| import OAI.Combinatorics.EditApproximation.Queries.QueryInitialGather |
| import OAI.Combinatorics.EditApproximation.Queries.QueryRepresentatives |
| import OAI.Combinatorics.EditApproximation.Definitions |
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|
| namespace OAI |
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| /-! The band-data stage constructs its keys by counted Boolean routines, |
| then gathers mass and initial words in the reference order. -/ |
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|
| namespace EditApproximation |
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| theorem queryBandGather_refines {ι β : Type*} {nx ny : ℕ} {relation : β → ℚ → Prop} |
| (M : ℕ) (parent : TargetInterval nx) (N P F exponent : ℕ) (hP : 0 < P) |
| (a : BinaryFraction) (initial : TargetInterval ny → BinaryFraction × ℕ) (q : TargetInterval ny) |
| (R : ℕ) (hR : ∀ r, (initial r).2 ≤ R) |
| (massReader initialReader : (Fin M × TargetInterval ny) → BitQuery ι BinaryFraction) |
| (expectedMass expectedInitial : (Fin M × TargetInterval ny) → FiniteQuery ι) |
| (next : List (Fin M × TargetInterval ny) → List BinaryFraction → List BinaryFraction → |
| BitQuery ι β) |
| (expectedNext : List (Fin M × TargetInterval ny) → List ℚ → List ℚ → FiniteQuery ι) |
| (hm : ∀ key, BitQuery.Refines (fun word value => word.value = value) |
| (massReader key) (expectedMass key)) |
| (hi : ∀ key, BitQuery.Refines (fun word value => word.value = value) |
| (initialReader key) (expectedInitial key)) |
| (hn : ∀ mass words, |
| let keys := refinementBandInputList (M := M) parent N P F exponent a.value |
| (fun r => (initial r).1.value) q |
| BitQuery.Refines relation (next keys mass words) |
| (expectedNext keys (mass.map BinaryFraction.value) (words.map BinaryFraction.value))) : |
| BitQuery.Refines relation |
| (queryBandGather M parent N P F exponent hP a initial q massReader initialReader next) |
| (let keys := refinementBandInputList (M := M) parent N P F exponent a.value |
| (fun r => (initial r).1.value) q |
| FiniteQuery.collect expectedMass keys fun mass => |
| FiniteQuery.collect expectedInitial keys (expectedNext keys mass)) := by |
| change BitQuery.Refines relation (.charge _ _) _ |
| apply BitQuery.Refines.charge |
| change BitQuery.Refines relation (BitQuery.collect massReader _ _) _ |
| rw [BinaryFraction.queryBandInputsWithWork_value M parent N P F exponent hP a initial q R hR] |
| apply BitQuery.Refines.collect massReader expectedMass hm |
| intro mass |
| exact BitQuery.Refines.collect initialReader expectedInitial hi _ _ _ (hn mass) |
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| theorem queryBandGather_work {ι β : Type*} {nx ny : ℕ} (M : ℕ) (parent : TargetInterval nx) |
| (N P F exponent : ℕ) (hP : 0 < P) (a : BinaryFraction) |
| (initial : TargetInterval ny → BinaryFraction × ℕ) (q : TargetInterval ny) |
| (massReader initialReader : (Fin M × TargetInterval ny) → BitQuery ι BinaryFraction) |
| (next : List (Fin M × TargetInterval ny) → List BinaryFraction → List BinaryFraction → |
| BitQuery ι β) (oracle : ι → BinaryFraction) (readWork : ι → ℕ) : |
| let keys := BinaryFraction.queryBandInputsWithWork M parent N P F exponent hP a initial q |
| (queryBandGather M parent N P F exponent hP a initial q massReader initialReader next).work |
| oracle readWork = keys.2 + |
| (keys.1.map fun key => (massReader key).work oracle readWork + 3).sum + |
| (keys.1.map fun key => (initialReader key).work oracle readWork + 3).sum + |
| (next keys.1 (keys.1.map fun key => (massReader key).value oracle) |
| (keys.1.map fun key => (initialReader key).value oracle)).work oracle readWork := by |
| simp only [queryBandGather, BitQuery.work_bind, BitQuery.compute, |
| BitQuery.work, BitQuery.value, BitQuery.work_collect, Nat.add_zero, Nat.add_assoc] |
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| end EditApproximation |
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| end OAI |
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