Multilevel functions in Martin-Löf's type theory

  • Bengt Nordström
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 217)


Multilevel arrays have been used in the VDL and VDM projects for representing abstract syntax trees. In the same way as the function type can be seen as a generalization of the array type, it is possible to generalize multilevel arrays to multilevel functions. They are general trees with finite depth but arbitrary branching. In this paper, a definition of multilevel functions is given in the framework of Martin-Löf's type theory. The formal rules associated with the new data type is given and justified using the semantics of type theory. The paper contains some programs for manipulating the functions and some data types (vectors, natural numbers, lists, binary trees and functions) are seen as special cases of multilevel functions.


Function Type Type Theory Form Leaf Finite Depth Constructive Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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9. References

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    J. A. Bergstra, H. J. M. Goeman, A. Ollongren, G. A. Terpstra, and Th. P. van der Weide, "Axioms for Multilevel Objects", Annales Societatis Mathematicae Polonae, Series IV: Fundamenta Informaticae, Vol. III.2, pp. 171–180 (1979).Google Scholar
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    B. Nordström, K. Petersson, and J. Smith, An Introduction to Type Theory, Programming Methodology Group, Chalmers University of Technology, Göteborg (1985), In preparation.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Bengt Nordström
    • 1
  1. 1.Programming Methodology Group Department of Computer SciencesUniversity of Göteborg Chalmers University of TechnologyGöteborgSweden

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