Name-passing calculi: from fusions to preorders and types (Appendix)

A. Reduction-closed barbed congruence (Section II) Definition 28 (Reduction-closed barbed congruence). Let L be a process calculus, in which a reduction relation −→L and barb predicates ↓a , for each a in a given set of names, have been defined. A relationR on the processes of L is context-closed if PRQ implies C[P ]RC[Q], for each context C of L; the relation is barb-preserving if for any name a, P ↓a implies Q ↓a ; it is reduction-closed if whenever P −→L P ′, there is Q′ s.t. Q −→L Q′ and P ′RQ′. Then reduction-closed barbed congruence in L, written 'L, is the largest symmetric relation on the processes of L that is context-closed, reduction-closed, and barb-preserving.