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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 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
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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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
The Partial LambdaCalculus
, 1988
"... This thesis investigates various formal systems for reasoning about partial functions or partial elements, with particular emphasis on lambda calculi for partial functions. Beeson's (intuitionistic) logic of partial terms (LPT) is taken as the basic formal system and some of its metamathematica ..."
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Cited by 35 (4 self)
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of LPT are introduced for reasoning about partial terms with a restriction operator (LPT + ¯), monotonic partial functions (monLPT), terms ( p calculus) and Yterms ( p ¯Ycalculus). The expressive powers of some (in)equational fragments are compared in LPT and its variants. Two equational formal
Games and Full Abstraction for the Lazy lambdacalculus
 In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typ ..."
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Cited by 149 (9 self)
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ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a
..., 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
Typing of Selective lambdaCalculus
, 1993
"... Record calculi have recently been a very active field of research, but its reciprocal, i.e. the use of keywords in functions, is still ignored. Selective calculus is a conservative extension of lambda calculus which, by labeling abstractions and applications, enables some form of commutation betwee ..."
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Record calculi have recently been a very active field of research, but its reciprocal, i.e. the use of keywords in functions, is still ignored. Selective calculus is a conservative extension of lambda calculus which, by labeling abstractions and applications, enables some form of commutation
OPTICS: Ordering Points To Identify the Clustering Structure
, 1999
"... Cluster analysis is a primary method for database mining. It is either used as a standalone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of ..."
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Cited by 511 (49 self)
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the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its densitybased clustering structure. This clusterordering
M.: The algebraicity of the lambdacalculus
 CoRR abs/0704.2900 (2007), http://arxiv.org/abs/0704.2900
"... Abstract. We propose a new definition for abstract syntax (with binding constructions), and, accordingly, for initial semantics and algebraicity. Our definition is based on the notion of module over a monad and its companion notion of linearity. In our setting, we give a oneline definition of an un ..."
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Cited by 2 (1 self)
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of an untyped lambdacalculus. Among untyped lambdacalculi, the initial one, the pure untyped lambdacalculus, appears as defined by two algebraic constructions (abs and the unary application app 1), together with two algebraic equations which are essentially the β and η rules. 1
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
Sharing in the weak lambdacalculus
 In Processes, Terms and Cycles: Steps on the Road
, 2005
"... Abstract. Despite decades of research in the λcalculus, the syntactic properties of the weak λcalculus did not receive great attention. However, this theory is more relevant for the implementation of programming languages than the usual theory of the strong λcalculus. In fact, the frameworks of w ..."
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Cited by 5 (1 self)
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of weak explicit substitutions, or computational monads, or λcalculus with a let statement, or supercombinators, were developed for adhoc purposes related to programming language implementation. In this paper, we concentrate on sharing of subterms in a confluent variant of the weak λcalculus. We
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