| import OAI.Combinatorics.ContingencyTables.Sampling.ProfileExchangeProgram |
| import OAI.Combinatorics.ContingencyTables.Machines.ListWordProgram |
| import OAI.Combinatorics.ContingencyTables.Dense.DenseAxisProposal |
|
|
| namespace OAI |
|
|
| /-! |
|
|
| namespace ContingencyTables.DensePrograms |
| open MatchingFPRAS MatchingFPRAS.TreeTyped ProfilePrograms |
|
|
| abbrev AxisData := ((ℕ×List ℕ)×ℕ)×Bool |
|
|
| def axisListStep (z : AxisData) : Option (List ℕ) := |
| let K := z.1.1.1 |
| let xs := z.1.1.2 |
| let i := z.1.2 |
| if i<xs.length then |
| if z.2 then |
| if xs.getD i 0+1<K then some (listExchange (xs,(i,xs.length))) else none |
| else |
| if 0<xs.getD i 0 then some (listExchange (xs,(xs.length,i))) else none |
| else none |
|
|
| def axisListStepRealizer : Realizer axisListStep := by |
| let K : Realizer (fun z : AxisData => z.1.1.1) := |
| composition (composition first first) first |
| let X : Realizer (fun z : AxisData => z.1.1.2) := |
| composition (composition first first) second |
| let I : Realizer (fun z : AxisData => z.1.2) := composition first second |
| let L := composition X listLength |
| let V := composition (pair X I) (getDFast 0) |
| let up := composition (composition (pair X (pair I L)) listExchangeRealizer) TreeTyped.some |
| let down := composition (composition (pair X (pair L I)) listExchangeRealizer) TreeTyped.some |
| exact (choose (composition (pair I L) less) |
| (choose second (choose (composition (pair (composition V successor) K) less) |
| up (constant none)) |
| (choose (composition (pair (constant 0) V) less) down (constant none))) |
| (constant none)).congr (by |
| intro z |
| simp only [Function.comp_apply,decide_eq_true_eq,axisListStep]) |
|
|
| / |
| never used as an iteration count. -/ |
| theorem polynomial_axisListStep : PolynomialTime axisListStepRealizer := by |
| have hK : PolynomialTime (composition |
| (composition (first (A := (ℕ×List ℕ)×ℕ) (B := Bool)) first) first) := |
| polynomial_composition (polynomial_composition polynomial_first polynomial_first) polynomial_first |
| have hX : PolynomialTime (composition |
| (composition (first (A := (ℕ×List ℕ)×ℕ) (B := Bool)) first) second) := |
| polynomial_composition (polynomial_composition polynomial_first polynomial_first) polynomial_second |
| have hI : PolynomialTime (composition |
| (first (A := (ℕ×List ℕ)×ℕ) (B := Bool)) second) := |
| polynomial_composition polynomial_first polynomial_second |
| have hL := polynomial_composition hX polynomial_listLength |
| have hV := polynomial_composition (polynomial_pair hX hI) (polynomial_getDFast 0) |
| have hup := polynomial_composition (polynomial_composition |
| (polynomial_pair hX (polynomial_pair hI hL)) polynomial_listExchange) polynomial_some |
| have hdown := polynomial_composition (polynomial_composition |
| (polynomial_pair hX (polynomial_pair hL hI)) polynomial_listExchange) polynomial_some |
| unfold axisListStepRealizer |
| exact polynomial_congr _ (polynomial_choose |
| (polynomial_composition (polynomial_pair hI hL) polynomial_less) |
| (polynomial_choose polynomial_second |
| (polynomial_choose (polynomial_composition (polynomial_pair |
| (polynomial_composition hV polynomial_successor) hK) polynomial_less) |
| hup (polynomial_constant none)) |
| (polynomial_choose (polynomial_composition (polynomial_pair (polynomial_constant 0) hV) |
| polynomial_less) hdown (polynomial_constant none))) (polynomial_constant none)) |
|
|
| end ContingencyTables.DensePrograms |
|
|
| end OAI |
|
|
