Optimizing programs to run efficiently on modern parallel hardware is hard but crucial for many applications. The predominantly used imperative languages-like C or OpenCL-force the programmer to intertwine the code describing functionality and optimizations. This results in a portability nightmare that is particularly problematic given the accelerating trend towards specialized hardware devices to further increase efficiency. Many emerging DSLs used in performance demanding domains such as deep learning or high-performance image processing attempt to simplify or even fully automate the optimization process. Using a high-level-often functional-language, programmers focus on describing functionality in a declarative way. In some systems such as Halide or TVM, a separate schedule specifies how the program should be optimized. Unfortunately, these schedules are not written in well-defined programming languages. Instead, they are implemented as a set of ad-hoc predefined APIs that the compiler writers have exposed. In this functional pearl, we show how to employ functional programming techniques to solve this challenge with elegance. We present two functional languages that work together-each addressing a separate concern. RISE is a functional language for expressing computations using well known functional data-parallel patterns. ELEVATE is a functional language for describing optimization strategies. A high-level RISE program is transformed into a low-level form using optimization strategies written in ELEVATE. From the rewritten low-level program high-performance parallel code is automatically generated. In contrast to existing high-performance domain-specific systems with scheduling APIs, in our approach programmers are not restricted to a set of built-in operations and optimizations but freely define their own computational patterns in RISE and optimization strategies in ELEVATE in a composable and reusable way. We show how our holistic functional approach achieves competitive performance with the state-of-the-art imperative systems Halide and TVM. CCS Concepts: • Software and its engineering → Functional languages; Compilers; • Theory of computation → Rewrite systems.

We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non meaningful compositions of rewrites that otherwise would fail during rewriting at runtime. Furthermore, our type system enables reasoning about how rewriting transforms the shape of the computational program. We present a formalization of our language at its type system and demonstrate its practical use for expressing compiler optimization strategies.Our type system builds the foundation for many interesting future applications, including verifying the correctness of program transformations and synthesizing program transformations from specifications encoded as types.

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