In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function....

recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions...

function, a computable partial function from natural numbers to natural numbers Primitive recursive function, a function which can be computed with loops...

Primitive recursive arithmetic (PRA) is a quantifier-free formalization of the natural numbers. It was first proposed by Norwegian mathematician Skolem...

In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets...

= 2 and S(2) = 3. The successor function is one of the basic components used to build a primitive recursive function. Successor operations are also known...

property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose that R(y, x1, ..., xk) is...

functions and the general recursive functions. According to the Church–Turing thesis, computable functions are exactly the functions that can be calculated...

functions used in computability theory. Every function in the Grzegorczyk hierarchy is a primitive recursive function, and every primitive recursive function...