Type stability in Julia: avoiding performance pathologies in JIT compilation

As a scientific programming language, Julia strives for performance but also provides high-level productivity features. To avoid pathologies, users are expected to adhere coding discipline that enables so-called type stability. Informally, function is stable if the of output depends only on types inputs, not their values. This paper formal definition stability as well stronger property groundedness, shows groundedness compiler optimizations, and proves correct. We perform corpus analysis uncover how these type-related properties manifest in practice.