Date of Award
Doctor of Philosophy (PhD)
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 itsmetatheory, delineate a practical algorithmfor refinement type reconstruction, andpresent 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.
Lovas, William, "Refinement Types for Logical Frameworks" (2010). Dissertations. 74.