Higher-order subtyping

  • 47 Pages
  • 0.78 MB
  • 141 Downloads
  • English
by
LFCS, Dept. of Computer Science, University of Edinburgh , Edinburgh
Lambda calculus., Object-oriented programming (Computer sci
StatementMartin Steffen, Benjamin Pierce.
SeriesLFCS report series -- ECS-LFCS-94-280, Interner Bericht -- IMMD7-01 / 94, Interner Bericht (Friedrich-Alexander-Universität Erlangen-Nürnberg) -- IMMD7-01/94.
ContributionsPierce, Benjamin C., University of Edinburgh. Laboratory for Foundations of Computer Science., Friedrich-Alexander-Universität Erlangen-Nürnberg.
The Physical Object
Pagination47 p. ;
ID Numbers
Open LibraryOL18817317M

System F⩽ω is an extension with subtyping of the higher-order polymorphic λ-calculus —an orthogonal combination of Girard's system Fω with Cardelli Higher-order subtyping book Cited by: ied in [37] and [47]. Higher-order generalizations of subtyping appear in [11,12,31,45]. Treating the interaction between interface refinement and encapsulation of objects in object-oriented pro-gramming has required higher-order generalizations of subtyping: the F-bounded quantification of Canning, Cook et al.

[12] or system Fω [11,14–16,45]. Higher-order subtyping and its decidability. is a platform for academics to share research papers. The treatment of subtyping and higher-order polymorphism is Higher-order subtyping book on recent papers on static type systems for object-oriented languages Car84, Bru94, CCH + 89, CHC90, PT94, FM94, etc.] and the.

This paper proposes a session typing system for the higher-order π-calculus (the HOπ-calculus) with asynchronous communication subtyping, which allows partial commutativity of actions in higher-ord.

The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance [11]. The target calculus, F, a natural. We present a new proof of decidability of higher-order subtyping in the presence of bounded quantification.

The algorithm is formulated as a judgement which operates on beta-eta-normal forms. Transitivity and closure under application are proven directly and syntactically, without the need for a model construction or reasoning on longest beta.

A.B. CompagnoniDecidability of higher-order subtyping with intersection types in: CSL’94, Lecture Notes in Computer Science, vol.Springer () Preliminary version available as University of Edinburgh Technical Report ECS-LFCS, January Abel A and Rodriguez D Syntactic Metatheory of Higher-Order Subtyping Proceedings of the 22nd international workshop on Computer Science Logic, () Jeffrey A and Rathke J () Full abstraction for polymorphic π-calculus, Theoretical Computer Science,(), Online publication date: Jan VI Higher-Order Systems (pg.

) 29 Type Operators and Kinding (pg. ) 30 Higher-Order Polymorphism (pg. ) 31 Higher-Order Subtyping (pg. ) 32 Case Study: Purely Functional Objects (pg. ) Appendices (pg. ) A Solutions to Selected Exercises (pg.

) B Notational Conventions (pg. ) References (pg. ) Index (pg. This paper proposes a session typing system for the higher-order π-calculus (the HOπ-calculus) with asynchronous communication subtyping, which allows partial commutativity of actions in higher-order system enables two complementary kinds of optimisation, mobile code and asynchronous permutation of session actions, within processes that utilise structured, typed.

Details Higher-order subtyping FB2

Search ACM Digital Library. Search. Advanced Search. Abstract. We present an algorithm for deciding polarized higher-order subtyping without bounded quantification. Constructors are identified not only modulo β, but also give a direct proof of completeness, without constructing a model or establishing a strong normalization theorem.

This paper gives the first proof that the subtyping relation of a higher-order lambda calculus, ℱ ⩽ ω, is anti-symmetric, establishing in the process that the subtyping relation is a partial.

Unlike subtyping, matching does not support subsumption, but it does support inheritance of binary methods. We argue that matching is a good idea, but that it should not be regarded as a form of F-bounded subtyping (as was originally intended).

We show that a new interpretation of matching as higher-order subtyping has better properties. Higher-order subtyping and bounded polymorphism (1 and 2) have been formalized in F-omega-sub and its many variants; type definitions of various degrees of opacity (3) have been formalized through extensions of F-omega with singleton types.

In this dissertation, I propose type intervals as a unifying concept for expressing () and other. Title: Higher-Order Size Checking without Subtyping: Author(s): Góbi, A.; Shkaravska, O.; Eekelen, M.C.J.D. van Publication year: In: Loidl, H.-W.; Peña, R. Abstract. This paper studies one important aspect of distributed systems, locality, using a calculus of distributed higher-order processes in which not only basic values or channels, but also parameterised processes are transferred across distinct integration of the subtyping of λ-calculus and IO-subtyping of the π-calculus offers a tractable tool to control the locality of.

The compiler would require to be extended with something like "higher-order subtyping".

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I am however unsure if this is something that exists or if this is the best solution. I will provide a (simplified) example of my problem and am curious what are known solutions (with academic papers and text books) to. Unlike subtyping, matching does not support subsumption, but it does support inheritance of binary methods.

We argue that matching is a good idea, but that it should not be regarded as a form of F-bounded subtyping (as was originally intended). We show that a new interpretation of matching as higher-order subtyping has better properties. Abstract.

Description Higher-order subtyping EPUB

This paper shows that the subtyping relation of a higher-order lambda calculus, \(\mathcal{F}_ \leqslant ^w \), is exhibits the first such proof, establishing in the process that the subtyping relation is a partial order—reflexive, transitive, and.

The first-order theory of subtypes as inclusions developed in Part I is extended to a higher-order context.

This involves providing a higher-order equational logic for (inclusive) subtypes, a categorical semantics for such a logic that is complete and has initial models, and a proof that this higher-order logic is a conservative extension of its first-order counterpart.

This higher-order. When you are revising your papers, not every element of your work should have equal priority. The most important parts of your paper, often called "Higher Order Concerns (HOCs)," are the "big picture" elements such as thesis or focus, audience and purpose, organization, and development.

Decidability of higher-order subtyping with intersection types. Pages Towards machine-checked compiler correctness for higher-order pure functional languages. Pages Lester, David (et al.) *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and. Type Systems for Programming Languages Benjamin C. Pierce [email protected] en n. ed u Working draft of Janu This is preliminary draft of a book in progress. Gang Chen. Subtyping calculus of construction. In Mathematical Foundations of Computer Science (MFCS'97), Bratislava, Slovakia, volumepages Springer-Verlag, August Google Scholar; Adriana B.

Compagnoni. Higher-Order Subtyping with Intersection Types. PhD thesis, University of Nijmegen, The Netherlands, Google Scholar. Abstract. System F is an extension with subtyping of Girard's higher-order polymorphic -calculus. We develop the fundamental metatheory of this calculus: decidability of fi-conversion on well-kinded types, elimination of the "cut-rule" of transitivity from the subtype relation, and the soundness, completeness, and termination of algorithms for subtyping and typechecking.

Explicit instruction in thinking skills must be a priority goal of all teachers. In this book, the author presents a framework of the five Rs: Relevancy, Richness, Relatedness, Rigor, and Recursiveness. The framework serves to illuminate instruction in critical and creative thinking skills for K teachers across content chapter treats one category of thinking skills.

Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators.

30 Higher-Order Polymorphism Definitions Example Properties Fragments of Fω Going Further: Dependent Types 31 Higher-Order Subtyping Intuitions Definitions Properties Notes 32 Case Study: Purely Functional Objects Simple Objects Constructor subtyping. In Proceedings of the 8th European Symposium on Programming (ESOP) Amsterdam, The Netherlands.

Lecture Notes in Computer Science, vol.Springer Verlag, Berlin, Germany. ]] Google Scholar; Barthe, G. and van Raamsdonk, F. Constructor subtyping in the calculus of inductive constructions. Using a set-theoretic model of predicate transformers and ordered data types, we give a total-correctness semantics for a typed higher-order imperative programming language that includes record extension, local variables, and procedure-type variables and parameters.