On the style of mechanical proving

Abstract

It is quite surprising that — after 5 years of experience — there has been still very little written about how to present and construct mechanical proofs. Such guidelines would definitely help a novice. Since mechanical proving is very different from proving on paper, it may take a long time before one gets accustomed to it and develops an efficient style for constructing and presenting such proofs. Traditional styles, like e.g. decomposing a problem into lemmas and incorporating hints to make the logic of a proof visible, are not straightforwardly taken over to the HOL world. In this paper we present two extensions to HOL, the DERIVATION and LEMMA packages, by which proofs can be written in very much the same format as one would on paper. They are not intended as a replacement of existing HOL mechanisms, but rather as an extension for enabling work in a higher level proof environment.