, Volume 28, Issue 3, pp 605-619

Terminating general recursion

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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.