Proving Properties about Lists Using Containers

Bundy and Richardson [7] presented a technique for reasoning about lists using ellipsis (the dots in 1+2+ . . .+10), where a polymorphic function, denoted by 2, is used to encapsulate recursive definitions of list functions and a portrayal system using ellipsis gives an informal proof. We highlight certain limitations of this technique and address these limitations using the recently developed theory of containers which capture the idea that many important datatypes consist of templates where data is stored. We implement our ideas in Coq and demonstrate how they can be used to prove theorems that eluded Bundy and Richardson in [7].