Part II Computer Science

BIT Numerical Mathematics

, Volume 28, Issue 3, pp 605-619

First online:

Terminating general recursion

  • Bengt NordströmAffiliated withDepartment of Computer Science, Chalmers University of Technology and the University of Göteborg

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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