Pure patterns type systems

Barthe, Gilles; CirsteaHoratiu,; KirchnerClaude,; LiquoriLuigi,

doi:10.1145/640128.604152

Cited by 11 publications

(21 citation statements)

References 24 publications

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“…Together with the consistency of normalising terms, which has already been proved in Barthe et al (2003), this result makes P 2 T S a good candidate for a proof-term language integrating deduction and computation at the same level. Therefore, in order to ensure consistency of the type systems, strong normalisation is an important and desirable property, but it has remained an open problem until now.…”

Section: B Wack and C Houtmann 432supporting

confidence: 53%

“…a clearer presentation of the type systems of P 2 T S -compared with the systems presented in Barthe et al (2003), we introduce a signature in the typing judgments and make some corrections to the product rules (in Sections 2 and 3); a compilation of pattern matching in the λ-calculus, which has other potential applications for the encoding of term rewriting systems (in Section 5); a translation of the simply-typed system of P 2 T S to System Fω emphasising some particular typing mechanisms of P 2 T S (in Sections 6 and 7); a proof of strong normalisation for simply-typed P 2 T S terms and for dependently typed P 2 T S terms (in Sections 7 and 8).…”

Section: B Wack and C Houtmann 432mentioning

confidence: 99%

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Strong normalisation in two Pure Pattern Type Systems

Wack¹,

Houtmann²

2008

Math. Struct. Comp. Sci.

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Pure Pattern Type Systems (P 2 T S) combine the frameworks and capabilities of rewriting and λ-calculus within a unified setting. Their type systems, which are adapted from Barendregt's λ-cube, are especially interesting from a logical point of view. Until now, strong normalisation, which is an essential property for logical soundness, has only been conjectured: in this paper, we give a positive answer for the simply-typed system and the dependently-typed system. The proof is based on a translation of terms and types from P 2 T S into the λ-calculus. First, we deal with untyped terms, ensuring that reductions are faithfully mimicked in the λ-calculus. For this, we rely on an original encoding of the pattern matching capability of P 2 T S into the System Fω. Then we show how to translate types: the expressive power of System Fω is needed in order to fully reproduce the original typing judgments of P 2 T S. We prove that the encoding is correct with respect to reductions and typing, and we conclude with the strong normalisation of simply-typed P 2 T S terms. The strong normalisation with dependent types is in turn obtained by an intermediate translation into simply-typed terms.

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Section: B Wack and C Houtmann 432supporting

confidence: 53%

Section: B Wack and C Houtmann 432mentioning

confidence: 99%

Strong normalisation in two Pure Pattern Type Systems

Wack¹,

Houtmann²

2008

Math. Struct. Comp. Sci.

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“…The chief exception is a typed rewriting calculus of [8] where an abstraction λ P : C .T binds only the variables in C allowing other variables in the pattern P to be available for substitution. The chief exception is a typed rewriting calculus of [8] where an abstraction λ P : C .T binds only the variables in C allowing other variables in the pattern P to be available for substitution.…”

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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“…Observe that, w.r.t. "non strategic" implementations of the Rewriting-calculus [2,[6][7][8], the delayed matchingconstraint [P ∆ A].B, becomes now just syntactic sugar for (P :∆ → A) B (hence omitted from the source language but still presents in the set of output values). Moreover, the shape of patterns has been limited to algebraic terms (i.e.…”

Section: Syntaxmentioning

confidence: 99%

“…no function-as-pattern). This restriction is strictly related to the current software development of our interpreter, and of the current mechanical development of the metatheory underneath iRho and not to theoretical problems (see [2]). The choice of call-by-value too was suggested by the practice of current functional languages.…”

Section: Syntaxmentioning

confidence: 99%

iRho

Liquori

Serpette

2004

Proceedings of the 6th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

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We propose an imperative version of the Rewriting-calculus, a calculus based on pattern-matching, pattern-abstraction, and side-effects, which we call iRho.We formulate a static and a call-by-value dynamic semantics of iRho like that of Gilles Kahn's Natural Semantics. The operational semantics is deterministic, and immediately suggests how to build an interpreter for the calculus. The static semantics is given via a first-order type system based on a form of product-type, which can be assigned to iRho-terms like structures (i.e. pairs).The calculus isà la Church, i.e. pattern-abstractions are decorated with the types of the free variables of the pattern.iRho is a good candidate for a core or an intermediate language, because it can safely access and modify a (monomorphic) typed store, and because fixed-points can be defined.Properties like determinism of the interpreter, and subject reduction are completely checked by a machine assisted approach, using the Coq proof assistant. Progress and decidability of type-checking are proved by pen and paper.

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Pure patterns type systems

Cited by 11 publications

References 24 publications

Strong normalisation in two Pure Pattern Type Systems

Strong normalisation in two Pure Pattern Type Systems

Pattern Calculus

iRho

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