# A Coalgebraic Foundation for Linear Time Semantics

###
In *Proceedings of the Eighth Category Theory
in Computer Science conference, CTCS '99*,
M. Hofmann, D. Pavlovic, and G. Rosolini editors,
volume 29 of
Electronic Notes in Theoretical Computer Science.
Elsevier, 1999.

Available as

### Abstract

We present a coalgebraic approach to trace
equivalence semantics based on lifting behaviour
endofunctors for deterministic action to Kleisli
categories of monads for non-deterministic choice.
In Set, this gives a category with ordinary
transition systems as objects and with morphisms
characterised in terms of a linear notion of
bisimulation. The final object in this category
is the canonical abstract model for trace equivalence
and can be obtained by extending the final coalgebra
of the deterministic action behaviour to the Kleisli
category of the non-empty powerset monad. The
corresponding final coalgebra semantics is fully
abstract with respect to trace equivalence.

@inProceedings{PowerTuri99,
author = {J. Power and D. Turi},
title = {A coalgebraic foundation for linear time semantics},
publisher = "Elsevier",
year = {1999},
volume = {29},
booktitle = {Proc.\ 8$^{\rm th}$ CTCS Conf.},
series = "Electronic Notes in Theoretical Computer Science",
editor = {M. Hofmann and D. Pavlovi\'{c} and G. Rosolini},
source = {http://www.dcs.ed.ac.uk/home/dt/}
}

Daniele Turi
Last modified: Fri Jun 9 13:57:12 BST 2000