Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.forward-reachability

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

AHoF V33 Forward Reachability: over-approximate the set of states reachable from an initial set by forward-propagating an enclosure; a state is in the forward-reachable over-approximation when its distance to the reachable-set representative is within the enclosure radius: in-reachable-set? distance radius = decide (distance <= radius). 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.forward-reachability` prints this classification.

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

forward-reach/within-enclosure-reachable :
  → ce-is/elite? 1/2 3/4 = data/true

forward-reach/boundary-reachable :
  → ce-is/elite? 1/2 1/2 = data/true

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

forward-reach/outside-enclosure-unreached :
  → ce-is/elite? 3/4 1/2 = data/false