In computer programming, Walther recursion is a method of analysing recursive functions that can determine if the function is definitely terminating, given finite inputs. It allows a more natural style of expressing computation than simply using primitive recursive functions.

Walther recursion does not solve the halting problem

Halting problem

In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever...

, as there are still classes of programs that will terminate, but which Walther recursion cannot prove to terminate. Walther recursion may be used in total functional languages

Total functional programming

Total functional programming is a programming paradigm that restricts the range of programs to those that are provably terminating....

in order to allow a more liberal style of showing primitive recursion.

(1) http://ttic.uchicago.edu/~dmcallester/walther.ps