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

This e-book constitutes the refereed court cases of the fifth overseas convention on Algebra and Coalgebra in machine technology, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 complete papers provided including four invited talks have been conscientiously reviewed and chosen from 33 submissions. The papers disguise subject matters within the fields of summary types and logics, really expert 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 booklet additionally contains 6 papers from the CALCO instruments Workshop, co-located with CALCO 2013 and devoted to instruments in response to algebraic and/or coalgebraic principles.

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Exploiting Algebraic Laws to Improve Mechanized Axiomatizations 41 We are now ready to present a syntactic restriction on the GSOS format that guarantees Σ commutativity with respect to a set of partitions modulo any notion of behavioural equivalence that includes strong bisimilarity. Unlike the format for {[n]}-commutativity given in [16], the format offered below applies to generalized commutativity, in the sense of Definition 5, and is defined for TSSs whose rules can have negative premises.

TLCA 1999. LNCS, vol. 1581, pp. 129–146. Springer, Heidelberg (1999) 9. : Induction–recursion and initial algebras. Annals of Pure and Applied Logic 124(1-3), 1–47 (2003) 10. : Indexed induction–recursion. Journal of Logic and Algebraic Programming 66(1), 1–49 (2006) 11. : Formalizing Arne Andersson trees and Leftleaning Red-Black trees in Agda. Bachelor thesis, Chalmers University of Technology (2009) 12. : Abstract syntax and variable binding. In: Proc. Logic in Computer Science, pp. 193–202 (1999) 13.

In IR+ the type of of codes and the type of morphisms between codes are simultaneously defined in an inductive-inductive way, and therefore they are also decoded simultaneously as functors and natural transformations respectively. This is exactly what the elimination principle for an inductive-inductive definition gives. In the following theorem, note that there is no restriction on the category C – all structure that we need comes for free from the families construction Fam. Theorem 8 (IR+ functors).

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