Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.reachability-spec

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

AHoF V8 Reachability Specification: a reachability property asks whether the system can reach a target set; concretely a trajectory reaches the target when its distance to the target set falls within the specification tolerance: reaches-target? distance tolerance = decide (distance <= tolerance). 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.reachability-spec` prints this classification.

reach-spec/reaches-target? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

reach-spec/within-tolerance-reaches :
  → lis/extends? 1/2 3/4 = data/true

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

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

reach-spec/outside-tolerance-unreached :
  → lis/extends? 3/4 1/2 = data/false