Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.order-reduction

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

AHoF V38 Order Reduction: reduce the generator/complexity order of a set representation while over-approximating; the reduction is sound when the incurred over-approximation error stays within the tolerance: reduction-sound? error tolerance = decide (error <= tolerance). 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.order-reduction` prints this classification.

order-reduction/reduction-sound? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

order-reduction/small-error-sound :
  → lis/extends? 1/4 1/2 = data/true

order-reduction/boundary-sound :
  → lis/extends? 1/2 1/2 = data/true

order-reduction/error-certificate :
  → 1/4 ≤ 1/2

order-reduction/large-error-unsound :
  → lis/extends? 3/4 1/2 = data/false