Abstract
Classical single-sorted algebraic signatures are defined as sets of operation symbols together with arities. In their many-sorted variant they also list sort symbols and use sort-sequences as operation types. An operation type not only indicates sorts of parameters, but also constitutes dependency between an operation and a set of sorts. In the paper we define algebraic signatures with dependency relation on their symbols. In modal logics theory, structures like 〈W,R〉, where W is a set and R ⊆ W×W is a transitive relation, are called transitive Kripke frames [Seg70]. Part of our result is a definition of a construction of non-empty products in the category of transitive Kripke frames and p-morphisms. In general not all such products exist, but when the class of relations is restricted to bounded strict orders, the category lacks only the final object to be finitely (co)complete. Finally we define a category AlgSigDep of signatures with dependencies and we prove that it also has all finite (co)limits, with the exception of the final object.
Keywords
- Dependency Structure
- Full Subcategory
- Dependency Relation
- Operation Type
- Nonempty Product
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Bidoit, M., Sannella, D., Tarlecki, A.: Architectural Specifications in CASL. In: Haeberer, A.M. (ed.) AMAST 1998. LNCS, vol. 1548, pp. 341–357. Springer, Heidelberg (1998)
Gumm, H.P., Schröder, T.: Products of coalgebras. Algebra Universalis 46, 163–185 (2001)
Segerberg, K.: Modal logics with linear alternative relations. Theoria 36, 301–322 (1970)
Sannella, D., Tarlecki, A.: Toward formal development of programs from algebraic specifications: Implementations revisited. Acta Informatica 25(3), 233–281 (1988)
Sannella, D., Tarlecki, A.: Essential Concepts of Algebraic Specification and Program Development. Formal Asp. Comput. 9(3), 229–269 (1997)
Walicki, M., Wolter, U.: Universal multialgebra. In: New Topics in Theoretical Computer Science, pp. 27–93. Nova Science Publishers (2008)
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Marczyński, G. (2012). Algebraic Signatures Enriched by Dependency Structure. In: Mossakowski, T., Kreowski, HJ. (eds) Recent Trends in Algebraic Development Techniques. WADT 2010. Lecture Notes in Computer Science, vol 7137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28412-0_15
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DOI: https://doi.org/10.1007/978-3-642-28412-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28411-3
Online ISBN: 978-3-642-28412-0
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