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Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck.\n  We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) that eliminates all intermediate arrays -- including the implicit transposed-key buffer and every softmax temporary -- by algebraic construction rather than empirical tuning. 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Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck.\n  We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) that eliminates all intermediate arrays -- including the implicit transposed-key buffer and every softmax temporary -- by algebraic construction rather than empirical tuning. 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