5 research outputs found
Iteration Algebras for UnQL Graphs and Completeness for Bisimulation
This paper shows an application of Bloom and Esik's iteration algebras to
model graph data in a graph database query language. About twenty years ago,
Buneman et al. developed a graph database query language UnQL on the top of a
functional meta-language UnCAL for describing and manipulating graphs.
Recently, the functional programming community has shown renewed interest in
UnCAL, because it provides an efficient graph transformation language which is
useful for various applications, such as bidirectional computation. However, no
mathematical semantics of UnQL/UnCAL graphs has been developed. In this paper,
we give an equational axiomatisation and algebraic semantics of UnCAL graphs.
The main result of this paper is to prove that completeness of our equational
axioms for UnCAL for the original bisimulation of UnCAL graphs via iteration
algebras. Another benefit of algebraic semantics is a clean characterisation of
structural recursion on graphs using free iteration algebra.Comment: In Proceedings FICS 2015, arXiv:1509.0282
A connection between concurrency and language theory
We show that three fixed point structures equipped with (sequential)
composition, a sum operation, and a fixed point operation share the same valid
equations. These are the theories of (context-free) languages, (regular) tree
languages, and simulation equivalence classes of (regular) synchronization
trees (or processes). The results reveal a close relationship between classical
language theory and process algebra
Completing categorical algebras : Extended abstract
Let Ī£ be a ranked set. A categorical Ī£-algebra, cĪ£a for C, for short, is a small category C equipped with a functor ĻC : C n each Ļ ā Ī£n , n ā„ 0. A continuous categorical Ī£-algebra is a cĪ£a which C; has an initial object and all colimits of Ļ-chains, i.e., functors N each functor ĻC preserves colimits of Ļ-chains. (N is the linearly ordered set of the nonnegative integers considered as a category as usual.) We prove that for any cĪ£a C there is an Ļ-continuous cĪ£a C Ļ , unique up to equivalence, which forms a āfree continuous completionā of C.
We generalize the notion of inequation (and equation) and show the inequations or equations that hold in C also hold in C Ļ . We then find examples of this completion when ā C is a cĪ£a of finite Ī£-trees ā C is an ordered Ī£ algebra ā C is a cĪ£a of finite A-sychronization trees ā C is a cĪ£a of finite words on A.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en InformĆ”tica (RedUNCI