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An Introduction to Triple Graph Grammars as an Implementation of the Delta-Lens Framework

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Bidirectional Transformations

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9715))

Abstract

Triple Graph Grammars (TGGs) provide a rule-based means of specifying a consistency relation over two graph languages, with correspondences between elements in the two different languages represented explicitly as a third “traceability” graph. Many useful tools can be derived automatically from a TGG including incrementally working synchronisers, which are able to realise forward and backward change propagation without incurring unnecessary information loss. TGGs are typically introduced based on the algebraic graph transformation framework, which is not particularly accessible to many members of the bidirectional transformation (bx) community, who are often more familiar with some variant of the lens framework as a theoretical foundation for bx.

This chapter, therefore, provides a self-contained, relatively gentle and tutorial-like introduction to TGGs as a pragmatic implementation of the symmetric delta-lens (sd-lens) framework proposed by Diskin et al., thereby mapping abstract and general terms used in the sd-lens framework such as models and deltas, to concrete realisations in the TGG framework such as typed graphs and spans of typed graphs.

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Notes

  1. 1.

    Subscripts on \(\varDelta \) are omitted if all arrows are meant.

  2. 2.

    The formal diagrams used in this chapter are placed in a frame with a label in the right-bottom corner denoting how to interpret the objects and arrows in the diagram. For example, a diagram with label Sets means that objects in the diagram are sets, and arrows in the diagram are total functions. All other diagrams are informal and require a diagram-specific legend or extra explanation.

  3. 3.

    As d and b can be seen as being derived by “pushing out” a and c along each other.

  4. 4.

    As d and b can be seen as being derived by “pulling back” a and c along each other.

  5. 5.

    Remember that not all squares can be combined.

  6. 6.

    This is analogous to notions of a “conservative copy” in the context of model migration, e.g., as exemplified in the Epsilon Flock tool [30].

  7. 7.

    www.emoflon.org.

  8. 8.

    Hence the suggestion to view source ignore rules as generating only fpg squares.

  9. 9.

    The diagram is more complex for constraints; the interested reader is referred to Anjorin et al. [4].

  10. 10.

    Most practical implementations also support attribute manipulation; some even support “moving” a subgraph in a containing graph.

  11. 11.

    This visualisation, as an attempt to impart to a geometric intuition for consistency, was suggested by James McKinna at the 2016 summer school on bidirectional transformations: https://www.cs.ox.ac.uk/projects/tlcbx/ssbx/.

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  1. University of Paderborn, Paderborn, Germany

    Anthony Anjorin

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  1. Anthony Anjorin
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  1. University of Oxford, Oxford, United Kingdom

    Jeremy Gibbons

  2. University of Edinburgh, Edinburgh, United Kingdom

    Perdita Stevens

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Anjorin, A. (2018). An Introduction to Triple Graph Grammars as an Implementation of the Delta-Lens Framework. In: Gibbons, J., Stevens, P. (eds) Bidirectional Transformations. Lecture Notes in Computer Science(), vol 9715. Springer, Cham. https://doi.org/10.1007/978-3-319-79108-1_2

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