A Coalgebraic Foundation for Linear Time Semantics

John Power, Daniele Turi
1999 Electronical Notes in Theoretical Computer Science  
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
more » ... ebra 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.
doi:10.1016/s1571-0661(05)80319-6 fatcat:dinawi2t75h7radvzp7ql3j7uy