File size: 2,779 Bytes
e5a97c6 | 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 Mathlib
import OAI.Combinatorics.MatchingCount.Algorithm.OnlineRequest
namespace OAI
namespace MatchingFPRAS.OnlineTrial
open PhysicalStream TreeTyped TreeFraction ExecutableSource ExecutableScaling OnlineSchedule
abbrev State := RequestInput×Fraction
def advance (x : SparseStageData×Vector) : SparseStageData :=
(((x.1.1.1.1,false::x.1.1.1.2),x.1.1.2),x.2)
def advanceRealizer : TreeTyped.Realizer advance :=
(TreeTyped.pair (TreeTyped.pair
(TreeTyped.pair first.fst.fst.fst (composition (TreeTyped.pair (constant false) first.fst.fst.snd) listCons))
first.fst.snd) second).congr (fun _=>rfl)
lemma polynomial_advance : PolynomialTime advanceRealizer := by
unfold advanceRealizer
apply polynomial_congr
dsimp only [Realizer.fst, Realizer.snd]
tree_cost
def carry (x : State×(Fraction×Vector)) : State :=
((advance (x.1.1.1,x.2.2),x.1.1.2),TreeFraction.mul (x.1.2,x.2.1))
def carryRealizer : TreeTyped.Realizer carry :=
(TreeTyped.pair (TreeTyped.pair
(composition (TreeTyped.pair first.fst.fst second.snd) advanceRealizer) first.fst.snd)
(composition (TreeTyped.pair first.snd second.fst) mulRealizer)).congr (fun _=>rfl)
lemma polynomial_carry : PolynomialTime carryRealizer := by
unfold carryRealizer
apply polynomial_congr
dsimp only [Realizer.fst, Realizer.snd]
have := polynomial_advance
have := polynomial_mul
tree_cost
def prepare (x : RequestInput) : OnlineStage.Input :=
(x.1,(x.2,sourceRequest x))
def prepareRealizer : TreeTyped.Realizer prepare :=
TreeTyped.pair first (TreeTyped.pair second sourceRequestRealizer)
lemma polynomial_prepare : PolynomialTime prepareRealizer :=
TreeTyped.polynomial_pair polynomial_first (TreeTyped.polynomial_pair polynomial_second polynomial_sourceRequest)
def step (x : State) : Experiment State :=
(OnlineStage.execute (prepare x.1)).map (fun y=>carry (x,y))
noncomputable def stepRealizer : OnlineTree.Realizer step :=
(OnlineTree.composition (OnlineTree.pair (OnlineTree.deterministic TreeTyped.identity)
(OnlineTree.composition (OnlineTree.deterministic (composition first prepareRealizer)) OnlineStage.executeRealizer))
(OnlineTree.deterministic carryRealizer)).congr (by
intro x h
simp only [step,Experiment.mean_bind,Experiment.mean_map,Experiment.mean,Function.comp_apply,id_eq])
def body (x : Bool×State) : Experiment State := step x.2
noncomputable def bodyRealizer : OnlineTree.Realizer body :=
(OnlineTree.composition (OnlineTree.deterministic TreeTyped.second) stepRealizer).congr (by
intro x h; rfl)
def sweep (x : List Bool×State) : Experiment State := OnlineTree.foldM body x.1 x.2
noncomputable def sweepRealizer : OnlineTree.Realizer sweep := OnlineTree.fold bodyRealizer
end MatchingFPRAS.OnlineTrial
end OAI
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