . . . . . . . . . . . . . . . . . . 13 1.2 Constructive real numbers (5.1  5.4, 6.1) . . . . . . . . . . . . . 15 1.2.1 Introduction of Z in HA, HA # (5.1.1) . . . . . . . . . . . 15 1.2.2 Introduction of Q in HA, HA # (5.1.1) . . . . . . . . . . . 15 1.2.3 Principal ideas for embedding R into HA # (5.1.2) . . . . . 16 1.2.4 Theory in which the following can be formalized . . . . . 17 1.2.5 Introduction of<F13.3
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