Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.ce-falsification

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

AHoF V15 Cross-Entropy for Falsification: fit the sampling distribution to the failure region by keeping the elite (lowest-cost) samples below the cross-entropy quantile: elite? cost quantile = decide (cost <= quantile). 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.ce-falsification` prints this classification.

ce-fal/elite? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

ce-fal/low-cost-elite :
  → ce-fal/elite? 1/4 1/2 = data/true

ce-fal/boundary-elite :
  → ce-fal/elite? 1/2 1/2 = data/true

ce-fal/elite-certificate :
  → 1/4 ≤ 1/2

ce-fal/high-cost-not-elite :
  → ce-fal/elite? 3/4 1/2 = data/false