Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.astar-falsification

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/astar_falsification.clj4 definitions, 3 theorems

AHoF V18 A* for Falsification: search the space of system behaviours for a specification violation using A*, ordering the frontier by the f-cost f = g + h (the cost so far plus an admissible heuristic to a likely violation) and always expanding the lowest-f node: priority g h = g + h prefers-lower? f0 f1 = decide (f0 <= f1) expand-value f0 f1 = if (f0 <= f1) then f0 else f1 (the lower f-cost) over exact rationals. Proved native and axiom-free: the priority sum (1/2 + 1/4 = 3/4 by cross-product equivalence), the min-f frontier selection, and the preference decision. Requires nnrat/add, audit/decide-nnrat-at-most, logic/if-data, nnrat/equivalent (all in the D63 checkpoint). Scope (measured by the kernel): this module has 3 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.astar-falsification` prints this classification.

astar-fal/priority :
  (x₁ x₂ : ℚ≥0)
  → ℚ≥0

astar-fal/prefers-lower? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

astar-fal/expand-value :
  (x₁ x₂ : ℚ≥0)
  → ℚ≥0

astar-fal/worked-priority :
  → ℚ≥0

astar-fal/priority-is-three-quarters :
  → astar-fal/worked-priority = 3/4

astar-fal/expands-lower-f :
  → astar-fal/expand-value 3/4 1 = 3/4

astar-fal/prefers-lower-example :
  → search/poll-improves 3/4 1 = data/true