| import OAI.Combinatorics.EditApproximation.Binary.BitQuery |
| import OAI.Combinatorics.EditApproximation.Geometry.ChargedSeedQuery |
| import OAI.Combinatorics.EditApproximation.Binary.BinaryInitialKernel |
| import OAI.Combinatorics.EditApproximation.Binary.BinarySeedMedianWork |
| import OAI.Combinatorics.EditApproximation.Geometry.MemoCodeWork |
| import OAI.Combinatorics.EditApproximation.Definitions |
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| namespace OAI |
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| /-! Seed values are computed by actual coarse-cache or previous-pass |
| requests. The copy median and the pass-zero test have explicit work. -/ |
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| namespace EditApproximation |
| namespace BinaryFraction |
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| @[simp] theorem querySeedMedianWithWork_value (N multiplier : ℕ) (words : List BinaryFraction) : |
| (querySeedMedianWithWork N multiplier words).1.value = |
| (min N (upperMedian (words.map fun word => ⌈(multiplier : ℚ) * word.value⌉₊)) : ℕ) := by |
| simp only [querySeedMedianWithWork, ofNaturalWord_value, seedMedianWithWork_value] |
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| end BinaryFraction |
|
|
| section Seed |
| variable {M J n passes copies T S : ℕ} |
| (parent : {r : PhysicalTableRequest M J n |
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| theorem queryChargedRead_refines |
| (key : {child : ChargedPhysicalRequest M J n passes copies T S |
| child.rank < ChargedPhysicalRequest.rank (.inr parent)}) : |
| BitQuery.Refines (fun word value => word.value = value) (queryChargedRead parent key) (.read key .done) := |
| .charge _ (.read key _ _ (fun _ => .done rfl)) |
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| theorem queryChargedPreviousRead_refines (hp : 0 < parent.val.pass) (q : TargetInterval n) |
| (copy : Fin copies) : |
| BitQuery.Refines (fun word value => word.value = value) |
| (queryChargedPreviousRead parent hp q copy) (chargedPreviousRead parent hp q copy) := |
| queryChargedRead_refines parent _ |
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| theorem queryChargedSeedAt_refines (N : ℕ) (multiplier : ℕ → ℕ) (q : TargetInterval n) : |
| BitQuery.Refines (fun word value => word.value = value) |
| (queryChargedSeedAt parent N multiplier q) |
| (chargedSeedQuery N multiplier parent (parent.val.node, q)) := by |
| unfold queryChargedSeedAt chargedSeedQuery |
| rw [dite_eq_left rfl] |
| apply BitQuery.Refines.charge |
| by_cases hp : parent.val.pass = 0 |
| · rw [dite_eq_left hp, dite_eq_left ((naturalEqualWithWork_value _ _).mpr hp)] |
| exact queryChargedRead_refines parent _ |
| · rw [dite_eq_right hp, dite_eq_right (fun h => hp ((naturalEqualWithWork_value _ _).mp h))] |
| apply BitQuery.Refines.charge |
| apply BitQuery.Refines.collect _ _ (fun copy => queryChargedPreviousRead_refines parent _ q copy) |
| intro words |
| apply BitQuery.Refines.charge |
| apply BitQuery.Refines.done |
| simp only [BinaryFraction.querySeedMedianWithWork_value, List.map_map, Function.comp_def] |
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| end Seed |
| end EditApproximation |
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| end OAI |
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