Stronger compositions for retrenchments

Noting that the usual ‘propositionally’ based way of composing retrenchments can yield many ‘junk’ cases, alternative approaches to composition are introduced (via notions of tidy, neat, and fastidious retrenchments) that behave better in this regard. These alternatives do however make other issues such as associativity harder. The technical details are presented for vertical composition of retrenchments (i.e. the composition of successive retrenchment steps).