Adelfa: A System for Reasoning about LF Specifications [preprint]
July 16, 2021
Mary Southern (Ph.D. 2021), Gopalan Nadathur (professor)
We present a system called Adelfa that provides mechanized support for reasoning about specifications developed in the Edinburgh Logical Framework or LF. Underlying Adelfa is a new logic named L_LF. Typing judgements in LF are represented by atomic formulas in L_LF and quantification is permitted over contexts and terms that appear in such formulas. Contexts, which constitute type assignments to uniquely named variables that are modelled using the technical device of nominal constants, are characterized in L_LF by context schemas that describe their inductive structure. We present these formulas and an associated semantics before sketching a proof system for constructing arguments that are sound with respect to the semantics. We then outline the realization of this proof system in Adelfa and illustrate its use through a few example proof developments. We conclude the paper by relating Adelfa to existing systems for reasoning about LF specifications.