An Algebraic Approach to Bi-directional Updating

Mu, Shin-Cheng; Hu, Zhenjiang; Takeichi, Masato

doi:10.1007/978-3-540-30477-7_2

Cited by 59 publications

(46 citation statements)

References 8 publications

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Section: Related Workmentioning

confidence: 99%

“…Such bidirectional languages are usually combinator based [4,8,13,16,17,25], and the programmer builds a bidirectional transformation by combining smaller ones with special combinators. Some combinator languages can be implemented as libraries [13,16], which is rather lightweight, while some languages [4,8,25] need richer type systems, which are not available in most general-purpose languages, to be effective. It is usually easy to extend the languages by adding or removing combinators for specific domains [4,17,25], and typically users of the bidirectional languages have better control of the behaviors of the programs by not relying on a black-box bidirectionalization system; but the users do have to program in an unusual style and is limited by the expressiveness of the languages.…”

Section: Related Workmentioning

confidence: 99%

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Bidirectionalization for free with runtime recording

Matsuda

Wang

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations. In particular, a technique known as bidirectionalization is able to analyze and transform unidirectional programs written in general purpose languages, and "bidirectionalize" them.Among others, a technique termed as semantic bidirectionalization proposed by Voigtländer stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorems that follow from the polymorphic type of the program allow a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic.In this paper, we lift this polymorphism requirement to improve the applicability of semantic bidirectionalization. Concretely, we provide a type class PackM γ α µ, which intuitively reads "a concrete datatype γ is abstracted to a type α, and the 'observations' made by a transformation on values of type γ are recorded by a monad µ". With PackM , we turn monomorphic transformations into polymorphic ones, that are ready to be bidirectionalized. We demonstrate our technique with a case study of standard XML queries, which were considered beyond semantic bidirectionalization because of their monomorphic nature.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Bidirectionalization for free with runtime recording

Matsuda

Wang

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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“…Some approaches [17,22] compromise the expressiveness; others ignore the totality requirement [12,20,21]; others maintain totality, but weaken the round-tripping laws [6]; some relax both totality and round-tripping laws [13,10,9,8]; finally, it also possible to avoid compromising the laws by developing a more refined type system, as proposed in the original lens framework [5]: in order to preserve totality, a powerful semantic type system with invariants was used to specify the exact domain and range of lenses, which allowed the definition of duplication and conditional combinators as total well-behaved lenses. Unfortunately, to retain decidability in the type system, the expressiveness was still restricted by forcing composed lenses to agree not only on types but also on invariants.…”

Section: Application Scenario: Bidirectional Transformationsmentioning

confidence: 99%

“…Most BX approaches rely on more standard and decidable type systems, at the cost of a more limited expressiveness [17,22], by allowing partial transformations [12,20,21] or by assuming both partiality and weaker round-tripping laws [13,10,9,8]. More closely related to our approach, some frameworks derive the backward transformations by calculation, but are less expressive than ours.…”

Section: Related Workmentioning

confidence: 99%

“…More closely related to our approach, some frameworks derive the backward transformations by calculation, but are less expressive than ours. In [13], Put is derived by inverting injective forward transformations through algebraic reasoning, while [12] bidirectionalizes a restricted first-order language (namely, without duplication) based on a notion of view-update under constant complement. They also calculate an automata that matches the exact domain of the transformations, and acts similarly to our invariants.…”

Section: Related Workmentioning

confidence: 99%

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Relations as Executable Specifications: Taming Partiality and Non-determinism Using Invariants

Macedo

Pacheco

Cunha

2012

Relational and Algebraic Methods in Computer Science

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Abstract. The calculus of relations has been widely used in program specification and reasoning. It is very tempting to use such specifications as running prototypes of the desired program, but, even considering finite domains, the inherent partiality and non-determinism of relations makes this impractical and highly inefficient. To tame partiality we prescribe the usage of invariants, represented by coreflexives, to characterize the exact domains and codomains of relational specifications. Such invariants can be used as pre-condition checkers to avoid runtime errors. Moreover, we show how such invariants can be used to narrow the non-deterministic execution of relational specifications, making it viable for a relevant class of problems. In particular, we show how the proposed techniques can be applied to execute specifications of bidirectional transformations, a domain where partiality and non-determinism are paramount.

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Composing Bidirectional Programs Monadically

Xia

Orchard

Wang

2019

Programming Languages and Systems

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Software frequently converts data from one representation to another and vice versa. Naïvely specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming techniques allow programs to be written which can be interpreted in both directions. However, these techniques often employ unfamiliar programming idioms via restricted, specialised combinator libraries. Instead, we introduce a framework for composing bidirectional programs monadically, enabling bidirectional programming with familiar abstractions in functional languages such as Haskell. We demonstrate the generality of our approach applied to parsers/printers, lenses, and generators/predicates. We show how to leverage compositionality and equational reasoning for the verification of round-tripping properties for such monadic bidirectional programs.

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An Algebraic Approach to Bi-directional Updating

Cited by 59 publications

References 8 publications

Bidirectionalization for free with runtime recording

Bidirectionalization for free with runtime recording

Relations as Executable Specifications: Taming Partiality and Non-determinism Using Invariants

Composing Bidirectional Programs Monadically

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