Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.lp-reachability

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

AHoF V39 LP-Based Reachability: compute reachable-set bounds by solving linear programs; a candidate is reachable within a facet when the LP objective value stays within the facet bound: lp-reachable? objective bound = decide (objective <= 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.lp-reachability` prints this classification.

lp-reach/lp-reachable? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

lp-reach/objective-within-facet :
  → lis/extends? 1/2 3/4 = data/true

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

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

lp-reach/objective-over-facet :
  → lis/extends? 3/4 1/2 = data/false