Algebra and Coalgebra in Computer Science: 5th International by Andrej Bauer, Matija Pretnar (auth.), Reiko Heckel, Stefan

By Andrej Bauer, Matija Pretnar (auth.), Reiko Heckel, Stefan Milius (eds.)

This booklet constitutes the refereed lawsuits of the fifth foreign convention on Algebra and Coalgebra in desktop technological know-how, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 complete papers awarded including four invited talks have been conscientiously reviewed and chosen from 33 submissions. The papers disguise themes within the fields of summary types and logics, really good versions and calculi, algebraic and coalgebraic semantics, process specification and verification, in addition to corecursion in programming languages, and algebra and coalgebra in quantum computing. The publication additionally comprises 6 papers from the CALCO instruments Workshop, co-located with CALCO 2013 and devoted to instruments in accordance with algebraic and/or coalgebraic principles.

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A type U consisting of codes for small types is introduced, together with a decoding function T , which maps codes to the types they denote. The definition is both inductive and recursive; the type U is defined inductively, and the decoding function T is defined recursively on the way the elements of U are generated. The definition needs to be simultaneous, since the introduction rules for U refer to T . We illustrate this by means of a concrete example: say we want to define a data type representing a universe containing a name for the natural numbers, closed under Σ-types.

In this paper, we take the first steps in marrying these two research areas and in using rule formats for algebraic properties (specifically, for commutativity) to enhance the The first three authors have been partially supported by the project ‘Meta-theory of Algebraic Process Theories’ (nr. 100014021) of the Icelandic Research Fund. Eugen-Ioan Goriac is also funded by the project ‘Extending and Axiomatizing Structural Operational Semantics: Theory and Tools’ (nr. 1102940061) of the Icelandic Research Fund.

In the remainder of this paper, following [10], we shall tacitly assume that each TSS in the GSOS format contains these operators with the rules given above. The import of this assumption is that, as is well known, within each TSS in the GSOS format it is possible to express each finite synchronization tree over L. Following [12], the TSS containing the operators 0, a. (a ∈ L) and + , with the above-given rules, is denoted by BCCSP. The transition relation associated with a TSS in the GSOS format is the one defined by structural induction over closed terms using the rules.

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