Uniform ideals and strictness analysis

Abstract

We propose a notion of uniform ideal (certain Scott-closed sets) to characterise strictness properties. This enables us to explain why Hughes’ and Wadler’s H projection for lazy list strictness analysis is not in general expressible as an abstract interpretation property of the standard semantics. We give circumstances when it is so expressible. Doing so casts light on Bum’s HB projection and his question of its relationship to H. Uniform ideals axe a generalisation of the sets of values corresponding to types in (simple) polymorphic type systems. Wadler’s doubly-lifted abstract domain constructor for lazy lists can be seen as a special case which only uses certain uniform ideals. The confluence of strictness and type theory furthers Kuo and Mishra’s notion of “strictness types”.