Defining soft sortedness by abstract interpretation

Abstract

Sorted languages can improve the expressiveness and efficiency of reasoning. A conventional sorted language typically includes well-sortedness rules amongst the rules for well-formedness. A major disadvantage of this approach is that many intuitively meaningful expressions are ill-sorted and hence not part of the language. To overcome this limitation, soft sorting regards as well-formed, all firstorder expressions of the corresponding unsorted language, and lets the semantics be the basis for defining the significance of the sort syntax. In this paper we show how soft sortedness can be defined by abstract interpretations which characterise semantic properties of softly sorted expressions.