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Mathematical linear-algebra surface (spec stub)

Status: Partial (Phase 2i + 7e) — 1d @/dot, sum(array), 2d @ (2i-c); simd_dot/matmul_naive pure-Li benches; explicit SIMD MIR (7e-a) deferred
Plan: docs/superpowers/plans/2026-05-16-li-math-linalg-surface.md
Gaps: Provability gaps G-math

No runtime math dispatch

Mathematical notation is static:

  • A @ B — matrix multiply is shape-checked at compile time; wrong dimensions → lic build fails
  • a * b — element-wise/broadcast rules decided in the typechecker, not at run time
  • dot, sum — lowering to SIMD/reduction MIR at compile time

Users never call simd(...) or lane intrinsics in normal code. There is no “slow path” that discovers shapes at runtime.

Goal: linear-algebra mistakes are compile-time errors, same class as type errors — not ValueError at run time.

Users write C += A @ B, y[i] = alpha * x[i] + y[i], dot(x, y) — not simd(...) or __li_simd_* in handbook or Tier 1 benchmarks.

Execution control remains decorators (@parallel, @vectorized, @cpu) — also compile-time only.

Tier 1 cross-lang regression: Li within 1.2× C++ on same machine.