We derive four memory-optimal inference artifacts for transformer attention using the Mathematics of Arrays (MoA), each following directly from the forward-pass Denotational Normal Form (DNF) of with the query-row index fixed to the current decode step. The artifacts are: (1)~a single-query decode DNF in which the
ψ-reduction eliminates the
K⊤ buffer algebraically, achieving
(dk+ndk+ndv+dv)×4B Dynamic Random Access Memory (DRAM) traffic result numerically verified to
∥err∥≤2×10−7; (2)~a C/OpenACC Graphics Processing Unit (GPU) kernel with Operational Normal Form (ONF) stride arithmetic and hardware-coalesced memory access, verified to
∥err∥∞=0 (exact IEEE-754 floating-point arithmetic); (3)~a multi-step KV-cache with
O(dk+dv) per-step append via MoA concatenation
#; and (4)~Grouped-Query Attention (GQA) and Multi-Query Attention (MQA) derived via
ψ-selection, achieving a proven
hkvhq reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.