Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.zonotope

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

AHoF V35 Zonotope Propagation: represent a reachable set as a zonotope (center plus generator vectors) and propagate it; a point lies in the zonotope when each generator coordinate stays within its unit bound: in-zonotope? coefficient bound = decide (coefficient <= 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.zonotope` prints this classification.

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

zonotope/within-generator-inside :
  → lis/extends? 1/2 3/4 = data/true

zonotope/boundary-inside :
  → lis/extends? 1/2 1/2 = data/true

zonotope/generator-certificate :
  → 1/2 ≤ 3/4

zonotope/over-generator-outside :
  → lis/extends? 3/4 1/2 = data/false