Trace Semantics for Coalgebras

Trace Semantics for Coalgebras

Traditionally, traces are the sequences of labels associated with paths in transition systems X → P(A×X). Here we describe traces more generally, for coalgebras of the form X → P(F (X)), where F is a polynomial functor. The main result states that F ’s final coalgebra Z ∼= −→ F (Z) gives rise to a weakly final coalgebra with state space P(Z), in a suitable category of coalgebras. Weak finality ...

On Coalgebras and Final Semantics: Progress Report

Symbolic and Asynchronous Semantics via Normalized Coalgebras

The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transitio...

Trace semantics for concurrent objects

The theory of traces (the theory of free partial commutative monoids) is used to describe the behavior of systems of concurrent objects. A composition operation on systems and a synchronization operation on behaviors are presented: they allow to derive the behavior of complex systems from the behavior of its components. To address fundamental issues of concurrent semantics for objects in genera...

Trace Semantics via Determinization

This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories, stemming from an initial algebra in the underlying category. This approach requires some non-trivial assumptions, like dcpo enrichment, which do not always hold, even in cases where one can reasonably speak o...