An example of a non adequate numeral system

Karim Nour (1)

1 LAMA - Laboratoire de Mathématiques

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 $({S_d}^{i} ~ d_0)$ are normalizable and have different normal forms. A numeral system is said adequate iff it has a closed $\lambda$-term for Predecessor. This Note gives a simple example of a non adequate numeral system.

Domaines: Logique [math.LO]

Karim Nour. An example of a non adequate numeral system. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1996, 323, pp.439-442. ⟨hal-00381045⟩