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arXiv · 2207.13291

Correct Compilation of Semiring Contractions

Scott Kovach·Fredrik Kjolstad
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Abstract

We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph algorithms. We prove that the model is correct with respect to a functional semantics. We also develop a compiler for variable contraction expressions and show that its performance is equivalent to a state-of-the art sparse tensor algebra compiler, while providing greater generality and correctness guarantees.

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Scott Kovach, Fredrik Kjolstad. 2022-07-27. Correct Compilation of Semiring Contractions. https://arxiv.org/abs/2207.13291

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