General recursive function: Difference between revisions

Revision as of 10:04, 13 November 2021

Revision as of 10:18, 14 November 2021

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#::<math>C_n^k(x_1,\ldots,x_k) \ \stackrel{\mathrm{def}}{=}\ n</math>

#:Alternative definitions use instead a ''zero function'' as a primitive function that always returns zero, and built the constant functions from the zero function, the successor function and the composition operator.

# ''Successor function S:''<br />&nbsp;&nbsp;&nbsp;&nbsp;
#::<math>S(x) \ \stackrel{\mathrm{def}}{=}\ x + 1\,</math>

# ''Projection function'' <math>P_i^k</math> (also called the ''Identity function''): For all natural numbers <math>i, k</math> such that <math>1\le i\le k</math>:

#::<math>P_i^k(x_1,\ldots,x_k) \ \stackrel{\mathrm{def}}{=}\ x_i \, .</math>