Primitive Recursive Functions are Pure Iterative: Simplifications of the Recursion Scheme
In this video, I go through the proof in Gladstone's 1971 paper "Simplifications of the Recursion Scheme", which shows us how we don't lose anything by restricting our construction of primitive recursive functions to require that f(x+1,y) only depend on f(x,y). You may also be interested in reading Robinson's earlier paper "Primitive Recursive Functions" which sets up this question. Many thanks to the users of cstheory.stackexchange who pointed me in the direction of Gladstone's paper in the first place: https://cstheory.stackexchange.com/qu... https://cstheory.stackexchange.com/qu...
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