Double recursion
In recursive function theory, double recursion is an extension of primitive recursion which allows the definition of non-primitive recursive functions like the Ackermann function.
Raphael M. Robinson called functions of two natural number variables G double recursive with respect to given functions, if
- G is a given function of x.
- G is obtained by substitution from the function G and given functions.
- G is obtained by substitution from G, the function G and given functions.
Robinson goes on to provide a specific double recursive function
where the given functions are primitive recursive, but G is not primitive recursive. In fact, this is precisely the function now known as the Ackermann function.
