Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.support-function

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

AHoF V37 Support Function Method: represent a convex reachable set by its support function; a halfspace in a direction is respected when the set's support value in that direction is within the halfspace bound: within-support? support-value bound = decide (support-value <= bound). 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.support-function` prints this classification.

support-fn/within-support? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

support-fn/support-within-bound :
  → lis/extends? 1/2 3/4 = data/true

support-fn/boundary-support :
  → lis/extends? 1/2 1/2 = data/true

support-fn/support-certificate :
  → 1/2 ≤ 3/4

support-fn/support-exceeds-bound :
  → lis/extends? 3/4 1/2 = data/false