An example of a non adequate numeral system. (English. Abridged French version) Zbl 0864.03011

Nour, Karim

C. R. Acad. Sci., Paris, Sér. I 323, No. 5, 439-442 (1996).

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

Keywords:

lambda calculus; closed \(\lambda\)-terms; numeral system; normal forms