By Andrej Bauer, Matija Pretnar (auth.), Reiko Heckel, Stefan Milius (eds.)
This booklet constitutes the refereed court cases of the fifth overseas convention on Algebra and Coalgebra in laptop 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 subject matters within the fields of summary types 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 e-book additionally contains 6 papers from the CALCO instruments Workshop, co-located with CALCO 2013 and devoted to instruments according 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 resources for Algebra and Coalgebra in Computer Science: 5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013. Proceedings
In this paper we remove this constraint and hence explore a further generalization of IR, orthogonal to the one proposed in Ghani et al. . We investigate the necessary changes of IR needed to provide a class of codes which can be interpreted as functors Fam C → Fam C. This leads us to consider a new variation IR+ of inductive-recursive deﬁnitions which we call positive inductive-recursive deﬁnitions. The most substantial aspect of this Positive Inductive-Recursive Deﬁnitions 21 new theory is that in order to deﬁne these new codes, one needs also to deﬁne the morphisms between those codes.
We also use ﬁbrational terminology occasionally when we feel it adds insight, but those not familiar with ﬁbrations can simply ignore such comments. 2 Induction Recursion The original presentation of induction recursion given by Dybjer  was as a schema. Dybjer and Setzer  further developed the theory to internalize the concept of an inductive-recursive deﬁnition. They developed a ﬁnite axiomatization of the theory through the introduction of a special type of codes for inductive-recursive deﬁnitions.
Jacobs ). e. if Q = P ◦ h. – Fam C is the free set indexed coproduct completion of C; that is Fam C has all set indexed coproducts and there is an embedding C → Fam C universal among functors F : C → D where D is a category with set indexed coproducts. Given an A-indexed collection of objects (Xa , Pa )a :A in Fam C, its A-indexed coproduct is the family ( a :A Xa , [Pa ]a :A ). – Fam C is cocomplete if and only if C has all small connected colimits (Carboni and Johnstone [6, dual of Prop. 1]).