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ea76aac | 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 | import OAI.Computability.MatchingCount.RawOptimizerDataCompiler
namespace OAI
section
namespace BinaryMatching.Raw.Optimize.Compiler
open StackCode StackCode.Poly BinaryMatching.Raw.Compiler
local instance : Preorder ℤ := Int.instLinearOrder.toPreorder
@[fun_prop] theorem capacities_poly : Poly (fun z : ℕ×Matrix ℤ => capacities z.1 z.2) := by
have h := Poly.rawMatrix Prod.fst (fun z : ((ℕ×Matrix ℤ)×ℕ)×ℕ =>
if decide (z.1.2<z.2) then (get z.1.1.2 z.1.2 z.2).toNat else
if decide (z.2<z.1.2) then (get z.1.1.2 z.2 z.1.2).toNat else 0) (by fun_prop) (by fun_prop)
exact h.congr (fun _ => by simp only [capacities,decide_eq_true_eq])
@[fun_prop] theorem zeroRow_poly : Poly zeroRow := by
unfold zeroRow
apply Poly.pair
· exact Poly.rawMatrix id (fun _ => (0:ℤ)) (by fun_prop) (by fun_prop)
· fun_prop
@[fun_prop] theorem degreeRow_poly : Poly (fun z : ℕ×(ℕ×Bool) => degreeRow z.1 z.2.1 z.2.2) := by
have h := Poly.rawMatrix Prod.fst (fun z : ((ℕ×(ℕ×Bool))×ℕ)×ℕ =>
if decide (z.1.2<z.2) then
if decide (z.1.2=z.1.1.2.1) || decide (z.2=z.1.1.2.1) then (if z.1.1.2.2 then (1:ℤ) else -1) else 0 else 0)
(by fun_prop) (by fun_prop)
have hh := Poly.pair _ (fun z : ℕ×(ℕ×Bool) => if z.2.2 then (-1:ℤ) else 1) h (by fun_prop)
exact hh.congr (fun _ => by simp only [degreeRow,Bool.or_eq_true,decide_eq_true_eq])
@[fun_prop] theorem cutRow_poly : Poly (fun z : ℕ×Cut => cutRow z.1 z.2) := by
have h := Poly.rawMatrix Prod.fst (fun z : ((ℕ×Cut)×ℕ)×ℕ =>
if decide (z.1.2<z.2) then
if (mem z.1.1.2 z.1.2 && !mem z.1.1.2 z.2) || (mem z.1.1.2 z.2 && !mem z.1.1.2 z.1.2) then (-1:ℤ) else 0 else 0)
(by fun_prop) (by fun_prop)
exact (Poly.pair _ (fun _ => (1:ℤ)) h (by fun_prop)).congr (fun _ => by simp only [cutRow,decide_eq_true_eq])
@[fun_prop] theorem rows_poly : Poly (fun z : ℕ×Matrix ℤ => rows z.1 z.2) := by
have hd : Poly (fun z : ℕ×Matrix ℤ => (List.range z.1).flatMap (fun v => [degreeRow z.1 v true,degreeRow z.1 v false])) :=
Poly.flatMapWith (fun z : ℕ×Matrix ℤ => List.range z.1)
(fun z : (ℕ×Matrix ℤ)×ℕ => [degreeRow z.1.1 z.2 true,degreeRow z.1.1 z.2 false]) (by fun_prop) (by fun_prop)
unfold rows
fun_prop
@[fun_prop] theorem selectedRow_poly : Poly (fun z : ℕ×(ℕ×Matrix ℤ) => selectedRow z.1 z.2.1 z.2.2) := by
let arg (z : ℕ×(ℕ×Matrix ℤ)) := (rows z.1 z.2.2).argmax (rowNumerator z.2.1 z.2.2)
have ha : Poly arg :=
Poly.comp _ (fun z : ℕ×(ℕ×Matrix ℤ) => (z,rows z.1 z.2.2))
(Poly.listArgmaxParam Poly.intLT (fun z : (ℕ×(ℕ×Matrix ℤ))×Row => rowNumerator z.1.2.1 z.1.2.2 z.2)
(by fun_prop)) (by fun_prop)
have h : Poly (fun z : ℕ×(ℕ×Matrix ℤ) => if (arg z).isSome then (arg z).getD (default:Row) else zeroRow z.1) := by fun_prop
exact h.congr (fun z => by change _=(arg z).getD _; cases arg z <;> rfl)
end BinaryMatching.Raw.Optimize.Compiler
end
end OAI
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