Trace Semantics for Coalgebras

@article{Jacobs2004TraceSF,
  title={Trace Semantics for Coalgebras},
  author={Bart Jacobs},
  journal={Electr. Notes Theor. Comput. Sci.},
  year={2004},
  volume={106},
  pages={167-184}
}
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 means that there is a coalgebra map X → P(Z), but there is no uniqueness. We show that there is a… CONTINUE READING