We consider the formulation of a symbolic execution (SE) procedure for functional programs that interact with effectful, opaque libraries. Our procedure allows specifications of libraries and abstract data type (ADT) methods that are expressed in Linear Temporal Logic over Finite Traces (LTL f ), interpreting them as symbolic finite automata (SFAs) to enable intelligent specification-guided path exploration in this setting. We apply our technique to facilitate the falsification of complex data structure safety properties in terms of effectful operations made by ADT methods on underlying opaque representation type(s). Specifications naturally characterize admissible traces of temporally-ordered events that ADT methods (and the library methods they depend upon) are allowed to perform. We show how to use these specifications to construct feasible symbolic input states for the corresponding methods, as well as how to encode safety properties in terms of this formalism. More importantly, we incorporate the notion of symbolic derivatives , a mechanism that allows the SE procedure to intelligently underapproximate the set of precondition states it needs to explore, based on the automata structures latent in the provided specifications and the safety property that is to be falsified. Intuitively, derivatives enable symbolic execution to exploit temporal constraints defined by trace-based specifications to quickly prune unproductive paths and discover feasible error states. Experimental results on a wide-range of challenging ADT implementations demonstrate the effectiveness of our approach.

Julia is a modern scientific-computing language that relies on multiple dispatch to implement generic libraries. While the language does not have a static type system, method declarations are decorated with expressive type annotations to determine when they are applicable. To find applicable methods, the implementation uses subtyping at run-time. We show that Julia’s subtyping is undecidable, and we propose a restriction on types to recover decidability by stratifying types into method signatures over value types—where the former can freely use bounded existential types but the latter are restricted to use-site variance. A corpus analysis suggests that nearly all Julia programs written in practice already conform to this restriction.

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.

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.

Semantic subtyping enables simple, set-theoretical reasoning about types by interpreting a type as the set of its values. Previously, semantic subtyping has been studied primarily in the context of statically typed languages with structural typing. In this paper, we explore the applicability of semantic subtyping in the context of a dynamic language with nominal types. Instead of static type checking, dynamic languages rely on run-time checking of type tags associated with values, so we propose using the tags for semantic subtyping. We base our work on a fragment of the Julia language and present tag-based semantic subtyping for nominal types, tuples, and unions, where types are interpreted set-theoretically as sets of type tags. The proposed subtyping relation is shown to be decidable, and a corresponding analytic definition is provided. The implications of using semantic subtyping for multiple dispatch are also discussed.

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.

In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in abstract way. We advocate the design of a generic Coq library, which is aimed to provide three building blocks for each checking mechanism: propositional, computable, and correctness proofs. Implemented part of the library is justified by applying it to a certified static checker of an extension of STLC.