TY - JOUR
T1 - Many more predecessors
T2 - A representation workout
AU - Kiselyov, O. L.E.G.
N1 - Publisher Copyright:
© The Author(s) 2020. Published by Cambridge University Press.
PY - 2020
Y1 - 2020
N2 - From the outset, lambda calculus represented natural numbers through iterated application. The successor hence adds one more application, and the predecessor removes. In effect, the predecessor un-applies a term - which seemed impossible, even to Church. It took Kleene a rather oblique glance to sight a related representation of numbers, with an easier predecessor. Let us see what we can do if we look at this old problem with today's eyes. We discern the systematic ways to derive more predecessors - smaller, faster, and sharper - while keeping all teeth.
AB - From the outset, lambda calculus represented natural numbers through iterated application. The successor hence adds one more application, and the predecessor removes. In effect, the predecessor un-applies a term - which seemed impossible, even to Church. It took Kleene a rather oblique glance to sight a related representation of numbers, with an easier predecessor. Let us see what we can do if we look at this old problem with today's eyes. We discern the systematic ways to derive more predecessors - smaller, faster, and sharper - while keeping all teeth.
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U2 - 10.1017/S095679682000009X
DO - 10.1017/S095679682000009X
M3 - Article
AN - SCOPUS:85082676339
SN - 0956-7968
JO - Journal of Functional Programming
JF - Journal of Functional Programming
M1 - e7
ER -