Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.symbolic-reachability

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

AHoF V49 Symbolic Reachability (BDDs): represent reachable state sets symbolically (e.g. as BDDs) and test membership; a state is in the symbolic set when its distance to the set representative is within the radius: in-symbolic-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.symbolic-reachability` prints this classification.

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

symbolic/within-set-member :
  → lis/extends? 1/2 3/4 = data/true

symbolic/boundary-member :
  → lis/extends? 1/2 1/2 = data/true

symbolic/symbolic-certificate :
  → 1/2 ≤ 3/4

symbolic/outside-set-nonmember :
  → lis/extends? 3/4 1/2 = data/false