Program analysis and specialisation using tree automata

Static analysis of programs using regular tree grammars has been studied for more than 30 years, the earliest example being Reynolds’ work on automatic derivation of data-type definitions from untyped functional programs. Recently the topic has attracted renewed attention, with applications in program specialisation, data flow analysis, shape analysis, mode and type inference, termination analysis and infinite state model checking. There are several related viewpoints on analysis using regular tree grammars, including set constraints, abstract interpretation over tree automata domain, directed types, regular approximation and regular type inference. The lectures will first summarise the relevant properties of finite tree automata, which provide a common foundation for these different viewpoints. It will then be shown how to construct an abstract interpretation over a domain of finite tree automata. Various program analyses based on this domain will be presented, such as “soft” type construction, checking of safety properties in infinite state systems, and derivation of term-size measures for termination analysis. The lectures will also cover the construction of static analyses based on a given tree grammar capturing some properties of interest. It will be shown (for logic programs) how to build a precise analysis for a program based on an arbitrary regular tree grammar. This has applications in type and mode inference, binding time analysis for offline partial evaluation, and control of online partial evaluation.