Higher type program schemes and their tree languages

Abstract

We introduce classes of program schemes, which generalize the notion of a recursive program scheme in the sense of Nivat [8], by allowing recursion on higher functional types. The equivalence class of such a scheme can be characterized by an infinite tree and by a tree language. We extend the concept of schematic tree grammars (Nivat [7,8]) and prove, that this allows to generate new tree languages. With this result we prove, that the class of schemes introduced is not translatable into the class of recursive program schemes.