On calculational proofs

This note is about the \calculational style" of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We deene the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The deenition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate formula has a calculational proof.