# How to Program an Infinite Abacus

@article{Lambek1961HowTP, title={How to Program an Infinite Abacus}, author={Joachim Lambek}, journal={Canadian Mathematical Bulletin}, year={1961}, volume={4}, pages={295 - 302} }

This is an expository note to show how an “infinite abacus” (to be defined presently) can be programmed to compute any computable (recursive) function. Our method is probably not new, at any rate, it was suggested by the ingenious technique of Melzak [2] and may be regarded as a modification of the latter. By an infinite abacus we shall understand a countably infinite set of locations (holes, wires etc.) together with an unlimited supply of counters (pebbles, beads etc.). The locations are…

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