Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.shubert

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/shubert.clj2 definitions, 3 theorems

AHoF O11 Shubert-Piyavskii: build a piecewise-linear (sawtooth) lower bound of a Lipschitz objective and sample where the lower bound is smallest; between two candidate lower- bound values it keeps the smaller value: prefers-lower? a b = decide ('a 'b) sample-value a b = if ('a 'b) then 'a else 'b over exact rationals. Proved native and axiom-free: the preference decision, the selected value, and the switch. Requires audit/decide-nnrat-at-most, logic/if-data (both in the D63 checkpoint). Scope (measured by the kernel): this module has 3 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.shubert` prints this classification.

shubert/prefers-lower? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

shubert/sample-value :
  (x₁ x₂ : ℚ≥0)
  → ℚ≥0

shubert/prefers-example :
  → lis/extends? 1/2 3/4 = data/true

shubert/selected-value :
  → ppo/nnrat-min 1/2 3/4 = 1/2

shubert/switches :
  → lis/extends? 3/4 1/2 = data/false