Handbook of logic in computer science (vol. 1)
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Mongruences and Cofree Coalgebras
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
PVS: Combining Specification, Proof Checking, and Model Checking
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Category Theory and Computer Science
Proof Principles for Datatypes with Iterated Recursion
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
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Relation lifting [Hermida, C. and B. Jacobs, Structural induction and coinduction in a fibrational setting, Information and Computation 145 (1998), pp. 107-152] extends an endofunctor F:C-C to a functor Rel(F):Rel(C)-Rel(C), where Rel(C) is a suitable category of relations over C. The relation lifting for the functor F can be used to define the notion of bisimulation for coalgebras X-F(X). The related notion of predicate lifting can be used to define invariants for F-coalgebras. Predicate and relation lifting can be directly defined for a rich class of polynomial functors [Hensel, U. and B. Jacobs, Proof principles for datatypes with iterated recursion, in: E. Moggi and G. Rosolini, editors, Category Theory and Computer Science, LNCS 1290 (1997), pp. 220-241; Hermida, C. and B. Jacobs, Structural induction and coinduction in a fibrational setting, Information and Computation 145 (1998), pp. 107-152; Tews, H., Coalgebras for binary methods: Properties of bisimulations and invariants, Theoretical informatics and applications 35 (2001), pp. 83-111]. In this paper I investigate the case where the functor F is defined as the initial semantics of a (single sorted) parametric algebraic specification.