File size: 2,784 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 | import OAI.Combinatorics.EditApproximation.Queries.QueryPhysicalScalarReads
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
/-! Counted pass/copy indexing for the independent scalar family. Both
remainders and the complete family address are computed before lookup. -/
namespace EditApproximation
theorem queryFinOfNatWithWork_value (bound value : ℕ) (hb : 0 < bound) [NeZero bound] :
(queryFinOfNatWithWork bound value hb).1 = Fin.ofNat bound value := by
apply Fin.ext
exact (binaryNaturalDivModWithWork_spec value bound hb).2
theorem queryFinOfNatWithWork_cost (bound value B : ℕ) (hb : 0 < bound)
(hbound : Nat.size bound ≤ B) (hvalue : Nat.size value ≤ B) :
(queryFinOfNatWithWork bound value hb).2 ≤ 60 * (B + 1) ^ 2 + 1 := by
have h := binaryNaturalDivModWithWork_cost value bound
change (binaryNaturalDivModWithWork value bound).2.2 + 1 ≤ _
nlinarith only [h, hbound, hvalue, Nat.zero_le B]
section Family
variable {α : Type*} {M J R : ℕ} (target : List α)
(N P F exponent H Q passes copies pass copy : ℕ)
theorem queryFamilyTagWithWork_value
(scalar : PhysicalScalarKey M J N target.length exponent F Q R (localOnlineMassBound M P H)) :
(queryFamilyTagWithWork target N P F exponent H Q passes copies pass copy scalar).1 =
(Fin.ofNat (passes + 1) pass, Fin.ofNat (copies + 1) copy, scalar) := by
simp only [queryFamilyTagWithWork, queryFinOfNatWithWork_value]
theorem queryFamilyGroupRead_refines (node : PhysicalInternalNode M J) (time : Fin R)
(key : GroupScalarKey M F Q) :
BitQuery.Refines (fun word value => word.value = value)
(queryFamilyGroupRead target N P F exponent H Q passes copies pass copy node time key)
(physicalFamilyGroupRead target N P F exponent H Q passes copies pass copy node time key) := by
exact (queryPhysicalScalarGroupRead_refines M J N target.length exponent F Q R
(localOnlineMassBound M P H) node time key).mapKeysWithWork _ _
(queryFamilyTagWithWork_value target N P F exponent H Q passes copies pass copy)
theorem queryFamilyOnlineRead_refines (node : PhysicalInternalNode M J) (time : Fin R)
(key : ℕ × TargetInterval target.length) (range : ℕ) :
BitQuery.Refines (fun word value => word.value = value)
(queryFamilyOnlineRead target N P F exponent H Q passes copies pass copy node time key range)
(physicalFamilyOnlineRead target N P F exponent H Q passes copies pass copy node time key range) := by
exact (queryPhysicalScalarOnlineRead_refines M J N target.length exponent F Q R
(localOnlineMassBound M P H) node time key range).mapKeysWithWork _ _
(queryFamilyTagWithWork_value target N P F exponent H Q passes copies pass copy)
end Family
end EditApproximation
end OAI
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