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An example of a non adequate numeral system. (English. Abridged French version) Zbl 0864.03011
Summary: A numeral system is defined by three closed $$\lambda$$-terms: a normal $$\lambda$$-term $$d_0$$ for Zero, a $$\lambda$$-term $$S_d$$ for Successor, and a $$\lambda$$-term for Zero Test, such that the $$\lambda$$-terms $$(S^i_d\;d_0)$$ are normalizable and have different normal forms. A numeral system is called adequate if and only if it has a $$\lambda$$-term for Predecessor. This note gives a simple example of a nonadequate numeral system.

##### MSC:
 03B40 Combinatory logic and lambda calculus