Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.partitioning

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

AHoF V46 Partitioning: recursively split the state/input set into cells so each is small enough for an accurate local over-approximation; a cell is fine enough when its diameter is within the tolerance: fine-enough? diameter tolerance = decide (diameter <= 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.partitioning` prints this classification.

partitioning/fine-enough? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

partitioning/small-cell-fine :
  → lis/extends? 1/4 1/2 = data/true

partitioning/boundary-fine :
  → lis/extends? 1/2 1/2 = data/true

partitioning/diameter-certificate :
  → 1/4 ≤ 1/2

partitioning/large-cell-coarse :
  → lis/extends? 3/4 1/2 = data/false