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97c3405 | 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 69 70 71 72 73 74 75 76 77 78 79 80 81 | import OAI.Combinatorics.ContingencyTables.Counting.CompanionInitializedRestartProgram
import OAI.Combinatorics.ContingencyTables.Counting.CompanionRestartDataLaw
import OAI.Combinatorics.ContingencyTables.Counting.CompanionRestartScheduleSemantics
namespace OAI
/-! # Literal inputs and disjoint slices of initialized restarts -/
namespace ContingencyTables.CompanionInitializedRestartProgram
open MatchingFPRAS CommonBasesFPRAS FairBits DensePrograms
open CompanionFactorialApplication CompanionComputedInitial CompanionComputedProposal
open CompanionArithmeticProposal CompanionEvaluatedWeightProgram CompanionMultiplierMatrixProgram
open CompanionOracleDensity GridBoundary
open scoped BigOperators Classical
noncomputable section
variable {m n : ℕ}
def data (A : Instance (Fin m) (Fin n)) (C K H T N R L j : ℕ)
(epsilon : TreeFraction.Fraction) (z : View A → ℕ)
(v : Grid (I := Fin (RootedCatalogGrid.freeCount A)) K)
(w : ℕ → LabelIndex A → LabelIndex A → TreeFraction.Fraction)
(estimates : Fin j → TreeFraction.Fraction) (bits : List Bool) : Input :=
((CompanionRestartInitializer.data A C K H T N R L epsilon z v,
List.ofFn (fun i : Fin j => (matrixCode (w (i.val+1)),estimates i))),bits)
lemma stages_data (A : Instance (Fin m) (Fin n)) (C K H T N R L j : ℕ)
(epsilon : TreeFraction.Fraction) (z : View A → ℕ)
(v : Grid (I := Fin (RootedCatalogGrid.freeCount A)) K)
(w : ℕ → LabelIndex A → LabelIndex A → TreeFraction.Fraction)
(estimates : Fin j → TreeFraction.Fraction) (bits : List Bool) :
stages (data A C K H T N R L j epsilon z v w estimates bits)=
CompanionRestartProgram.stagesData A C K j
([Fintype.card (Labels A),A.W,H,T,N,R,L],epsilon) z v (List.replicate bits.length false) w := by
unfold stages indices data
rw [List.length_ofFn,DirectedBFSCode.range_eq_map]
simp only [List.map_map,Function.comp_def]
rw [←List.ofFn_eq_map]
apply congrArg List.ofFn
funext i
unfold stageAt reserve
simp only [List.getD_eq_getElem?_getD,List.getElem?_ofFn,i.isLt,dite_true,Option.getD_some,
List.map_const']
rfl
lemma initialWidth_data (A : Instance (Fin m) (Fin n)) (C K H T N R L j : ℕ)
(epsilon : TreeFraction.Fraction) (z : View A → ℕ)
(v : Grid (I := Fin (RootedCatalogGrid.freeCount A)) K)
(w : ℕ → LabelIndex A → LabelIndex A → TreeFraction.Fraction)
(estimates : Fin j → TreeFraction.Fraction) (bits : List Bool) :
initialWidth (data A C K H T N R L j epsilon z v w estimates bits)=
wordLength A (CompanionInitialDraw.precision A (CountingPhaseSchedule.initialPrecision H)) :=
CompanionRestartInitializer.width_data A C K H T N R L epsilon z v
/-- Exact physical splitting: the initializer sees the first block,
the restart loop sees the remaining block, and all markers are fixed. -/
theorem output_split (A : Instance (Fin m) (Fin n)) (C K H T N R L j s : ℕ)
(epsilon : TreeFraction.Fraction) (z : View A → ℕ)
(v : Grid (I := Fin (RootedCatalogGrid.freeCount A)) K)
(w : ℕ → LabelIndex A → LabelIndex A → TreeFraction.Fraction)
(estimates : Fin j → TreeFraction.Fraction)
(bits : Fin (wordLength A (CompanionInitialDraw.precision A (CountingPhaseSchedule.initialPrecision H))+s) → Bool) :
output (data A C K H T N R L j epsilon z v w estimates (List.ofFn bits))=
CompanionRestartProgram.output
((CompanionRestartProgram.stagesData A C K j
([Fintype.card (Labels A),A.W,H,T,N,R,L],epsilon) z v
(List.replicate (wordLength A (CompanionInitialDraw.precision A (CountingPhaseSchedule.initialPrecision H))+s) false) w,
CompanionRestartInitializer.output
(CompanionRestartInitializer.data A C K H T N R L epsilon z v,
List.ofFn (splitWordEquiv
(wordLength A (CompanionInitialDraw.precision A (CountingPhaseSchedule.initialPrecision H))) s bits).1)),
List.ofFn (splitWordEquiv
(wordLength A (CompanionInitialDraw.precision A (CountingPhaseSchedule.initialPrecision H))) s bits).2) := by
unfold output prepare initialCode initialInput
rw [stages_data,initialWidth_data,List.length_ofFn]
dsimp only [data]
rw [ofFn_split_take,ofFn_split_drop]
end
end ContingencyTables.CompanionInitializedRestartProgram
end OAI
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