Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.state-abstraction

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

AHoF V52 Discrete State Abstraction (classical: map concrete states to abstract cells of a partition). This module does NOT model an abstraction map or a partition; it defines a PROXIMITY test, true when the distance between two states is within a radius: same-cell? distance radius = decide (distance <= radius). Proximity is not transitive, so it cannot in general represent equality of abstract cells: with radius 1 and states 0, 3/4, 3/2 both adjacent pairs pass while the endpoints (distance 3/2) fail. Proved native and axiom-free, as worked instances: distance 1/2 within radius 3/4 passes, distance 1/2 at radius 1/2 passes, the certificate 1/2 <= 3/4, and distance 3/4 at radius 1/2 fails. 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.state-abstraction` prints this classification.

abstraction/same-cell? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

abstraction/within-cell-same :
  → lis/extends? 1/2 3/4 = data/true

abstraction/boundary-same :
  → lis/extends? 1/2 1/2 = data/true

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

abstraction/across-cell-different :
  → lis/extends? 3/4 1/2 = data/false