A parameterized graph transformation calculus for finite graphs with monadic branches

Asada, Kazuyuki; Hidaka, Soichiro; Kato, Hirokazu; Hu, Zhenjiang; Nakano, Kazushi

doi:10.1145/2505879.2505903

Cited by 9 publications

(26 citation statements)

References 26 publications

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“…This paper is also related to our another submission (Asada et al 2013), which also treats an extension of UnCAL. In the current paper, we provide a novel solution to the problem of querying over the ordered graphs, while Asada et al (2013) shows that the solution can be partially generalized with less expressiveness of queries.…”

Section: Related Workmentioning

confidence: 98%

“…The two graphs on the left are bisimilar, but if we apply the structural recursion function even remove in Example 12, the resulting graphs are not bisimilar. Note that the following definition is more concise than the one given in (Asada et al 2012), which mimics the original bulk semantics of UnCAL given in (Buneman et al 2000); and this simplification makes the proof of bisimulation genericity clearer.…”

Section: Grouping New Graphs With ε-Edgesmentioning

confidence: 99%

“…In the current paper, we provide a novel solution to the problem of querying over the ordered graphs, while Asada et al (2013) shows that the solution can be partially generalized with less expressiveness of queries. More specifically, the two papers are technically independent in the following two points.…”

Section: Related Workmentioning

confidence: 99%

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Structural recursion for querying ordered graphs

Hidaka

Asada

et al. 2013

Proceedings of the 18th ACM SIGPLAN International Conference on Functional Programming

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Structural recursion, in the form of, for example, folds on lists and catamorphisms on algebraic data structures including trees, plays an important role in functional programming, by providing a systematic way for constructing and manipulating functional programs. It is, however, a challenge to define structural recursions for graph data structures, the most ubiquitous sort of data in computing. This is because unlike lists and trees, graphs are essentially not inductive and cannot be formalized as an initial algebra in general. In this paper, we borrow from the database community the idea of structural recursion on how to restrict recursions on infinite unordered regular trees so that they preserve the finiteness property and become terminating, which are desirable properties for query languages. We propose a new graph transformation language called λFG for transforming and querying ordered graphs, based on the well-defined bisimulation relation on ordered graphs with special ε-edges. The language λFG is a higher order graph transformation language that extends the simply typed lambda calculus with graph constructors and more powerful structural recursions, which is extended for transformations on the sibling dimension. It not only gives a general framework for manipulating graphs and reasoning about them, but also provides a solution to the open problem of how to define a structural recursion on ordered graphs, with the help of the bisimilarity for ordered graphs with ε-edges.

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Section: Related Workmentioning

confidence: 98%

Section: Grouping New Graphs With ε-Edgesmentioning

confidence: 99%

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Structural recursion for querying ordered graphs

Hidaka

Asada

et al. 2013

Proceedings of the 18th ACM SIGPLAN International Conference on Functional Programming

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“…In the original and subsequent formulation of UnCAL (Buneman et al, 2000;Hidaka et al, 2013aHidaka et al, , 2010Asada et al, 2013), there are complications of this kind. The relationship between terms and graphs in UnCAL is not a one-to-one correspondence.…”

Section: Uncal Overviewmentioning

confidence: 99%

The algebra of recursive graph transformation language UnCAL: complete axiomatisation and iteration categorical semantics

Hamana

Matsuda²,

Asada

2016

Math. Struct. Comp. Sci.

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The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation. In order to make UnCAL more flexible and fruitful for further extensions and applications, in this paper, we give a more conceptual understanding of UnCAL using categorical semantics. Our general interest of this paper is to clarify what is the algebra of UnCAL. Thus, we give an equational axiomatisation and categorical semantics of UnCAL, both of which are new. We show that the axiomatisation is complete for the original bisimulation semantics of UnCAL. Moreover, we provide a clean characterisation of the computation mechanism of UnCAL called "structural recursion on graphs" using our categorical semantics. We show a concrete model of UnCAL given by the λG-calculus, which shows an interesting connection to lazy functional programming.

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“…For example, in a certain model of graphs in which we identify graphs with infinite trees, the contract operation may convert a finite graph to an infinite one and does not terminate in such a case without careful treatment [41,42]. Our framework is applicable even to such model of graphs, as long as the parametricity and the totality assumption, including the termination of a graph transformation, are kept (Section 4).…”

Section: Programming the Forward Transformationmentioning

confidence: 99%

“Bidirectionalization for free” for monomorphic transformations

Matsuda

Wang

2015

Science of Computer 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, an approach termed semantic bidirectionalization proposed by Voigtländer stands out in terms of user-friendliness. A unidirectional program can be written using arbitrary language constructs, as long as the function it represents 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, as 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 case studies of typical applications of bidirectional transformation, namely text processing, XML query and graph transformation, which were commonly considered beyond semantic bidirectionalization because of their monomorphic nature.

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A parameterized graph transformation calculus for finite graphs with monadic branches

Cited by 9 publications

References 26 publications

Structural recursion for querying ordered graphs

Structural recursion for querying ordered graphs

The algebra of recursive graph transformation language UnCAL: complete axiomatisation and iteration categorical semantics

“Bidirectionalization for free” for monomorphic transformations

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