IO and OI

Resumé

A fixed point characterization of the inside-out (IO) and the outside- in (OI) context-free tree languages is given. This characterization is used to obtain a theory of nondeterministic systems of context-free equations with parameters. Several ''Mezei and Wright like'' results are obtained which relate to context-free tree languages, to recognizable tree languages and to nondeterministic recursive program(scheme)s (called by value and called by name). The emptiness problem and closure properties of the context-free tree languages are discussed. Hierarchies of higher level equational subsets of an algebra are considered.