Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.opt-reachability

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

AHoF V45 Optimization-Based Reach: bound the reachable set by solving an optimization in each direction; a direction's reach is certified when the optimal reach value stays within the bound: reach-bounded? reach-value bound = decide (reach-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.opt-reachability` prints this classification.

opt-reach/reach-bounded? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

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

opt-reach/boundary-reach :
  → lis/extends? 1/2 1/2 = data/true

opt-reach/reach-certificate :
  → 1/2 ≤ 3/4

opt-reach/reach-over-bound :
  → lis/extends? 3/4 1/2 = data/false