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

This ebook constitutes the refereed court cases 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 offered including four invited talks have been conscientiously reviewed and chosen from 33 submissions. The papers hide themes within the fields of summary versions and logics, really good types and calculi, algebraic and coalgebraic semantics, method specification and verification, in addition to corecursion in programming languages, and algebra and coalgebra in quantum computing. The publication 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.

**Read Online or Download Algebra and Coalgebra in Computer Science: 5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013. Proceedings PDF**

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**Extra info for Algebra and Coalgebra in Computer Science: 5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013. Proceedings**

**Example text**

For all letter a, ta (X) f (R) ta (Y ). For well-chosen functions f , bisimulations up to f are contained in a bisimulation, so that the improvement is sound. So is the function mapping each relation to its equivalence closure. In this particular case, one recover the standard algorithm by Hopcroft and Karp [2]: two sets can be skipped whenever they can already be related by a sequence of pairwise related states. t. set union: Work partially funded by the PiCoq and PACE projects, ANR-10-BLAN-0305 and ANR-12IS02001.

TLCA 2013. LNCS, vol. 7941, pp. 156–172. Springer, Heidelberg (2013) 15. : Fibred data types. In: LICS 2013 (2013) 16. : Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. North Holland, Elsevier (1999) 17. : Familial 2-functors and parametric right adjoints. Theory and Applications of Category Theory 18(22), 665–732 (2007) 18. : An intuitionistic theory of types (1972), published in Twenty-Five Years of Constructive Type Theory 19. : Intuitionistic type theory.

G. one could classify the natural transformations between them and operate on them using, for example, the derivative. While the latter has clear practical importance, note that the canonical recursion operator fold associated to inductive types is, when analysed for nested data types, a natural transformation. We give a positive answer to the above question using IR+ . We sketch our overall development as follows: – we deﬁne a grammar Nest for deﬁning nested types and a decoding function − : Nest → [Set, Set] → [Set, Set].