Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.sobol

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/sobol.clj1 definitions, 4 theorems

AHoF O60 Sobol Sequences: a quasi-random low-discrepancy sequence for uniform space-filling sampling; the sequence meets its uniformity target when the star discrepancy stays within the bound: low-discrepancy? discrepancy bound = decide (discrepancy <= bound). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.sobol` prints this classification.

sobol/low-discrepancy? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

sobol/within-bound-uniform :
  → lis/extends? 1/4 1/2 = data/true

sobol/boundary-uniform :
  → lis/extends? 1/2 1/2 = data/true

sobol/discrepancy-certificate :
  → 1/4 ≤ 1/2

sobol/over-bound-nonuniform :
  → lis/extends? 3/4 1/2 = data/false