| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Sampling.TreePreparedMarked |
| import OAI.Combinatorics.MatchingCount.Machines.OnlineTraverse |
| import OAI.Combinatorics.MatchingCount.Tapes.OnlineWord |
|
|
| namespace OAI |
|
|
| namespace MatchingFPRAS.OnlineSample |
| open PhysicalStream TreeTyped |
|
|
| abbrev word (k : ℕ) : Experiment (List Bool) := OnlineWord.prepend k [] |
|
|
| variable {A : Type} [Codec A] |
| def repeatInputRealizer : TreeTyped.Realizer (fun x : ℕ×A=>List.replicate x.1 x.2) := |
| (TreeTyped.composition (TreeTyped.pair TreeTyped.second (TreeTyped.composition TreeTyped.first TreeTyped.range)) |
| (TreeTyped.mapWith TreeTyped.first)).congr (by intro x; simp) |
| |
| def words (x : ℕ×ℕ) : Experiment (List (List Bool)) := |
| OnlineTree.traverseM word (List.replicate x.2 x.1) |
| noncomputable def wordsRealizer : OnlineTree.Realizer words := |
| (OnlineTree.composition (OnlineTree.deterministic (TreeTyped.composition |
| (TreeTyped.pair TreeTyped.second TreeTyped.first) repeatInputRealizer)) |
| (OnlineTree.traverse OnlineWord.naturalRealizer)).congr (by intro x h; rfl) |
| |
| def localWords (x : ℕ×ℕ) : Experiment NumericLadder.Bits := |
| (word x.1).bind (fun w=>(words x).map (Prod.mk w)) |
| noncomputable def localRealizer : OnlineTree.Realizer localWords := |
| OnlineTree.pair (OnlineTree.composition (OnlineTree.deterministic TreeTyped.first) OnlineWord.naturalRealizer) |
| wordsRealizer |
|
|
| def scan (x : ℕ×ℕ) : Experiment (List Bool×NumericLadder.Bits) := |
| (word x.1).bind (fun w=>(localWords x).map (Prod.mk w)) |
| noncomputable def scanRealizer : OnlineTree.Realizer scan := |
| OnlineTree.pair (OnlineTree.composition (OnlineTree.deterministic TreeTyped.first) OnlineWord.naturalRealizer) |
| localRealizer |
|
|
| def scans (x : (ℕ×ℕ)×ℕ) : Experiment (List (List Bool×NumericLadder.Bits)) := |
| OnlineTree.traverseM scan (List.replicate x.2 x.1) |
| noncomputable def scansRealizer : OnlineTree.Realizer scans := |
| (OnlineTree.composition (OnlineTree.deterministic (TreeTyped.composition |
| (TreeTyped.pair TreeTyped.second TreeTyped.first) repeatInputRealizer)) |
| (OnlineTree.traverse scanRealizer)).congr (by intro x h; rfl) |
| |
| def markWord (x : ℕ×ℕ) : Experiment (ℕ×List Bool) := (word x.2).map (Prod.mk x.1) |
| noncomputable def markWordRealizer : OnlineTree.Realizer markWord := |
| OnlineTree.mapSecond OnlineWord.naturalRealizer |
|
|
| def markRequests (x : ℕ×List ℕ) : List (ℕ×ℕ) := x.2.map (fun i=>(i,x.1)) |
| def markRequestsRealizer : TreeTyped.Realizer markRequests := |
| (TreeTyped.mapWith (TreeTyped.pair TreeTyped.second TreeTyped.first)).congr (fun _=>rfl) |
| def marks (x : ℕ×List ℕ) : Experiment (List (ℕ×List Bool)) := |
| OnlineTree.traverseM markWord (markRequests x) |
| noncomputable def marksRealizer : OnlineTree.Realizer marks := |
| OnlineTree.composition (OnlineTree.deterministic markRequestsRealizer) (OnlineTree.traverse markWordRealizer) |
|
|
| abbrev Request := ((ℕ×ℕ)×ℕ)×(ℕ×List ℕ) |
| def sample (x : Request) : Experiment NumericMarking.SampleBits := |
| (scans x.1).bind (fun s=>(marks x.2).map (Prod.mk s)) |
| noncomputable def sampleRealizer : OnlineTree.Realizer sample := |
| OnlineTree.pair (OnlineTree.composition (OnlineTree.deterministic TreeTyped.first) scansRealizer) |
| (OnlineTree.composition (OnlineTree.deterministic TreeTyped.second) marksRealizer) |
| def many (x : ℕ×Request) : Experiment (List NumericMarking.SampleBits) := |
| OnlineTree.traverseM sample (List.replicate x.1 x.2) |
| noncomputable def manyRealizer : OnlineTree.Realizer many := |
| OnlineTree.composition (OnlineTree.deterministic repeatInputRealizer) (OnlineTree.traverse sampleRealizer) |
| end MatchingFPRAS.OnlineSample |
|
|
| end OAI |
|
|
