Reference · Logic

rainbow.math.logic.clamp-range

Logicsrc/rainbow/math/logic/clamp_range.clj1 definitions, 2 theorems

In Rainbow 1.4.1, lein verify rainbow.math.logic.clamp-range fails on its own: the module uses lemmas from math.rational.nnrat.minmax without listing them in its dependencies. It checks once those are installed.

Universal correctness of clamping (the PPO / trust-region clip of AHoF D52), built on the general nnrat min/max bounds: clamp r lo hi = min (max r lo) hi Proved for ALL r, lo, hi (not just worked instances): clamp-at-most-hi : clamp r lo hi <= hi lo-at-most-clamp : lo <= hi -> lo <= clamp r lo hi Together: whenever lo <= hi, the clamped value provably lies in the interval [lo, hi] for every input r -- the guarantee the clip step relies on. Native and axiom-free; chains rainbow.math.rational.nnrat.minmax.

clamp/clamp :
  (x₁ x₂ x₃ : ℚ≥0)
  → ℚ≥0

clamp/clamp-at-most-hi :
  (r lo hi : ℚ≥0)
  → clamp/clamp r lo hi ≤ hi

clamp/lo-at-most-clamp :
  (r lo hi : ℚ≥0)
  (ordered : lo ≤ hi)
  → lo ≤ clamp/clamp r lo hi