  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.
