Pattern matching as cut elimination

Cerrito, Serenella; Kesner, Delia

doi:10.1109/lics.1999.782596

Cited by 13 publications

(6 citation statements)

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“…Note that computations can use case splittings x[t | u] to choose between the subterms t or u depending on the contents of the data bound to x. The use of patterns rather than plain variables to annotate formulas in the context of typing judgement is taken from [8] and allows to express more directly the equational style found in Agda. For example, we could write:…”

Section: Focusing and Polarities In The Sequent Calculusmentioning

confidence: 99%

Sequent Calculus and Equational Programming

Guenot

Gustafsson

2015

Electron. Proc. Theor. Comput. Sci.

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Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

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Section: Focusing and Polarities In The Sequent Calculusmentioning

confidence: 99%

Sequent Calculus and Equational Programming

Guenot

Gustafsson

2015

Electron. Proc. Theor. Comput. Sci.

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“…Pattern matching has been central to their exploitation. Connections to logic were explored in [17,66]. For example, the pattern-matching calculus [65] characterises different approaches to match failure.…”

Section: Notesmentioning

confidence: 99%

Pattern Calculus

Jay

2009

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: KünkelLopka, GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my parents VII VIII ForewordIntegrating the new technology in established settings in order to enhance their expressive power may well have a significant practical impact. People are much more prepared to accept new functionality in their known settings than totally changing paradigm. Another approach would be to use the pattern calculus as an "embedded technology" for dealing with matching and adaptation. Promising application scenarios for such an enterprise include Web Service discovery and mediation.The described multiple dimensions of impact of the pattern calculus indicate the potential audience. It may range from students who want to get a deeper insight into the basic principles, to language designers interested in enhancing the power of their languages, to tool and service designers in need of new, powerful technologies. The "How to Read This Book" chapter shows that the author wants to address all these communities, and he stands a good chance of being successful.It should not be forgotten, however, that the book focuses on foundations, and that it assumes a good theoretical background. Therefore interpreters will be needed so that the technology reaches the places where it will eventually have the largest impact, and I hope that the book will inspire this kind of technology transfer, whose value cannot be overestimated. Dortmund,Bernhard Steffen March, 2009 I am particularly indebted to Microsoft Research (Cambridge) for their support while writing this book, and to the University of Technology, Sydney for giving me the freedom to pursue my thoughts.

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“…We first learned to view pattern matching as arising from the invertible left rules of the sequent calculus due to the work of Kesner et al (1996), and Cerrito and Kesner (2004). We have extended their work by building on a focused sequent calculus.…”

Section: Related Workmentioning

confidence: 99%