File size: 4,474 Bytes
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 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | import OAI.Combinatorics.EditApproximation.Queries.QueryChargedFamily
import OAI.Combinatorics.EditApproximation.Binary.BitSourceRanked
import OAI.Combinatorics.EditApproximation.Binary.BitRankedNormalize
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRequestGrid
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalFamilyProgram
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
/-! One binary memo stores independent scalar draws, coarse values, and
all recursive tables. The raw implementation preserves the exact
reference trace; normalization is justified on its reachable values. -/
namespace EditApproximation
section Family
variable {M J R passes copies T S : ℕ} [NeZero M] [NeZero R]
(source target : List ℕ) (N P F exponent H Q eM eF : ℕ)
(hP : 0 < P) (hM : M = 2 ^ eM) (hF : F = 2 ^ eF)
(A a : ℕ → BinaryFraction) (tau eta kappa delta : BinaryFraction) (multiplier : ℕ → ℕ)
(occurrence : BinaryMemo PositionCounts) (symbolBits positionBits : ℕ)
(coarse : PhysicalEntry M J target.length → BinaryFraction × ℕ)
(draw : PhysicalFamilyScalarDraw (M := M) (J := J) (R := R)
target N P F exponent H Q passes copies)
def queryFamilyMemoRaw (key : QueryFamilyMemoKey (M := M) (J := J) (R := R) (passes := passes) (copies := copies) (T := T) (S := S) target N P F exponent H Q) :=
SourceRanked.bitBody ChargedPhysicalRequest.rank
(queryChargedFamilyGlobal (R := R) source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits coarse)
(queryFamilySourceWordWithWork target N P F exponent H Q draw) key
theorem queryFamilyMemoRaw_refines
(ha : ∀ pass, pass ≤ passes → (a pass).value = refinementFactor (A pass).value F)
(hs : ∀ z ∈ source, z < 2 ^ symbolBits) (ht : ∀ z ∈ target, z < 2 ^ symbolBits)
(hp : target.length ≤ 2 ^ positionBits)
(htable : occurrence = occurrenceBuild symbolBits positionBits target.zipIdx)
(initial : PhysicalEntry M J target.length → ℕ)
(hc : ∀ entry, (coarse entry).1.value = initial entry)
(key : QueryFamilyMemoKey (M := M) (J := J) (R := R) (passes := passes) (copies := copies) (T := T) (S := S) target N P F exponent H Q) :
BitQuery.Refines (fun word value => word.value = value)
(queryFamilyMemoRaw source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits coarse draw key)
(SourceRanked.body ChargedPhysicalRequest.rank
(physicalFamilyProgram source target N P F exponent H Q T S passes copies
(fun pass => (A pass).value) multiplier tau.value eta.value kappa.value delta.value initial)
(physicalFamilyAnswer target N P F exponent H Q passes copies draw) key) := by
have hr := SourceRanked.bitBody_refines ChargedPhysicalRequest.rank
(queryChargedFamilyGlobal (R := R) source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits coarse)
(physicalFamilyProgram source target N P F exponent H Q T S passes copies
(fun pass => (A pass).value) multiplier tau.value eta.value kappa.value delta.value initial)
(queryFamilySourceWordWithWork target N P F exponent H Q draw)
(fun parent => queryChargedFamilyGlobal_refines source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits ha hs ht hp htable
coarse initial hc parent) key
have hsources : (fun key => (queryFamilySourceWordWithWork target N P F exponent H Q draw key).1.value) =
physicalFamilyAnswer target N P F exponent H Q passes copies draw := by
funext key
exact BinaryFraction.nat_value _
rw [hsources] at hr
exact hr
def queryFamilyMemoNormalized (base : List Bool) (hbase : 0 < bitWordValue base)
(key : QueryFamilyMemoKey (M := M) (J := J) (R := R) (passes := passes) (copies := copies) (T := T) (S := S) target N P F exponent H Q) :=
rankedNormalizeBody (SourceRanked.rank ChargedPhysicalRequest.rank)
(queryFamilyMemoRaw source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits coarse draw)
base hbase (queryFamilyMemoRemaining (M := M) (J := J) (R := R) (passes := passes) (copies := copies) (T := T) (S := S) target N P F exponent H Q) key
end Family
end EditApproximation
end OAI
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