File size: 3,133 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 | import OAI.Combinatorics.EditApproximation.Queries.QueryInitialConeSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryIndexedSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryChargedSeedSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryWarmupSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryChargedWarmup
namespace OAI
namespace EditApproximation
open BitQuery
section Initial
variable (source target : List ℕ) {M J passes copies T S : ℕ}
(N P F : ℕ) (A a : BinaryFraction) (multiplier : ℕ → ℕ)
(parent : {r : PhysicalTableRequest M J target.length // r.Bounded passes copies T S})
(occurrence : BinaryMemo PositionCounts) (symbolBits positionBits : ℕ)
def queryPhysicalInitialHeap (q : TargetInterval target.length) :
Heap (queryPhysicalInitial source target N P F A a multiplier parent occurrence symbolBits positionBits q) := by
let interval := physicalSourceInterval source.length parent.val.node
have hl := saturatingSubtractAllocation_le_work interval.hi interval.lo
have ht := naturalWordLEAllocation_le_work (saturatingSubtractWithWork interval.hi interval.lo).1 [true]
refine Heap.chargeOf (saturatingSubtractAllocation interval.hi interval.lo +
naturalWordLEAllocation (saturatingSubtractWithWork interval.hi interval.lo).1 [true]) (by
dsimp only [interval] at hl ht ⊢
omega) ?_
split
· exact Heap.computeOf _ (queryIndexedSliceAllocation source interval target.length q occurrence symbolBits positionBits)
(queryIndexedSliceAllocation_le_work source interval target.length q occurrence symbolBits positionBits)
· exact queryInitialConeProgramAtHeap _ N P F A a (queryChargedSeedAt parent N multiplier) q
(queryChargedSeedAtHeap parent N multiplier)
def queryChargedWarmupHeap :
Heap (queryChargedWarmup source target N P F A a multiplier parent occurrence symbolBits positionBits) := by
have hinit := queryPhysicalInitialHeap source target N P F A a multiplier parent occurrence symbolBits positionBits
unfold queryChargedWarmup
refine Heap.chargeOf (naturalEqualAllocation parent.val.index 0)
((naturalEqualAllocation_le_work _ _).trans (Nat.le_succ _)) ?_
split
· exact hinit _
· refine Heap.chargeOf (parent.val.node.1.val.bits.length + J.bits.length)
((bitCompareWithWork_input_cells _ _).trans (Nat.le_succ _)) ?_
split
· let interval := physicalSourceInterval source.length parent.val.node
have hl := saturatingSubtractAllocation_le_work interval.hi interval.lo
have ht := naturalWordLEAllocation_le_work (saturatingSubtractWithWork interval.hi interval.lo).1 [true]
refine Heap.chargeOf (saturatingSubtractAllocation interval.hi interval.lo +
naturalWordLEAllocation (saturatingSubtractWithWork interval.hi interval.lo).1 [true]) (by
dsimp only [interval] at hl ht ⊢
omega) ?_
split
· exact hinit _
· apply queryWarmupProgramHeap
· exact hinit
· intro input
exact queryChargedReadHeap parent _
· exact hinit _
end Initial
end EditApproximation
end OAI
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