A Verified Compositional Algorithm for AI Planning

We report on our HOL4 verification of an AI planning algorithm. The algorithm is compositional in the following sense: a planning problem is divided into multiple smaller abstractions, then each of the abstractions is solved, and finally the abstractions\u27 solutions are composed into a solution for the given problem. Formalising the algorithm, which was already quite well understood, revealed nuances in its operation which could lead to computing buggy plans. The formalisation also revealed that the algorithm can be presented more generally, and can be applied to systems with infinite states and actions, instead of only finite ones. Our formalisation extends an earlier model for slightly simpler transition systems, and demonstrates another step towards formal treatments of more and more of the algorithms and reasoning used in AI planning, as well as model checking

A formalisation of the normal forms of context-free grammars in HOL4

Abstract. We describe the formalisation of the normal forms of context-free grammars (CFGs) using the HOL4 theorem prover. These straightforward pen and paper proofs easily understood from the text turn out to be much harder to mechanise. The informal observations in the text become deductive gaps for a theorem prover that need to be patched

BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Proving

Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread across several ITP systems. This presents a significant challenge to the comparison of methods, which are often complex and difficult to replicate. Addressing this, we present BAIT, a framework for fair and streamlined comparison of learning approaches in ITP. We demonstrate BAIT's capabilities with an in-depth comparison, across several ITP benchmarks, of state-of-the-art architectures applied to the problem of formula embedding. We find that Structure Aware Transformers perform particularly well, improving on techniques associated with the original problem sets. BAIT also allows us to assess the end-to-end proving performance of systems built on interactive environments. This unified perspective reveals a novel end-to-end system that improves on prior work. We also provide a qualitative analysis, illustrating that improved performance is associated with more semantically-aware embeddings. By streamlining the implementation and comparison of Machine Learning algorithms in the ITP context, we anticipate BAIT will be a springboard for future research

Draining the Swamp: Micro Virtual Machines as Solid Foundation for Language Development

Many of today\u27s programming languages are broken. Poor performance, lack of features and hard-to-reason-about semantics can cost dearly in software maintenance and inefficient execution. The problem is only getting worse with programming languages proliferating and hardware becoming more complicated. An important reason for this brokenness is that much of language design is implementation-driven. The difficulties in implementation and insufficient understanding of concepts bake bad designs into the language itself. Concurrency, architectural details and garbage collection are three fundamental concerns that contribute much to the complexities of implementing managed languages. We propose the micro virtual machine, a thin abstraction designed specifically to relieve implementers of managed languages of the most fundamental implementation challenges that currently impede good design. The micro virtual machine targets abstractions over memory (garbage collection), architecture (compiler backend), and concurrency. We motivate the micro virtual machine and give an account of the design and initial experience of a concrete instance, which we call Mu, built over a two year period. Our goal is to remove an important barrier to performant and semantically sound managed language design and implementation