An Investigation of the Laws of Traversals

Jaskelioff, Mauro; Rypacek, Ondrej

doi:10.4204/eptcs.76.5

Cited by 15 publications

(17 citation statements)

References 8 publications

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“…Like many cherished tools in a crowded toolbox, the Representation Theorem is surprisingly versatile. Using it, we have resolved several more general open questions, in addition to the specific programming problem we designed it for: the property of 'naturality' in the datatype, the illegality of half-hearted and duplicitous traversals (Gibbons and Oliveira 2009), the correspondence between traversable datatypes and finitary containers (Moggi et al 1999), and more precisely the bijection between traversal strategies for a data structure (shape) and permutations of its elements (Jaskelioff and Rypáček 2012).…”

Section: Discussionmentioning

confidence: 99%

Understanding idiomatic traversals backwards and forwards

Bird

Gibbons

Mehner

et al. 2013

Proceedings of the 2013 ACM SIGPLAN Symposium on Haskell

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We present new ways of reasoning about a particular class of effectful Haskell programs, namely those expressed as idiomatic traversals. Starting out with a specific problem about labelling and unlabelling binary trees, we extract a general inversion law, applicable to any monad, relating a traversal over the elements of an arbitrary traversable type to a traversal that goes in the opposite direction. This law can be invoked to show that, in a suitable sense, unlabelling is the inverse of labelling. The inversion law, as well as a number of other properties of idiomatic traversals, is a corollary of a more general theorem characterising traversable functors as finitary containers: an arbitrary traversable object can be decomposed uniquely into shape and contents, and traversal be understood in terms of those. Proof of the theorem involves the properties of traversal in a special idiom related to the free applicative functor.Life can only be understood backwards; but it must be lived forwards.-Søren Kierkegaard

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Section: Discussionmentioning

confidence: 99%

Understanding idiomatic traversals backwards and forwards

Bird

Gibbons

Mehner

et al. 2013

Proceedings of the 2013 ACM SIGPLAN Symposium on Haskell

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“…Among others, each layer defines a pair of applicative atoms as infix operators, e.g. (·, * ), which, aided by a type traversal [18] utility ' ', allows to form m-input and n-output entities in the sense of (2). The implied composition of a generic pattern which maps function f on a series of structures C, as a typical constructor, is shown in (5).…”

Section: A Layered Process Modelmentioning

confidence: 99%

A layered formal framework for modeling of cyber-physical systems

Ungureanu

Sander

2017

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2017

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Designing cyber-physical systems is highly challenging due to its manifold interdependent aspects such as composition, timing, synchronization and behavior. Several formal models exist for description and analysis of these aspects, but they focus mainly on a single or only a few system properties. We propose a formal composable framework which tackles these concerns in isolation, while capturing interaction between them as a single layered model. This yields a holistic, fine-grained, hierarchical and structured view of a cyber-physical system. We demonstrate the various benefits for modeling, analysis and synthesis through a typical example.

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“…Following our free monad principle, we capture de Bruijn terms in a free monadic structure that is parameterized by namespaces and whose underlying functor covers the regular constructors of sorts. To model the underlying functors we use the universe of finitary containers [1,13,15,20] Finitary containers closely model our specification language: a set of shapes (constructors) with a finite number of fields. We use an indexed [2] version to model mutually recursive types and use a higher-order presentation to obtain better induction principles for which we assume functional extensionality 5 .…”

Section: The Generic Knot Implementationmentioning

confidence: 99%

Needle & Knot: Binder Boilerplate Tied Up

Keuchel

Weirich

Schrijvers

2016

Programming Languages and Systems

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In order to lighten the burden of programming language mechanization many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages. This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its metatheory constructively guarantees for well-formed specifications the coverage of a considerable amount of binder boilerplate, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in Coq and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems. Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables.

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An Investigation of the Laws of Traversals

Cited by 15 publications

References 8 publications

Understanding idiomatic traversals backwards and forwards

Understanding idiomatic traversals backwards and forwards

A layered formal framework for modeling of cyber-physical systems

Needle & Knot: Binder Boilerplate Tied Up

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