Abstract
The algebraic approach to graph transformation is a general framework for the definition of transformation mechanisms for complex structures that achieves its generality by using category-theoretic abstractions.
We present a framework for modular implementations of categoric graph transformation mechanisms that uses abstractions of relation categories as internal interfaces. Doing this in a dependently-typed programming language enables us to manage implementations of functionality together with their correctness proofs in the same language, thus progressing towards fully verified graph transformation system implementations.
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References
Berghammer, R.: A Functional, Successor List Based Version of Warshall’s Algorithm with Applications. In: [ds11], pp. 109–124
Braibant, T., Pous, D.: Deciding Kleene Algebras in Coq. Logical Methods in Computer Science 8, 16 (2012)
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1, ch. 3, pp. 163–245. World Scientific, Singapore (1997)
de Swart, H. (ed.): RAMICS 2011. LNCS, vol. 6663. Springer, Heidelberg (2011)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer (2006)
Ehrig, H., Padberg, J., Prange, U., Habel, A.: Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation. Fund. Inform. 74, 1–29 (2006)
Freyd, P.J., Scedrov, A.: Categories, Allegories, North-Holland Mathematical Library, vol. 39. North-Holland, Amsterdam (1990)
Kahl, W.: Relational Semigroupoids: Abstract Relation-Algebraic Interfaces for Finite Relations between Infinite Types. J. Logic and Algebraic Programming 76, 60–89 (2008)
Kahl, W.: Collagories: Relation-Algebraic Reasoning for Gluing Constructions. J. Logic and Algebraic Programming 80, 297–338 (2011)
Kahl, W.: Dependently-Typed Formalisation of Relation-Algebraic Abstractions. In: [ds11], pp. 230–247
Kawahara, Y.: Pushout-Complements and Basic Concepts of Grammars in Toposes. Theoretical Computer Science 77, 267–289 (1990)
Kozen, D.: A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events. Inform. and Comput. 110, 366–390 (1994)
Kozen, D.: Typed Kleene Algebra. Technical Report 98-1669, Computer Science Department, Cornell University (1998)
Mu, S.-C., Ko, H.-S., Jansson, P.: Algebra of Programming in Agda: Dependent Types for Relational Program Derivation. J. Functional Programming 19, 545–579 (2009) See also AoPA at, http://www.iis.sinica.edu.tw/~scm/2008/aopa/
Norell, U.: Towards a Practical Programming Language Based on Dependent Type Theory. PhD thesis, Department of Computer Science and Engineering, Chalmers University of Technology (2007)
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Kahl, W. (2012). Towards Certifiable Implementation of Graph Transformation via Relation Categories. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_6
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DOI: https://doi.org/10.1007/978-3-642-33314-9_6
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