Associative property

Pure mathematics

Mathematics

Data parallelism

Evolutionary biology

Biology

Geodesy

Function (biology)

Compiler

Parallel computing

Benchmark (surveying)

Artificial intelligence

Geography

Chemistry

Programming language

Geometry

Programming style

CLARITY

Computer science

Parallelism (grammar)

Search engine indexing

Point (geometry)

Implicit parallelism

Functional programming

Biochemistry

Proceedings of the ACM on Programming Languages

We present a novel programming language design that attempts to combine the clarity and safety of high-level functional languages with the efficiency and parallelism of low-level numerical languages. We treat arrays as eagerly-memoized functions on typed index sets, allowing abstract function manipulations, such as currying, to work on arrays. In contrast to composing primitive bulk-array operations, we argue for an explicit nested indexing style that mirrors application of functions to arguments. We also introduce a fine-grained typed effects system which affords concise and automatically-parallelized in-place updates. Specifically, an associative accumulation effect allows reverse-mode automatic differentiation of in-place updates in a way that preserves parallelism. Empirically, we benchmark against the Futhark array programming language, and demonstrate that aggressive inlining and type-driven compilation allows array programs to be written in an expressive, "pointful" style with little performance penalty.

Getting to the point: index sets and parallelism-preserving autodiff for pointful array programming