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.

翻译：我们引入了一种正式的操作语义,描述可变收缩问题的结合实施,它通过一个精密和密集的稀散代数、相关代数和图表算法进行计算和概括计算指数算术,我们证明该模型在功能语义学方面是正确的。我们还为可变收缩表达式开发了一个汇编器,并表明其性能相当于一个最先进的稀疏高代数编译器,同时提供了更大的普遍性和正确性保障。