A parameterized graph transformation calculus for finite graphs with monadic branches

Kazuyuki Asada, Soichiro Hidaka, Hiroyuki Kato, Zhenjiang Hu, Keisuke Nakano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

We introduce a lambda calculus λFGT for transformations of finite graphs by generalizing and extending an existing calculus UnCAL. Whereas UnCAL can treat only unordered graphs, λFGT can treat a variety of graph models: directed edge-labeled graphs whose branch styles are represented by monads T. For example, λFGT can treat unordered graphs, ordered graphs, weighted graphs, probability graphs, and so on, by using the powerset monad, list monad, multiset monad, probability monad, respectively. In λFGT, graphs are considered as extension of tree data structures, i.e. as infinite (regular) trees, so the semantics is given with bisimilarity. A remarkable feature of UnCAL and λFG T is structural recursion for graphs, which gives a systematic programming basis like that for trees. Despite the non-well-foundedness of graphs, by suitably restricting the structural recursion, UnCAL and λFGT ensures that there is a termination property and that all transformations preserve the finiteness of the graphs. The structural recursion is defined in a "divide-and-aggregate" way; "aggregation" is done by connecting graphs with ε-edges, which are similar to the -transitions of automata. We give a suitable general definition of bisimilarity, taking account of ε-edges; then we show that the structural recursion is well defined with respect to the bisimilarity.

Original languageEnglish
Title of host publicationProceedings of the 15th Symposium on Principles and Practice of Declarative Programming, PPDP 2013
Pages73-84
Number of pages12
DOIs
Publication statusPublished - 2013 Oct 15
Externally publishedYes
Event15th Symposium on Principles and Practice of Declarative Programming, PPDP 2013 - Madrid, Spain
Duration: 2013 Sep 162013 Sep 18

Publication series

NameProceedings of the 15th Symposium on Principles and Practice of Declarative Programming, PPDP 2013

Other

Other15th Symposium on Principles and Practice of Declarative Programming, PPDP 2013
CountrySpain
CityMadrid
Period13/9/1613/9/18

Keywords

  • bisimilarity
  • epsilon edge
  • graph algebra
  • graph transformation
  • monad
  • structural recursion

ASJC Scopus subject areas

  • Software

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