General recursive function: Difference between revisions

Revision as of 22:09, 23 November 2021

Revision as of 16:26, 2 February 2022

Line 15:

#''Constant functions {{mvar|C{{su|b=n|p=k}}}}'': For each natural number {{mvar|n}} and every {{mvar|k}}

#::<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 builtbuild the constant functions from the zero function, the successor function and the composition operator.

# ''Successor function S:''

#::<math>S(x) \ \stackrel{\mathrm{def}}{=}\ x + 1\,</math>

Line 43:

:<math>f(x_1,\ldots,x_k) \simeq g(x_1,\ldots,x_l)</math>

holds if and only if for any choice of arguments either both functions are defined and their values are equal or both functions are undefined.

==Examples==

Examples not involving the minimization operator can be found at [[Primitive recursive function#Examples]].