William Lovas

The logical framework LF and its metalogic Twelf can be used to encode and reason about a wide variety of logics, languages, and other deductive systems in a formal, machine-checkable way.

Recent studies have shown that ML-like languages can profitably be extended with a notion of subtyping called refinement types. A refinement type discipline uses an extra layer of term classification above the usual type system to more accurately capture certain properties of terms.

I propose that adding refinement types to LF is both useful and practical. To support the claim, I exhibit an extension of LF with refinement types called LFR,work out important details of its metatheory, delineate a practical algorithm for refinement type reconstruction, and present several case studies that highlight the utility of refinement types for formalized mathematics. In the end I find that refinement types and LF are a match made in heaven: refinements enable many rich new modes of expression, and the simplicity of LF ensures that they come at a modest cost.