Technical Reports (CIS)
Title
A Review of Three Techniques for Formally Representing Variable Binding
Document Type
Technical Report
Date of this Version
December 2006
Abstract
This paper compares three models for formal reasoning about programming languages with binding. Higher order abstract syntax (HOAS) uses meta-level binding to represent object-level binding [PE88]. Nominal Logic couples a concrete representation of bound variables with a formal apparatus for safely manipulating bound variables [Pit03]. The locally named binding representation places bound and free variables in different syntactic sorts [MP99]. This paper surveys each binding model, and compares it to the others and to Gordon and Melham’s axiomatization of the untyped lambda calculus [GM97]. Comparisons are made based on expressive power, transparency to human readers, and suitability for mechanized reasoning of each binding model. Each system excels in one area; HOAS is most expressive, Nominal Logic most transparent, and locally named most mechanizable.
Download
Date Posted: 08 February 2007
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-06-19.