openAI-math-dataset / lean /OAI /Combinatorics /ContingencyTables /Dense /DenseCanonicalProgram.lean
| import OAI.Combinatorics.ContingencyTables.Dense.DenseNormalizeSemantics | |
| import OAI.Combinatorics.ContingencyTables.Sampling.GreedyTableComplexity | |
| namespace OAI | |
| /-! # Dense sampling from margins with a computed grid and fallback -/ | |
| namespace ContingencyTables.DensePrograms | |
| open MatchingFPRAS.TreeTyped ProfilePrograms | |
| abbrev CanonicalParameters := (List ℕ×List ℕ)×(ℕ×ℕ) | |
| abbrev CanonicalDrawData := CanonicalParameters×List Bool | |
| def zeroGrid (z : List ℕ×List ℕ) : List ℕ := | |
| (cellPairs (z.1.tail,z.2.tail)).map (fun _ => 0) | |
| def zeroGridRealizer : Realizer zeroGrid := | |
| composition (composition (pair (composition first tail) (composition second tail)) | |
| cellPairsRealizer) (map (constant 0)) | |
| theorem polynomial_zeroGrid : PolynomialTime zeroGridRealizer := | |
| polynomial_composition (polynomial_composition | |
| (polynomial_pair (polynomial_composition polynomial_first polynomial_tail) | |
| (polynomial_composition polynomial_second polynomial_tail)) polynomial_cellPairs) | |
| (polynomial_map (polynomial_constant 0)) | |
| def canonicalInput (z : CanonicalDrawData) : DenseDrawData := | |
| (((((z.1.1,zeroGrid z.1.1),z.1.2.1),z.1.2.2), | |
| GreedyFeasibleTable.listMatrix z.1.1.1 z.1.1.2),z.2) | |
| def canonicalInputRealizer : Realizer canonicalInput := by | |
| let margins : Realizer (fun z : CanonicalDrawData => z.1.1) := composition first first | |
| let parameters : Realizer (fun z : CanonicalDrawData => z.1.2) := composition first second | |
| let grid := composition margins zeroGridRealizer | |
| let fallback := composition margins GreedyFeasibleTable.tableRealizer | |
| exact pair (pair (pair (pair (pair margins grid) (composition parameters first)) | |
| (composition parameters second)) fallback) second | |
| theorem polynomial_canonicalInput : PolynomialTime canonicalInputRealizer := by | |
| have hm : PolynomialTime (composition | |
| (first (A := CanonicalParameters) (B := List Bool)) first) := | |
| polynomial_composition polynomial_first polynomial_first | |
| have hp : PolynomialTime (composition | |
| (first (A := CanonicalParameters) (B := List Bool)) second) := | |
| polynomial_composition polynomial_first polynomial_second | |
| unfold canonicalInputRealizer | |
| exact polynomial_pair (polynomial_pair (polynomial_pair | |
| (polynomial_pair (polynomial_pair hm (polynomial_composition hm polynomial_zeroGrid)) | |
| (polynomial_composition hp polynomial_first)) | |
| (polynomial_composition hp polynomial_second)) | |
| (polynomial_composition hm GreedyFeasibleTable.polynomial_table)) polynomial_second | |
| def canonicalDenseDraw (z : CanonicalDrawData) : MatrixCode := | |
| normalizedDenseCode (canonicalInput z) | |
| def canonicalDenseDrawRealizer : Realizer canonicalDenseDraw := | |
| composition canonicalInputRealizer normalizedDenseCodeRealizer | |
| theorem polynomial_canonicalDenseDraw : PolynomialTime canonicalDenseDrawRealizer := | |
| polynomial_composition polynomial_canonicalInput polynomial_normalizedDenseCode | |
| end ContingencyTables.DensePrograms | |
| end OAI | |