| import OAI.Combinatorics.EditApproximation.Queries.QueryFamilyActive |
| import OAI.Combinatorics.EditApproximation.Queries.QueryChargedWarmup |
| import OAI.Combinatorics.EditApproximation.Geometry.ChargedRandomGlobalQuery |
| import OAI.Combinatorics.EditApproximation.Definitions |
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|
| namespace OAI |
|
|
| /-! All physical table branches run Boolean arithmetic and issue |
| address-charged adaptive requests. Coarse entries are supplied by the |
| separately executed coarse initializer. -/ |
|
|
| 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) |
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|
| def queryChargedFamilyTable |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S}) : |
| BitQuery (ChargedFamilyQueryKey (R := R) target N P F exponent H Q (.inr parent)) BinaryFraction := |
| let index := wordLEWithWork parent.val.index.bits T.bits |
| .charge (index.2 + 1) |
| (if hi : index.1 = true then |
| BitQuery.mapKeysWithWork (fun key => (Sum.inr key, 1)) |
| (queryChargedWarmup source target N P F (A parent.val.pass) (a parent.val.pass) multiplier |
| parent occurrence symbolBits positionBits) |
| else let depth := binaryNaturalCompareWithWork parent.val.node.1.val J |
| .charge (depth.2 + 1) |
| (if hb : depth.1 = .lt then |
| let interval := physicalSourceInterval source.length parent.val.node |
| let length := saturatingSubtractWithWork interval.hi interval.lo |
| let short := wordLEWithWork length.1 [true] |
| .charge (length.2 + short.2 + 1) |
| (if short.1 then |
| BitQuery.mapKeysWithWork (fun key => (Sum.inr key, 1)) |
| (queryPhysicalInitial source target N P F (A parent.val.pass) (a parent.val.pass) |
| multiplier parent occurrence symbolBits positionBits parent.val.state) |
| else BitQuery.mapKeysWithWork |
| (fun key => (Sum.map id (fun child => |
| ⟨Sum.inr child.val, ChargedPhysicalRequest.table_rank_lt parent child.val child.property⟩) |
| key, 1)) |
| (queryFamilyBoundedActive (R := R) source target N P F exponent H Q eM eF hP hM hF |
| tau (a parent.val.pass) eta kappa delta T S passes copies parent |
| (Nat.lt_of_not_ge (fun h => hi ((queryNaturalLEWithWork_value parent.val.index T).mpr h))) |
| ((binaryNaturalCompareWithWork_lt _ _).mp hb))) |
| else BitQuery.mapKeysWithWork (fun key => (Sum.inr key, 1)) |
| (queryPhysicalInitial source target N P F (A parent.val.pass) (a parent.val.pass) |
| multiplier parent occurrence symbolBits positionBits parent.val.state))) |
|
|
| theorem queryChargedFamilyTable_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) |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S}) : |
| BitQuery.Refines (fun word value => word.value = value) |
| (queryChargedFamilyTable (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 parent) |
| (chargedRandomGlobalQuery (R := R) source target N P F exponent H Q T S (passes + 1) copies |
| (fun pass => (A pass).value) multiplier tau.value eta.value kappa.value delta.value |
| (physicalFamilyGroupRead target N P F exponent H Q passes copies) |
| (physicalFamilyOnlineRead target N P F exponent H Q passes copies) initial (.inr parent)) := by |
| have hinit := queryPhysicalInitial_refines source target N P F (A parent.val.pass) |
| (a parent.val.pass) multiplier parent occurrence symbolBits positionBits parent.val.state hP |
| (ha parent.val.pass (by have := parent.property.1; omega)) hs ht hp htable |
| unfold queryChargedFamilyTable chargedRandomGlobalQuery |
| dsimp only |
| apply BitQuery.Refines.charge |
| by_cases hi : parent.val.index ≤ T |
| · rw [ite_eq_left hi, dite_eq_left ((queryNaturalLEWithWork_value parent.val.index T).mpr hi)] |
| apply BitQuery.Refines.mapKeysWithWork _ _ (fun _ => rfl) |
| exact queryChargedWarmup_refines source target N P F (A parent.val.pass) (a parent.val.pass) |
| multiplier parent occurrence symbolBits positionBits (fun pass => (A pass).value) rfl hP |
| (ha parent.val.pass (by have := parent.property.1; omega)) hs ht hp htable |
| · rw [ite_eq_right hi, dite_eq_right (fun h => hi ((queryNaturalLEWithWork_value parent.val.index T).mp h))] |
| apply BitQuery.Refines.charge |
| by_cases hb : parent.val.node.1.val < J |
| · rw [ite_eq_left hb, dite_eq_left ((binaryNaturalCompareWithWork_lt _ _).mpr hb)] |
| apply BitQuery.Refines.charge |
| have hshort : (wordLEWithWork |
| (saturatingSubtractWithWork (physicalSourceInterval source.length parent.val.node).hi |
| (physicalSourceInterval source.length parent.val.node).lo).1 [true]).1 = true ↔ |
| (physicalSourceInterval source.length parent.val.node).hi - |
| (physicalSourceInterval source.length parent.val.node).lo ≤ 1 := by |
| rw [wordLEWithWork_value, saturatingSubtractWithWork_value] |
| rfl |
| by_cases hw : (physicalSourceInterval source.length parent.val.node).hi - |
| (physicalSourceInterval source.length parent.val.node).lo ≤ 1 |
| · rw [ite_eq_left hw, ite_eq_left (hshort.mpr hw)] |
| exact hinit.mapKeysWithWork _ _ (fun _ => rfl) |
| · rw [ite_eq_right hw, ite_eq_right (fun h => hw (hshort.mp h))] |
| apply BitQuery.Refines.mapKeysWithWork _ _ (fun _ => rfl) |
| exact queryFamilyBoundedActive_refines (R := R) source target N P F exponent H Q eM eF |
| hP hM hF tau (a parent.val.pass) eta kappa delta T S passes copies parent |
| (Nat.lt_of_not_ge hi) hb (fun pass => (A pass).value) multiplier initial (ha parent.val.pass (by have := parent.property.1; omega)) hw |
| · rw [ite_eq_right hb, dite_eq_right (fun h => hb ((binaryNaturalCompareWithWork_lt _ _).mp h))] |
| exact hinit.mapKeysWithWork _ _ (fun _ => rfl) |
| |
| def queryChargedFamilyGlobal |
| (coarse : PhysicalEntry M J target.length → BinaryFraction × ℕ) |
| (request : ChargedPhysicalRequest M J target.length (passes + 1) copies T S) : |
| BitQuery (ChargedFamilyQueryKey (R := R) target N P F exponent H Q request) BinaryFraction := |
| match request with |
| | .inl entry => BitQuery.compute (coarse entry) |
| | .inr parent => queryChargedFamilyTable (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 parent |
|
|
| theorem queryChargedFamilyGlobal_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) |
| (coarse : PhysicalEntry M J target.length → BinaryFraction × ℕ) |
| (initial : PhysicalEntry M J target.length → ℕ) |
| (hc : ∀ entry, (coarse entry).1.value = initial entry) |
| (request : ChargedPhysicalRequest M J target.length (passes + 1) copies T S) : |
| BitQuery.Refines (fun word value => word.value = value) |
| (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 request) |
| (chargedRandomGlobalQuery (R := R) source target N P F exponent H Q T S (passes + 1) copies |
| (fun pass => (A pass).value) multiplier tau.value eta.value kappa.value delta.value |
| (physicalFamilyGroupRead target N P F exponent H Q passes copies) |
| (physicalFamilyOnlineRead target N P F exponent H Q passes copies) initial request) := by |
| cases request with |
| | inl entry => exact .charge _ (.done (hc entry)) |
| | inr parent => |
| exact queryChargedFamilyTable_refines (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 ha hs ht hp htable initial parent |
|
|
| end Family |
| end EditApproximation |
|
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| end OAI |
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