An example of a non adequate numeral system
Nour, Karim
HAL, hal-00381045 / Harvested from HAL
Text on HAL
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.
Publié le : 1996-07-05
Classification:  [MATH.MATH-LO]Mathematics [math]/Logic [math.LO] 
@article{hal-00381045,
     author = {Nour, Karim},
     title = {An example of a non adequate numeral system},
     journal = {HAL},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00381045}
}

Nour, Karim. An example of a non adequate numeral system. HAL, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/hal-00381045/