Constant Function (Primitive Recursion)

Definition

Constant Function ( Primitive Recursion)

For and arity , the constant function with value is

It ignores its inputs and always returns . The subscript is the output value; the superscript is the number of arguments, not a power.

Construction from Zero

Starting with the zero function , each composition with the successor function increases the constant output by one:

For fixed , only applications of are needed. Hence every is primitive-recursive.

Example

Constant outputs with different arities