Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.multilevel-splitting

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

AHoF V32 Multilevel Splitting: estimate rare-event probability by splitting particles that cross intermediate levels toward the rare set; a particle reaches a level when its score meets that level: reaches-level? value level = decide (level <= value). 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.multilevel-splitting` prints this classification.

multilevel/reaches-level? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

multilevel/crosses-level :
  → bo/is-safe 3/4 1/2 = data/true

multilevel/boundary-level :
  → bo/is-safe 1/2 1/2 = data/true

multilevel/level-certificate :
  → 1/2 ≤ 3/4

multilevel/below-level :
  → bo/is-safe 1/4 1/2 = data/false