Nour, Karim An example of a non adequate numeral system. (English. Abridged French version) Zbl 0864.03011 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. Cited in 1 Document MSC: 03B40 Combinatory logic and lambda calculus Keywords:lambda calculus; closed \(\lambda\)-terms; numeral system; normal forms PDF BibTeX XML Cite \textit{K. Nour}, C. R. Acad. Sci., Paris, Sér. I 323, No. 5, 439--442 (1996; Zbl 0864.03011) Full Text: arXiv OpenURL