| 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 |
|
|
