Programming languages that support multiple dispatch rely on an expressive notion of subtyping to specify method applicability. In these languages, type annotations on method declarations are used to select, out of a potentially large set of methods, the one that is most appropriate for a particular tuple of arguments. Julia is a language for scientific computing built around multiple dispatch and an expressive subtyping relation. This paper provides the first formal definition of Julia's subtype relation and motivates its design. We validate our specification empirically with an implementation of our definition that we compare against the existing Julia implementation on a collection of real-world programs. Our subtype implementation differs on 122 subtype tests out of 6,014,476. The first 120 differences are due to a bug in Julia that was fixed once reported; the remaining 2 are under discussion. CCS Concepts: • Software and its engineering → Data types and structures; Semantics;

Dynamic programming languages face semantic and performance challenges in the presence of features, such as eval, that can inject new code into a running program. The Julia programming language introduces the novel concept of world age to insulate optimized code from one of the most disruptive side-effects of eval: changes to the definition of an existing function. This paper provides the first formal semantics of world age in a core calculus named juliette, and shows how world age enables compiler optimizations, such as inlining, in the presence of eval. While Julia also provides programmers with the means to bypass world age, we found that this mechanism is not used extensively: a static analysis of over 4,000 registered Julia packages shows that only 4-9% of packages bypass world age. This suggests that Julia's semantics aligns with programmer expectations.

Figure 1: Our type flow visualization showing type signatures for a subset of R's base package functions. Function names are listed at the top followed by the first two argument types. Complete signatures are shown in the full visualization (Fig. 2).

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

No abstract