second-order mathematical theory of computation
In this work we show that it is possible to formalize all properties regularly observed in (deterministic and non-deterministic) algorithms in second-order predicate calculus. Moreover, we show that for any given algorithm it suffices to know how to formalize its 'partial correctness' by a second-order formula in order to formalize all other properties by second-order formulas. This result is of special interest since 'partial correctness' has already been formalized in second-order predicate calculus for many classes of algorithms.
theory computation algorithm correctness order class