An official website of the United States government
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.
more »
« less
Julia's Efficient Algorithm for Subtyping Unions and Covariant Tuples
The Julia programming language supports multiple dispatch and provides a rich type annotation language to specify method applicability. When multiple methods are applicable for a given call, Julia relies on subtyping between method signatures to pick the correct method to invoke. Julia's subtyping algorithm is surprisingly complex, and determining whether it is correct remains an open question. In this paper, we focus on one piece of this problem: the interaction between union types and covariant tuples. Previous work normalized unions inside tuples to disjunctive normal form. However, this strategy has two drawbacks: complex type signatures induce space explosion, and interference between normalization and other features of Julia's type system. In this paper, we describe the algorithm that Julia uses to compute subtyping between tuples and unions - an algorithm that is immune to space explosion and plays well with other features of the language. We prove this algorithm correct and complete against a semantic-subtyping denotational model in Coq.
more »
« less
- PAR ID:
- 10172975
- Date Published:
- Journal Name:
- European Conference on Object-Oriented Programming (ECOOP)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
The programming language Julia is designed to solve the 'two language problem', where developers who write scientific software can achieve desired performance, without sacrificing productivity. Since its inception in 2012, developers who have been using other programming languages have transitioned to Julia. A systematic investigation of the questions that developers ask about Julia can help in understanding the challenges that developers face while using Julia. Such understanding can be helpful (i) for toolsmiths who can construct tools so that developers can maximize their experience of using Julia, and (ii) for Julia language maintainers with empirical evidence on areas to improve the language as well as the Julia ecosystem. We conduct an empirical study with 3,093 Stack Overflow posts where we identify 13 categories of questions related to Julia-based software development. We observe developers to ask about a diverse set of topics, such as GC, Julia's garbage collector, JuMP, a domain-specific language constructed using Julia, and symbols, a metaprogramming utility in Julia. Based on our emerging results, we recommend enhancing support for developers with Julia-based tools and techniques for cross language transfer, type-related assistance, and package resolution.more » « less
-
Automatic differentiation (AutoDiff) in machine learning is largely restricted to expressions used for neural networks (NN), with the depth rarely exceeding a few tens of layers. Compared to NN, numerical simulations typically involve iterative algorithms like time steppers that lead to millions of iterations. Even for modest-sized models, this may yield infeasible memory requirements when applying the adjoint method, also called backpropagation, to time-dependent problems. In this situation, checkpointing algorithms provide a trade-off between recomputation and storage. This paper presents the package Checkpointing.jl that leverages expression transformations in the programming language Julia and the package ChainRules.jl to automatically and transparently transform loop iterations into differentiated loops. The user may choose between various checkpointing algorithm schemes and storage devices. We describe the unique design of Checkpointing.jl and demonstrate its features on an automatically differentiated MPI implementation of Burgers’ equation on the Polaris cluster at the Argonne Leadership Computing Facility.more » « less
-
Aichholzer, Oswin; Wang, Haitao (Ed.)We show that a variant of the continuous Fréchet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming can be easily handled via refinement. Combined with a Dijkstra/Prim type algorithm, this leads to a realization of the Fréchet distance (i.e., a morphing) that is locally optimal (aka locally correct), that is both easy to compute, and in practice, takes near linear time on many inputs. The new morphing has the property that the leash is always as short as possible. These matchings/morphings are more natural, and are better than the ones computed by standard algorithms - in particular, they handle noise more graciously. This should make the Fréchet distance more useful for real world applications. We implemented the new algorithm, and various strategies to obtain fast practical performance. We performed extensive experiments with our new algorithm, and released publicly available (and easily installable and usable) Julia and Python packages. In particular, the Julia implementation, for computing the regular Fréchet distance, seems to be {significantly faster} than other currently available implementations. See Table 2.2. Our algorithms can be used to compute the almost-exact Fréchet distance between polygonal curves. Implementations and numerous examples are available here: https://frechet.xyz.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPIcs.ECOOP.2019.24
