The Joy of Sets

The semantics of many bulk data models depends on user-defined attributes such as definitions of element equality, ordering, and other domain predicates. While these attributes are an intrinsic part of the data model, they are not normally treated as part of the static type description. This leads to the occurrence of data modelling errors which are not statically detectable, such as a union operator accidentally being applied to two sets which have different equality semantics. Here we introduce a model of bulk types which includes such attributes as part of the type definition, along with a typechecking scheme which is statically decidable. The model relies upon the value dependencies being manifest to the typechecker; one neat way of achieving this is through the new paradigm of hyper-programming. For cases where the static typechecking introduced is unnecessarily restrictive a polymorphism scheme which provides controlled flexibility is introduced.