Abstract GSOS rules and a Modular Treatment of Recursive Definitions

Milius S, Moss L, Schwencke D (2013)

Publication Type: Journal article

Publication year: 2013

Journal

Logical Methods in Computer Science Logical Methods in Computer Science e.V.

Publisher: IfCoLog (International Federation of Computational Logic) / Technical University of Braunschweig

Book Volume: 9

Pages Range: 1-52

Journal Issue: 3:28

URI: https://www8.cs.fau.de/~milius/publications/papers.html

DOI: 10.2168/LMCS-9(3:28)2013

Abstract

Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive definitions in terminal coalgebras by combining two ideas: (1) abstract GSOS rules ℓ specify additional algebraic operations on a terminal coalgebra; (2) terminal coalgebras are also initial completely iterative algebras (cias). We also show that an abstract GSOS rule leads to new extended cia structures on the terminal coalgebra. Then we formalize recursive function definitions involving given operations specified by ℓ as recursive program schemes for ℓ, and we prove that unique solutions exist in the extended cias. From our results it follows that the solutions of recursive (function) definitions in terminal coalgebras may be used in subsequent recursive definitions which still have unique solutions. We call this principle modularity. We illustrate our results by the five concrete terminal coalgebras mentioned above, e. g., a finite stream circuit defines a unique stream function. © S. Milius, L. S. Moss, and D. Schwencke.

Authors with CRIS profile

Stefan Milius Lehrstuhl für Informatik 8 (Theoretische Informatik)

Involved external institutions

Indiana University US United States (USA) (US) Technische Universität Braunschweig DE Germany (DE)

How to cite

APA:

Milius, S., Moss, L., & Schwencke, D. (2013). Abstract GSOS rules and a Modular Treatment of Recursive Definitions. Logical Methods in Computer Science, 9(3:28), 1-52. https://dx.doi.org/10.2168/LMCS-9(3:28)2013

MLA:

Milius, Stefan, Lawrence Moss, and Daniel Schwencke. "Abstract GSOS rules and a Modular Treatment of Recursive Definitions." Logical Methods in Computer Science 9.3:28 (2013): 1-52.

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