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

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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 20 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.

本文言語English
ページ(範囲)287-337
ページ数51
ジャーナルMathematical Structures in Computer Science
28
2
DOI
出版ステータスPublished - 2018 2 1

ASJC Scopus subject areas

  • 数学(その他)
  • コンピュータ サイエンスの応用

フィンガープリント

「The algebra of recursive graph transformation language UnCAL: Complete axiomatisation and iteration categorical semantics」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル