Terminating general recursion Authors
Part II Computer Science
Received: 15 October 1987 Revised: 15 June 1988 DOI:
Cite this article as: Nordström, B. BIT (1988) 28: 605. doi:10.1007/BF01941137 Abstract
In Martin-Löf's type theory, general recursion is not available. The only iterating constructs are primitive recursion over natural numbers and other inductive sets. The paper describes a way to allow a general recursion operator in type theory (extended with propositions). A proof rule for the new operator is presented. The addition of the new operator will not destroy the property that all well-typed programs terminate. An advantage of the new program construct is that it is possible to separate the termination proof of the program from the proof of other properties.
D.2.1 D.2.4 D.3.1 F.3.1 F.3.3 Key Words recursion well-founded induction programming logic fixed point termination proof
Dedicated to Peter Naur on the occasion of his 60:th birthday.
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Peter Aczel. An introduction to inductive definitions. In J. Barwise, editor,
Handbook of Mathematical Logic, pages 739-, North-Holland Publishing Company, 1977.
R. L. Constable and et. al.
Implementing Mathematics with the NuPRL Proof Development System. Prentice-Hall, Englewood Cliffs, NJ, 1986.
Per Martin-Löf. Constructive mathematics and computer programming. In
Logic, Methodology and Philosophy of Science, VI, 1979, pages 153–175, North-Holland, 1982.
Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.
Bengt Nordström and Kent Petersson.
The Semantics of Module Specifications in Martin-Löf's Type Theory. PMG Report 36, Chalmers University of Technology, S-412 96 Göteborg, 1987.
Bengt Nordström and Kent Petersson. Types and specifications. In R. E. A. Mason, editor,
Proceedings of IFIP 83, pages 915–920, Elsevier Science Publishers, Amsterdam, October 1983.
Bengt Nordström and Jan Smith. Propositions, types and specifications in Martin-Löf's type theory.
BIT, 24(3):288–301, October 1984.
Lawrence C. Paulson. Constructing recursion operators in intuitionistic type theory.
Journal of Symbolic Computation, (2):325–355, 1986.
Lawrence C. Paulson.
Natural Deduction Proof as Higher-Order Resolution. Technical report 82, University of Cambridge Computer Laboratory, Cambridge, 1985.
A Programming System for Type Theory. PMG report 9, Chalmers University of Technology, S-412 96 Göteborg, 1982, 1984.
E. Saaman and G. Malcolm.
Well-founded Recursion in Type theory. Technical Report, Subfaculteit Wiskunde en Informatica, Rijksuniversiteit Groningen, Netherlands, 1987.
Jan M. Smith. The identification of propositions and types in Martin-Löf's type theory. In
Foundations of Computation Theory, Proceedings of the Conference, pages 445–456, 1983.