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Label-selective λ-calculus syntax and confluence

Hassan Aït-Kaci, Jacques Garrigue
1995 Theoretical Computer Science  
-calculus, called label-selective ).-calculus, in which arguments of functions are selected by labels. The set of labels combines symbolic keywords with numeric positions.  ...  -calculus is conservative, in the sense that when we restrict ourselves to using only one label, it coincides with ).-calculus. The main result of this paper is the proof that the label-selective ).  ...  Also, we are grateful to Patrick Baudelaire and Jean-Christophe Patat for kindly and thoroughly proofreading our manuscript.  ... 
doi:10.1016/0304-3975(95)00072-5 fatcat:6yxxbqyhfvht7gszxjxrnsryga

Page 2535 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
Sauro Tulipani (I-CAM; Camerino) 95e:03043 '03B40 Ait-Kaci, Hassan; Garrigue, Jacques (J-TOKYO-G; Bunkyo) Label-selective 4-calculus syntax and confluence.  ...  Summary: “We introduce an extension of A-calculus, called label- selective A-calculus, in which arguments of functions are selected by labels.  ... 

The transformation calculus [chapter]

Jacques Garrigue
1995 Lecture Notes in Computer Science  
This calculus remains very close to lambda-calculus, and keeps most of its properties.  ...  We prove here confluence, strong-normalization in presence of a typing system, and present a model of the typed calculus.  ...  By confluence of selective λ-calculus, we have T such that T r(P ) * → T and T r(Q) * → T .  ... 
doi:10.1007/3-540-60692-0_46 fatcat:j4ztlaffbngrhodhzmf3wof6w4

A non-deterministic call-by-need lambda calculus

Arne Kutzner, Manfred Schmidt-Schauß
1999 SIGPLAN notices  
In this paper we present a non-deterministic call-by-need (untyped) lambda calculus X,d with a constant choice and a let-syntax that models sharing.  ...  Our main result is that Xnd has the nice operational properties of the standard lambda calculus: confluence on sets of expressions, and normal order reduction is sufficient to reach head normal form.  ...  Abstract In this paper we present a non-deterministic call-by-need (untyped) lambda calculus X,d with a constant choice and a let-syntax that models sharing.  ... 
doi:10.1145/291251.289462 fatcat:ripsbkpct5apjepkaxwbhulmsu

A non-deterministic call-by-need lambda calculus

Arne Kutzner, Manfred Schmidt-Schauß
1998 Proceedings of the third ACM SIGPLAN international conference on Functional programming - ICFP '98  
In this paper we present a non-deterministic call-by-need (untyped) lambda calculus X,d with a constant choice and a let-syntax that models sharing.  ...  Our main result is that Xnd has the nice operational properties of the standard lambda calculus: confluence on sets of expressions, and normal order reduction is sufficient to reach head normal form.  ...  Abstract In this paper we present a non-deterministic call-by-need (untyped) lambda calculus X,d with a constant choice and a let-syntax that models sharing.  ... 
doi:10.1145/289423.289462 dblp:conf/icfp/KutznerS98 fatcat:33hsufnlkfc3jjst4j5myksctm

A Mechanized Model of the Theory of Objects [chapter]

Ludovic Henrio, Florian Kammüller
2007 Lecture Notes in Computer Science  
of objects reusing Nipkow's HOL-framework for the lambda calculus.  ...  In particular, we present (a) a formal model of objects and its operational semantics based on de Bruijn indices (b) a parallel reduction relation for objects (c) the proof of confluence for the theory  ...  We would like to thank Larry Paulson for providing us the formalization of the ς-calculus in Isabelle/ZF written by Ehmety.  ... 
doi:10.1007/978-3-540-72952-5_12 fatcat:zhdvufkxv5hrjnf4yfmv6btlnu

A lambda-calculus for dynamic binding

Laurent Dami
1998 Theoretical Computer Science  
This paper proposes AN, a compact extension of the i-calculus to model dynamic binding, where variables are labelled by names, and where arguments are passed to functions along named channels.  ...  The resulting formalism preserves familiar properties of the I-calculus, has a Curry-style-type inference system, and has a formal notion of compatibility for reasoning about extensible environments.  ...  The label-selective calculus [ 131 uses variables and A-abstractions as in the classical %-calculus, but assigns a label to each abstraction level.  ... 
doi:10.1016/s0304-3975(97)00150-3 fatcat:3x262x3ymvhzjomlc5o6gzo3oa

Simply typed lambda calculus with first-class environments

Shin-ya Nishizaki
1994 Publications of the Research Institute for Mathematical Sciences  
Syntax of /i^t, is obtained by merging the class of terms and the one of substitutions. Reduction is made from the weak reduction of Acr-calculus.  ...  We propose a lambda calculus X^n v where it is possible to handle first-class environments. This calculus is based on the idea of explicit substitution, that is; /la-calculus.  ...  Atsushi Ohori, and the referee for discussions, comments, and pointing out of errors in the draft.  ... 
doi:10.2977/prims/1195164948 fatcat:eqpqy3fz5veepps4qjhtbz5d2q

The Suspension Calculus and its Relationship to Other Explicit Treatments of Substitution in Lambda Calculi [article]

Andrew Gacek
2007 arXiv   pre-print
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs.  ...  In this paper we present the suspension calculus, an explicit treatment of meta level binding in the lambda calculus.  ...  Chapter 2 The Lambda Calculus The lambda calculus is a language of functions-a simple and concise syntax for describing a powerful and expressive language.  ... 
arXiv:cs/0702027v1 fatcat:32j2ndyzxnciroxzn4xhwzsgea

A Simplified Suspension Calculus and its Relationship to Other Explicit Substitution Calculi [article]

Andrew Gacek, Gopalan Nadathur
2007 arXiv   pre-print
The overall calculus is shown to have pleasing theoretical properties such as a strongly terminating sub-calculus for substitution and confluence even in the presence of term meta variables that are accorded  ...  This paper concerns the explicit treatment of substitutions in the lambda calculus.  ...  ACKNOWLEDGMENTS This work began while the second author was on a sabbatical visit to the Protheo group at LORIA and INRIA, Nancy and the Comete and Parsifal groups atÉcole Polytechnique and INRIA, Saclay  ... 
arXiv:cs/0702152v1 fatcat:rya2abpyczbkdahxdlpzspmdri

Operational and axiomatic semantics of PCF

Brian T. Howard, John C. Mitchell
1990 Proceedings of the 1990 ACM conference on LISP and functional programming - LFP '90  
PCF, as considered in this paper, is a lazy typed lambda calculus with functions, pairing, fixed-point operators and arbitrary algebraic data types.  ...  The natural equational axioms for PCF include η-equivalence and the so-called "surjective pairing" axiom for pairs.  ...  In lambda calculus, it is traditional to say that a confluent notion of reduction is Church-Rosser, since confluence for untyped lambda calculus was first proved by Church and Rosser [Chu41] .  ... 
doi:10.1145/91556.91677 dblp:conf/lfp/HowardM90 fatcat:vfqoypttzzhynj2uapkngnsr3i

Deriving interpretations of the gradually-typed lambda calculus

Álvaro García-Pérez, Pablo Nogueira, Ilya Sergey
2014 Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation - PEPM '14  
Siek and Garcia (2012) have explored the dynamic semantics of the gradually-typed lambda calculus by means of definitional interpreters and abstract machines.  ...  We establish the correspondence between the definitional interpreters and the reduction semantics of a closure-converted gradually-typed lambda calculus that unifies and amends various versions of the  ...  Acknowledgements We are thankful to Olivier Danvy for introducing us to [20] and for suggesting the problem.  ... 
doi:10.1145/2543728.2543742 dblp:conf/pepm/Garcia-PerezNS14 fatcat:x6raxsr7afdwrlsspdj4dydlai

The Grail theorem prover: Type theory for syntax and semantics [article]

Richard Moot
2016 arXiv   pre-print
Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem  ...  syntactic type and vice versa.  ...  In the multimodal Lambek calculus, the basic objects are labeled binary trees 4 . The labels come from a separate set of indices or modes I.  ... 
arXiv:1602.00812v2 fatcat:6bi2ipu2irfixmhtwdl4phtk4i

The Grail Theorem Prover: Type Theory for Syntax and Semantics [chapter]

Richard Moot
2017 Studies in Linguistics and Philosophy  
In the multimodal Lambek calculus, the basic objects are labeled binary trees 4 . The labels come from a separate set of indices or modes I.  ...  The "bridge" between syntax and semantics in the figure is the Curry-Howard isomorphism between linear lambda terms and proofs in multiplicative intuitionistic linear logic.  ... 
doi:10.1007/978-3-319-50422-3_10 fatcat:5rhcai7kwjdgxmssbmps3hbrse

Matching Power [chapter]

Horatiu Cirstea, Claude Kirchner, Luigi Liquori
2001 Lecture Notes in Computer Science  
We provide extensive examples of the calculus, and we focus on its ability to represent some object oriented calculi, namely the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell, and the Object  ...  Calculus of Abadi and Cardelli.  ...  We thank the referees for their constructive remarks, Hubert Dubois and all the members of the ELAN group for their comments and interactions on the topics of the Rho Calculus.  ... 
doi:10.1007/3-540-45127-7_8 fatcat:grylwumtnzh3ffmhkhnoe32rfq
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