Inferable Existential Quantification

Abstract interpretation is an excellent tool for designing complete dataflow analyses [6]. Existential quantification is an excellent tool for designing precise dataflow analyses. However, these two tools are difficult to combine. Abstract interpretation requires algorithms for deciding subtypes and constructing joins. This is problematic for existential quantification because simply subtyping with existential quantification is undecidable in general [17], not to mention the additional challenge of joining with existential quantification. This paper presents a category-theoretic framework for designing abstract domains for complete inference and analysis using constrained but expressive forms of existential quantification. This framework is constructive in that it supplies the abstract algorithms for deciding subtypes and constructing joins. This framework is also instructive in that it provides guidelines to follow while designing the abstract domain and existential quantification in order to guarantee inferability. Finally, the framework is practical for real-world applications, as demonstrated by its critical role in designing an inferable typed assembly language for C# [16].