General Bindings and Alpha-Equivalence in Nominal Isabelle

TL;DR

This paper extends Nominal Isabelle to support reasoning about general bindings involving multiple variables simultaneously, improving the formal handling of complex language constructs.

Contribution

It introduces new definitions of alpha-equivalence for general bindings and automates the reasoning infrastructure within Nominal Isabelle.

Findings

Supports reasoning about multi-variable bindings in programming languages

Establishes automated alpha-equivalence reasoning infrastructure

Provides strong induction principles with variable conventions

Abstract

Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to de-Bruijn indices). In this paper we present an extension of Nominal Isabelle for dealing with general bindings, that means term constructors where multiple variables are bound at once. Such general bindings are ubiquitous in programming language research and only very poorly supported with single binders, such as lambda-abstractions. Our extension includes new definitions of alpha-equivalence and establishes automatically the reasoning infrastructure for alpha-equated terms. We also prove strong induction principles that have the usual variable convention already built in.