Definition
Projection Function ( Primitive Recursion)
For arity
and , the projection function onto the -th argument is It returns the selected input and ignores the others. The subscript
is the selected position; the superscript is the number of arguments, not a power. Projection functions are basic functions in the definition of primitive-recursive functions.
Example
Selecting an argument
Reordering arguments
Combining two projections gives a function
that swaps its inputs: