A fixed-point characterization of the inside-out (IO) and 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 the context-free tree languages to recognizable tree languages and to nondeterministic recursive program(scheme)s (called by value and called by name). Closure properties of the context-free tree languages are discussed. Hierarchies of higher level equational subsets of an algebra are considered.
Journal of Computer and System Sciences, 1977, Vol 15, Issue 3, p. 328-353