| import OAI.Probability.MatroidProphet.Main | |
| import Mathlib.Logic.Equiv.Fintype | |
| namespace OAI | |
| namespace MatroidProphet | |
| /-- A one-hot code retains the entire finite seed, including unused coordinates. -/ | |
| noncomputable def finiteSeedEncode (α : Type*) [Fintype α] (a : α) : | |
| Seed (Fintype.card α) := by | |
| classical | |
| exact fun i => decide ((Fintype.equivFin α) a = i) | |
| /-- Total decoding, with an arbitrary fallback on codes outside the encoder range. -/ | |
| noncomputable def finiteSeedDecode (α : Type*) [Fintype α] [Nonempty α] : | |
| Seed (Fintype.card α) → α := | |
| Function.invFun (finiteSeedEncode α) | |
| /-- Change only the representation of the complete initial seed. -/ | |
| noncomputable def reindexOnlineSeed {n bits bits' : ℕ} (A : OnlineRule n bits) | |
| (f : Seed bits' → Seed bits) : OnlineRule n bits' where | |
| decide k r s h := A.decide k (f r) s h | |
| measurable_decide k := (A.measurable_decide k).comp | |
| (((measurable_of_finite f).comp measurable_fst).prodMk measurable_snd) | |
| /-- The sacrificed mask and every core decision use the same decoded seed. -/ | |
| noncomputable def reindexHiddenSeed {n bits bits' : ℕ} (A : HiddenRule n bits) | |
| (f : Seed bits' → Seed bits) : HiddenRule n bits' where | |
| mask r := A.mask (f r) | |
| core := reindexOnlineSeed A.core f | |
| end MatroidProphet | |
| end OAI | |