FUNCTIONAL PEARL Unfolding pointer algorithms

Abstract

A fair amount has been written on the subject of reasoning about pointer algorithms. There was a peak about 1980 when everyone seemed to be tackling the formal verification of the Schorr–Waite marking algorithm, including Gries (1979, Morris (1982) and Topor (1979). Bornat (2000) writes: “The Schorr–Waite algorithm is the first mountain that any formalism for pointer aliasing should climb”. Then it went more or less quiet for a while, but in the last few years there has been a resurgence of interest, driven by new ideas in relational algebras (Möeller, 1993), in data refinement Butler (1999), in type theory (Hofmann, 2000; Walker and Morrisett, 2000), in novel kinds of assertion (Reynolds, 2000), and by the demands of mechanised reasoning (Bornat, 2000). Most approaches end up being based in the Floyd–Dijkstra–Hoare tradition with loops and invariant assertions. To be sure, when dealing with any recursively-defined linked structure some declarative notation has to be brought in to specify the problem, but no one to my knowledge has advocated a purely functional approach throughout. Mason (1988) comes close, but his Lisp expressions can be very impure. Möller (1999) also exploits an algebraic approach, and the structure of his paper has much in common with what follows.This pearl explores the possibility of a simple functional approach to pointer manipulation algorithms.