General recursive functions of natural numbers.¶
Kleene, S. C. (1936). General recursive functions of natural numbers. Mathematische Annalen, 112(1), 727-742.
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Primes¶
- Well-Foundedness (Well-Ordering)
- … infinite structures via productivity (the dual of termination); dependently-typed languages (Coq, Agda, Lean) require a termination check for recursive definitions, implemented via structural or well-founded recursion combined with totality checking, with the underlying recursion theory tracing back to Kleene (1936).
This sourceFoundational definition of the general-recursive functions, the basis for later termination and well-founded-recursion theory.
- … infinite structures via productivity (the dual of termination); dependently-typed languages (Coq, Agda, Lean) require a termination check for recursive definitions, implemented via structural or well-founded recursion combined with totality checking, with the underlying recursion theory tracing back to Kleene (1936).
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