File size: 2,816 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 | import OAI.Combinatorics.EditApproximation.Binary.BitQueryKeys
import OAI.Combinatorics.EditApproximation.Geometry.SourceRankedRestriction
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalDependencyRank
import OAI.Combinatorics.EditApproximation.Queries.QueryPhysicalScalarGuards
import OAI.Combinatorics.EditApproximation.Binary.BinaryArithmeticWork
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
/-! Finite-domain guards execute binary comparisons on table coordinates.
Random-source coordinates pass through the guard unchanged. -/
namespace EditApproximation
@[simp] theorem queryNaturalLEWithWork_value (a b : ℕ) :
(wordLEWithWork a.bits b.bits).1 = true ↔ a ≤ b := by
simp only [wordLEWithWork_value, bitWordValue_bits]
@[simp] theorem queryPhysicalBoundedWithWork_value {M J n : ℕ}
(passes copies T S : ℕ) (request : PhysicalTableRequest M J n) :
(queryPhysicalBoundedWithWork passes copies T S request).1 = true ↔
request.Bounded passes copies T S := by
simp only [queryPhysicalBoundedWithWork, Bool.and_eq_true, decide_eq_true_eq,
binaryNaturalCompareWithWork_lt, wordLEWithWork_value, bitWordValue_bits,
binaryNaturalAddWithWork_value, PhysicalTableRequest.Bounded]
tauto
section Body
variable {σ : Type*} {M J n : ℕ} (passes copies T S : ℕ)
(parent : {r : PhysicalTableRequest M J n // r.Bounded passes copies T S})
@[simp] theorem querySupportedChildWithWork_value
(key : QueryPhysicalChild (σ := σ) passes copies T S parent) :
(querySupportedChildWithWork passes copies T S parent key).1 = true ↔
SourceRanked.supportedChild (PhysicalTableRequest.combinedRank T S)
(PhysicalTableRequest.Bounded passes copies T S) parent.val key := by
cases key with
| inl source => exact iff_of_true rfl trivial
| inr child => exact queryPhysicalBoundedWithWork_value passes copies T S child.val
theorem queryRestrictPhysicalBody_refines
(program : BitQuery (QueryPhysicalChild (σ := σ) passes copies T S parent) BinaryFraction)
(expected : (request : PhysicalTableRequest M J n) →
FiniteQuery (Sum σ {child : PhysicalTableRequest M J n //
child.combinedRank T S < request.combinedRank T S}))
(h : BitQuery.Refines (fun word value => word.value = value) program (expected parent.val)) :
BitQuery.Refines (fun word value => word.value = value)
(queryRestrictPhysicalBody passes copies T S parent program)
(SourceRanked.restrictBody (PhysicalTableRequest.combinedRank T S)
(PhysicalTableRequest.Bounded passes copies T S) expected parent) := by
classical
exact (h.restrictWithWork _ _ (querySupportedChildWithWork_value passes copies T S parent)).mapKeysWithWork
_ _ (fun _ => rfl)
end Body
end EditApproximation
end OAI
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