Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.failure-mode

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

AHoF V58 Failure Mode Characterization: cluster observed failures into modes and assign a new failure to a mode when its distance to the mode's centroid is within the mode radius: in-mode? distance radius = decide (distance <= radius). A failure at distance 1/2 from a centroid with radius 3/4 belongs to that mode; a failure at distance 3/4 with radius 1/2 is outside it (a new mode). Proved native and axiom-free (decision, in-mode and boundary instances, at-most membership certificate, out-of-mode). 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.failure-mode` prints this classification.

failure-mode/in-mode? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

failure-mode/within-radius-in-mode :
  → ce-is/elite? 1/2 3/4 = data/true

failure-mode/boundary-in-mode :
  → ce-is/elite? 1/2 1/2 = data/true

failure-mode/membership-certificate :
  → 1/2 ≤ 3/4

failure-mode/outside-radius-new-mode :
  → ce-is/elite? 3/4 1/2 = data/false