> It is simply impossible to prove that a given algorithm behaves well for all inputs (that is to say for all memory states). No, it's not. People write proof

> It is simply impossible to prove that a given algorithm behaves well for all inputs (that is to say for all memory states). No, it's not. People write proofs of algorithms all the time (see the Cormen Rivest book for several examples). This belief stems from a misinterpretation of Rice's theorem ( http://en.wikipedia.org/wiki/Rice%27s_theorem http://en.wikipedia.org/wiki/Rice%27s_theorem ), which says that you can not, in general, create a Turing machine that gives a yes or no answer to any particular property of an input algorithm. That does not, however, mean that you cannot prove particular properties of algorithms for particular algorithms.