Traces of i/o-automata in isabelle/HOLCF

Abstract

This paper presents a formalization of finite and infinite sequences in domain theory carried out in the theorem prover Isabelle. The results are used to model the metatheory of I/O automata; they are, however, applicable to any trace based model of parallelism which distinguishes internM and external actions. We make use of the logic HOLCF, an extension of HOL with domain theory and show how to move between HOL and HOLCF. This allows us to restrict the use of HOLCF to metatheoretic arguments while actual refinement proofs between I/O automata are carried out within the simpler logic HOL. In order to evaluate the formalization we prove the correctness of a generalized refinement concept in I/O automata.