Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.taylor-model

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

AHoF V43 Taylor Model Propagation: represent a function by a polynomial plus a guaranteed remainder interval and propagate it; the model is valid when the remainder magnitude stays within the bound: remainder-bounded? remainder bound = decide (remainder <= 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.taylor-model` prints this classification.

taylor/remainder-bounded? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

taylor/small-remainder-valid :
  → lis/extends? 1/4 1/2 = data/true

taylor/boundary-valid :
  → lis/extends? 1/2 1/2 = data/true

taylor/remainder-certificate :
  → 1/4 ≤ 1/2

taylor/large-remainder-invalid :
  → lis/extends? 3/4 1/2 = data/false