Evaluation Opportunities in Mechanized Theories

When evaluating logic solvers, it is essential to take into account the application domain in which they will operate. For example, a logic solver for reasoning about programs could be applied either inside a compiler to justify the validity of optimizing transformations, or in an IDE plugin to help developers find bugs in their programs. Despite the similarity of the domain, these two applications lead to different success criteria for the underlying logic solver. Soundness is essential in the compiler application, since no optimizing transformation is permitted to change the observable behavior of the program, but soundness in the bug-finding application can be traded-off if it results in a more productive false positive/false negative rate for the human developer [1]. This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.