Adelfa: A System for Reasoning about LF Specifications

TL;DR

Adelfa is a new system that enables formal reasoning about LF specifications using a novel logic, L_LF, which models contexts and typing judgements with sound proof mechanisms.

Contribution

It introduces L_LF, a logic for reasoning about LF, and implements it in Adelfa, providing a new tool for formal verification of LF-based specifications.

Findings

L_LF effectively models LF typing judgements.

Adelfa's proof system is sound and implemented successfully.

Demonstrated use cases show practical reasoning capabilities.

Abstract

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.