Understanding and maintaining tactics graphically OR how we are learning that a diagram can be worth more than 10K LoC

TL;DR

This paper explores the use of a graphical language, PSGraph, to represent proof strategies in theorem proving, demonstrating improved understandability and maintainability over traditional linear tactic languages.

Contribution

It extends PSGraph with new features for development and debugging, and compares its effectiveness to linear tactic languages through re-implementation of existing tactics.

Findings

PSGraph improves debugging and readability of proof tactics

Refactoring tactics in PSGraph enhances maintainability

Graphical representation aids understanding of complex proof strategies

Abstract

The use of a functional language to implement proof strategies as proof tactics in interactive theorem provers, often provides short, concise and elegant implementations. Whilst being elegant, the use of higher order features and combinator languages often results in a very procedural view of a strategy, which may deviate significantly from the high-level ideas behind it. This can make a tactic hard to understand and hence difficult to to debug and maintain for experts and non-experts alike: one often has to tear apart complex combinations of lower level tactics manually in order to analyse a failure in the overall strategy. In an industrial technology transfer project, we have been working on porting a very large and complex proof tactic into PSGraph, a graphical language for representing proof strategies, supported by the Tinker tool. The goal of this work is to improve understandability and maintainability of tactics. Motivated by some initial successes with this, we here extend PSGraph with additional features for development and debugging. Through the re-implementation and refactoring of several existing tactics, we demonstrates the advantages of PSGraph compared with a typical linear (term-based) tactic language with respect to debugging, readability and maintenance. In order to act as guidance for others, we give a fairly detailed comparison of the user experience with the two approaches. The paper is supported by a web page providing further details about the implementation as well as interactive illustrations of the examples.