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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
6. references
ADJ: GOGUEN, J.A./THATCHER, J.W./WAGNER, E.G./WRIGHT, J.B. Initial algebra semantics IBM-Report RC 5701, 1975
COURCELLE, B. Ensembles Algébriques d'Arbres et Langages Déterministes; quelques applications aux Schémas de Programme IRIA report 1975
DAMM, W. Higher type schemes and their tree languages to appear
ENGELFRIET, J./SCHMIDT, E.M. IO and OI Datalogisk Afdelning report, DAIMI PB-47, Aarhus University, Denmark, 1975
INDERMARK, K. Schemes with recursion on higher types in: Mathematical foundations of Computer Science, Proc. 5th conference in Gdansk, Polen, Lecture Notes in Computer Science, 45, 1976
MEZEI, J./WRIGHT, J.B. Algebraic automata and context-free sets Inf. and Control, 11, 1967
NIVAT, M. Langages algébriques sur le magma libre et sémantique des schémas de programme in: Automata, Languages and Programming, ed. M. Nivat, North-Holland Publishing Company, Amsterdam, 1972
NIVAT, M. On the interpretation of recursive program schemes Symposia Matematica, Atti del convegno d'Informatica teorica, Roma, 1973
WAND, M. A concrete approach to abstract recursive definitions in: Automata, Languages and Programming, ed. M. Nivat, North-Holland Publishing Company, Amsterdam, 1972
WAND, M. An algebraic formulation of the Chomsky hierarchy in: Category theory applied to computation and control, Lecture Notes in Computer Science, 25, 1975
Rights and permissions
Copyright information
© 1977 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Damm, W. (1977). Higher type program schemes and their tree languages. In: Theoretical Computer Science. Lecture Notes in Computer Science, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08138-0_5
Download citation
DOI: https://doi.org/10.1007/3-540-08138-0_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08138-8
Online ISBN: 978-3-540-37389-6
eBook Packages: Springer Book Archive