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### Page 4195 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews
over coalgebraic models for the z-calculus.  ...  The present paper introduces such interpretations over final coalgebra models for the z-calculus. These models do not exactly belong to the realm of the already existing work.  ...

### Pi-Calculus in Logical Form

Marcello Bonsangue, Alexander Kurz
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a modal calculus with primitives for input, free output and bound output.  ...  The π-Calculus We let a, b range over names; x over process variables; and P , Q over processes.  ...  In order to derive a logic for the π-calculus we give in Section 5 a presentation of each type constructor involved in the denotational model Pi of π-calculus.  ...

### Coinductive Interpreters for Process Calculi [chapter]

Luís Soares Barbosa, José Nuno Oliveira
2002 Lecture Notes in Computer Science
The approach is illustrated by the detailed development in Charity of an interpreter for a family of process languages.  ...  The proposed approach is independent of any particular process calculus and makes explicit the different ingredients present in the design of any such calculi.  ...  The authors wish to thank the Logic and Formal Methods group at Minho for the smooth working environment they had the chance to benefit from.  ...

### A coalgebraic approach to the semantics of the ambient calculus

Daniel Hausmann, Till Mossakowski, Lutz Schröder
2006 Theoretical Computer Science
Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems.  ...  Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus  ...  Catesbeiana for volunteering his opinion on the CoCasl empty carrier problem.  ...

### A Categorical Model of the Fusion Calculus

Marino Miculan
2008 Electronical Notes in Theoretical Computer Science
As a consequence, we get a semantics for the Fusion calculus which is both compositional and fully abstract: two processes have the same semantics iff they are bisimilar, that is, hyperequivalent.  ...  Coalgebras can be given a concrete presentation as "stateful indexed labelled transition systems"; the bisimilarity over these systems is a congruence, and corresponds to hyperequivalence.  ...  Acknowledgments The author thanks Sam Staton and the anonymous referees, for useful and important comments on the preliminary version of this work.  ...

### Indexed containers

THORSTEN ALTENKIRCH, NEIL GHANI, PETER HANCOCK, CONOR MCBRIDE, PETER MORRIS
2015 Journal of functional programming
As a result, we show indexed containers provide normal forms for strictly positive families in much the same way that containers provide normal forms for strictly positive types.  ...  AbstractWe show that the syntactically rich notion of strictly positive families can be reduced to a core type theory with a fixed number of type constructors exploiting the novel notion of indexed containers  ...  We also want to further investigate the relationship with interaction structures, formal topology and the refinement calculus.  ...

### Indexed Containers

Thorsten Altenkirch, Peter Morris
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science
The search for an expressive calculus of datatypes in which canonical algorithms can be easily written and proven correct has proved to be an enduring challenge to the theoretical computer science community  ...  Finally, and rather surprisingly, the extra structure inherent in indexed containers simplifies the theory of containers and thereby allows for a much richer and more expressive calculus.  ...  We also want to further investigate the relationship with interaction structures, formal topology and the refinement calculus.  ...

### A Presheaf Environment for the Explicit Fusion Calculus

Filippo Bonchi, Maria Grazia Buscemi, Vincenzo Ciancia, Fabio Gadducci
2011 Journal of automated reasoning
Bonchi et al. calculus, and propose to model its syntax and semantics using the presheaf category Set E , where E is the category of equivalence relations and equivalence preserving morphisms.  ...  Many efforts have been devoted to equip concurrent programming languages with a compositional denotational semantics, most often by restricting at first the analysis to simple computational models exhibiting  ...  Acknowledgements We are indebted to Sam Staton and to the anonymous referees for important insights that contributed to improve the quality of the paper.  ...

### Coalgebraic minimization of HD-automata for the π-calculus using polymorphic types

Gianluigi Ferrari, Ugo Montanari, Emilio Tuosto
2005 Theoretical Computer Science
We introduce finite-state verification techniques for the -calculus whose design and correctness are justified coalgebraically.  ...  The algorithm is a generalization of the partition refinement algorithm for classical automata and is specified as a coalgebraic construction defined using →, , , a polymorphic -calculus with dependent  ...  Acknowledgements We would like to thank the anonymous referees for their comments and suggestions.  ...

### Coinductive Field of Exact Real Numbers and General Corecursion

2006 Electronical Notes in Theoretical Computer Science
We use the machinery of Coq proof assistant for coinductive types to present the formalisation.  ...  The algorithms can be seen as coalgebra maps on the coalgebra of streams and hence they will be formalised as general corecursive functions.  ...  Acknowledgement The author wishes to thank the anonymous referees for their comments.  ...

### Axiomatizing Fully Complete Models for ML Polymorphic Types [chapter]

Samson Abramsky, Marina Lenisa
2000 Lecture Notes in Computer Science
We present axioms on models of system F, which are sucient to show full completeness for ML-polymorphic types.  ...  Then, we introduce an axiom which rules out in nite trees from the model. Finally, we discuss the necessity of the axioms.  ...  In HRR90], the category of Partial Equivalence Relations (PER) over the open term model of the untyped -calculus has been proved to be fully (and faithfully) complete for algebraic types, a small subclass  ...

### CoALP-Ty'16 [article]

Ekaterina Komendantskaya, František Farka
2016 arXiv   pre-print
Grant Coalgebraic Logic Programming for Type Inference, by E.  ...  of refereeing and selection for the formal proceedings.  ...  In the talk, we will discuss properties of the fixed point model. We will further discuss standard models, in which the interpretation of inductive relations is restricted.  ...

### Towards Squiggly Refinement Algebra [chapter]

D. A. Naumann
1998 Programming Concepts and Methods PROCOMET '98
We also give a data refinement from exponents of specifications to the concrete exponents needed for program semantics.  ...  Despite the importance of predicate transformers in imperative programming, the algebra of transformers has been less explored.  ...  But refinement calculus deals with imperative programming, for which predicate-transformer semantics is an accurate model.  ...

### Initial algebra and final coalgebra semantics for concurrency [chapter]

Jan Rutten, Daniele Turi
1994 Lecture Notes in Computer Science
The aim of this paper is to relate initial algebra semantics and final coalgebra semantics.  ...  Moreover, many facts about congruences (on algebras) and (generalized) bisimulations (on coalgebras) are shown to be dual as well.  ...  Special thanks to Bart Jacobs for joint work on linear final semantics.  ...

### Categorical Models for a Semantically Linear Lambda-calculus

Marco Gaboardi, Mauro Piccolo
2010 Electronic Proceedings in Theoretical Computer Science
Sll-Category extends in the natural way Benton, Bierman, Hyland and de Paiva's Linear Category, in order to soundly interpret all the constructs of Sll-calculus.  ...  This paper is about a categorical approach to model a very simple Semantically Linear lambda calculus, named Sll-calculus. This is a core calculus underlying the programming language SlPCF.  ...  with a term is modelled with the composition in the category of coalgebras.  ...
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