Planning problems as types, plans as programs : a dependent types infrastructure for verification and reasoning about automated plans in Agda

Abstract

Historically, the Artificial Intelligence and programming language fields have had a mutually beneficial relationship. Typically, theoretical results in the programming language field have practical utility in the Artificial Intelligence field. One example of this that has roots in both declarative languages and theorem proving is AI planning. In recent years, new programming languages have been developed that are founded on dependent type theory. These languages are not only more expressive than traditional programming languages but also have the ability to represent and prove mathematical properties within the language. This thesis will explore how dependently typed languages can benefit the AI planning field. On one side this thesis will show how AI planning languages can be enriched with more expressivity and stronger verification guarantees. On the other, it will show that AI planning is an ideal field to illustrate the practical utility of largely theoretical aspects of programming language theory. This thesis will accomplish this by implementing multiple inference systems for plan validation in the dependently-typed programming language Agda. Importantly, these inference systems will be automated, and embody the Curry-Howard correspondence where plans will not only be proof-terms but also executable functions. This thesis will then show how the dependently-typed implementations of the inference systems can be further utilised to add enriched constraints over plan validation.