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e63eb7f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | import OAI.Combinatorics.EditApproximation.Geometry.ChargedRandomGlobalQuery
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRandomValue
import OAI.Combinatorics.EditApproximation.Geometry.SourceRankedProgram
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
/-! The charged evaluator actually caches random source coordinates and
physical entries in one rank-decreasing memo computation. -/
namespace EditApproximation
section Memo
variable {σ α : Type*} [DecidableEq α] {M J R : ℕ} [NeZero M] [NeZero R]
(source target : List α) (N P F exponent H Q T S passes copies : ℕ)
(factor : ℕ → ℚ) (multiplier : ℕ → ℕ) (tau eta kappa delta : ℚ)
(readGroup : ℕ → ℕ → PhysicalInternalNode M J → Fin R → GroupScalarKey M F Q → FiniteQuery σ)
(readInteger : ℕ → ℕ → PhysicalInternalNode M J → Fin R →
(ℕ × TargetInterval target.length) → ℕ → FiniteQuery σ)
(initial : PhysicalEntry M J target.length → ℕ)
(sourceAnswer : σ → ℚ)
theorem chargedRandomMemoEvaluate_value
(group : ℕ → ℕ → PhysicalInternalNode M J → Fin R → CellGroupDraws M F Q)
(integer : ℕ → ℕ → PhysicalInternalNode M J → Fin R → ℕ → TargetInterval target.length → ℕ)
(hgroup : ∀ pass copy node time key, (readGroup pass copy node time key).value sourceAnswer =
groupScalarValue (group pass copy node time) key)
(honline : ∀ pass copy (node : PhysicalInternalNode M J) time key,
(readInteger pass copy node time key
(keyedOnlineSourceRange source target (physicalSourceInterval source.length node.val)
P exponent H tau (fun i r => (∑ j : Fin T, localRequestValue source target N P F exponent H Q T S
copies factor multiplier tau eta kappa delta group integer initial (PhysicalTableRequest.warmup
pass copy (physicalChild node.val node.property i) j.val r)) / T) key)).value sourceAnswer =
(integer pass copy node time key.1 key.2 : ℚ))
(bits : ℕ) (encode : Sum σ (ChargedPhysicalRequest M J target.length passes copies T S) → ℕ)
(hinjective : Function.Injective encode) (hbounded : ∀ key, encode key < 2 ^ bits)
(request : ChargedPhysicalRequest M J target.length passes copies T S) :
(chargedRandomMemoEvaluate source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta readGroup readInteger initial sourceAnswer bits encode request).value =
chargedRequestValue source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta group integer initial request := by
unfold chargedRandomMemoEvaluate
exact SourceRanked.memo_value ChargedPhysicalRequest.rank _ sourceAnswer
(chargedRequestValue source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta group integer initial)
(chargedRandomGlobalQuery_value source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta readGroup readInteger initial group integer sourceAnswer
(physicalRandomBoundedQuery_localValue source target N P F exponent H Q T S passes copies factor
multiplier tau eta kappa delta group integer initial readGroup readInteger sourceAnswer hgroup honline))
bits encode hinjective hbounded (.inr request)
end Memo
end EditApproximation
end OAI
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