Subtyping in alloy

Abstract

A type system for the Alloy modelling language is described that supports subtypes and allows overloading of relation names. No special syntactic features needed to be added to the language to support the type system; there are no casts, and the meaning of a model can be understood without reference to types. Type errors are associated with expressions that are irrelevant, in the sense that they can be replaced by an empty relation without affecting the value of their enclosing formula. Relevance is computed with an abstract interpretation that is relatively insensitive to standard algebraic manipulations. The typechecker for the system is presented in the context of Alloy Analyzer 3.0. Its architecture is explained in terms of key data abstractions, algorithms, and complexity analyses.