| import OAI.Computability.MatchingCount.RawOptimizer |
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| namespace OAI |
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| section |
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| namespace BinaryMatching.Raw.Optimize.Compiler |
| open StackCode StackCode.Poly |
| local instance : Preorder ℤ := Int.instLinearOrder.toPreorder |
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| @[fun_prop] theorem paramsRepr_poly : Poly Params.repr := |
| (Poly.identity (α := ParamData)).reindex Params.repr Params.repr (fun _ => rfl) (fun _ => rfl) |
| @[fun_prop] theorem paramsOfData_poly : Poly Params.ofData := |
| (Poly.identity (α := ParamData)).reindex Params.ofData id (fun _ => rfl) (fun _ => rfl) |
| @[fun_prop] theorem params_n : Poly Params.n := |
| Poly.comp (fun z : ParamData => z.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_q : Poly Params.q := |
| Poly.comp (fun z : ParamData => z.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_k : Poly Params.k := |
| Poly.comp (fun z : ParamData => z.2.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_L : Poly Params.L := |
| Poly.comp (fun z : ParamData => z.2.2.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_D : Poly Params.D := |
| Poly.comp (fun z : ParamData => z.2.2.2.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_M : Poly Params.M := |
| Poly.comp (fun z : ParamData => z.2.2.2.2.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_pow : Poly Params.pow := |
| Poly.comp (fun z : ParamData => z.2.2.2.2.2.2.1) Params.repr (by fun_prop) paramsRepr_poly |
| @[fun_prop] theorem params_beta : Poly Params.beta := |
| Poly.comp (fun z : ParamData => z.2.2.2.2.2.2.2) Params.repr (by fun_prop) paramsRepr_poly |
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| @[fun_prop] theorem doubleIntSum {α : Type} [Coding α] [Inhabited α] |
| (n : α → ℕ) (f : (α×ℕ)×ℕ → ℤ) (hn : Poly n) (hf : Poly f) : |
| Poly (fun a => (tab (n a) (fun i => (tab (n a) (fun j => f ((a,i),j))).sum)).sum) := by |
| apply Poly.comp List.sum _ Poly.listIntSum |
| apply Poly.rawTab n (fun z : α×ℕ => (tab (n z.1) (fun j => f (z,j))).sum) hn |
| apply Poly.comp List.sum _ Poly.listIntSum |
| exact Poly.rawTab (fun z : α×ℕ => n z.1) f (by fun_prop) hf |
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| @[fun_prop] theorem upperSum_poly {α : Type} [Coding α] [Inhabited α] |
| (n : α → ℕ) (f : (α×ℕ)×ℕ → ℤ) (hn : Poly n) (hf : Poly f) : |
| Poly (fun a => upperSum (n a) (fun i j => f ((a,i),j))) := by |
| have h := doubleIntSum n (fun z : (α×ℕ)×ℕ => if decide (z.1.2<z.2) then f z else 0) hn (by fun_prop) |
| exact h.congr (fun a => by simp only [upperSum,decide_eq_true_eq]) |
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| @[fun_prop] theorem rowNumerator_poly : Poly (fun z : ℕ×(Matrix ℤ×Row) => rowNumerator z.1 z.2.1 z.2.2) := by |
| have hh := upperSum_poly (fun z : ℕ×(Matrix ℤ×Row) => z.2.1.length) |
| (fun z : ((ℕ×(Matrix ℤ×Row))×ℕ)×ℕ => get z.1.1.2.2.1 z.1.2 z.2*get z.1.1.2.1 z.1.2 z.2) |
| (by fun_prop) (by fun_prop) |
| unfold rowNumerator |
| fun_prop |
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| @[fun_prop] theorem indexedSlope_poly : Poly (fun z : ℕ×ℕ => indexedSlope z.1 z.2) := by |
| have h : Poly (fun z : ℕ×ℕ => if decide (z.2<z.1) then (z.2:ℤ)-1 else (z.1:ℤ)) := by fun_prop |
| exact h.congr (fun _ => by simp only [indexedSlope,decide_eq_true_eq]) |
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| @[fun_prop] theorem pieceNumerator_poly : Poly (fun z : (ℕ×(ℕ×ℕ))×(ℤ×ℕ) => |
| pieceNumerator z.1.1 z.1.2.1 z.1.2.2 z.2.1 z.2.2) := by |
| have h : Poly (fun z : (ℕ×(ℕ×ℕ))×(ℤ×ℕ) => indexedSlope z.1.1 z.2.2*z.2.1*(z.1.2.2:ℤ)+ |
| if decide (z.2.2<z.1.1) then (z.1.2.1:ℤ)*(cappedPow2 z.1.2.2 (z.1.1-z.2.2):ℤ) else 0) := by fun_prop |
| exact h.congr (fun _ => by simp only [pieceNumerator,decide_eq_true_eq]) |
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| @[fun_prop] theorem selectedIndex_poly : Poly (fun z : (ℕ×(ℕ×ℕ))×ℤ => selectedIndex z.1.1 z.1.2.1 z.1.2.2 z.2) := by |
| let arg (z : (ℕ×(ℕ×ℕ))×ℤ) := (List.range (z.1.1+1)).argmin (pieceNumerator z.1.1 z.1.2.1 z.1.2.2 z.2) |
| have ha : Poly arg := by |
| apply Poly.comp _ (fun z : (ℕ×(ℕ×ℕ))×ℤ => (z,List.range (z.1.1+1))) |
| (Poly.listArgminParam Poly.intLT (fun z : ((ℕ×(ℕ×ℕ))×ℤ)×ℕ => pieceNumerator z.1.1.1 z.1.1.2.1 z.1.1.2.2 z.1.2 z.2) |
| (Poly.comp _ (fun z : ((ℕ×(ℕ×ℕ))×ℤ)×ℕ => (z.1.1,(z.1.2,z.2))) pieceNumerator_poly (by fun_prop))) |
| (by fun_prop) |
| have h : Poly (fun z : (ℕ×(ℕ×ℕ))×ℤ => if (arg z).isSome then (arg z).getD 0 else z.1.1) := by fun_prop |
| exact h.congr (fun z => by change _=(arg z).getD _; cases arg z <;> rfl) |
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| @[fun_prop] theorem selectedIndex_params_poly : Poly (fun z : Params×ℤ => selectedIndex z.1.k z.1.D z.1.pow z.2) := |
| Poly.comp _ (fun z : Params×ℤ => ((z.1.k,(z.1.D,z.1.pow)),z.2)) selectedIndex_poly (by fun_prop) |
| @[fun_prop] theorem scaledPsi_poly : Poly (fun z : Params×ℤ => scaledPsi z.1 z.2) := |
| Poly.comp _ (fun z : Params×ℤ => ((z.1.k,(z.1.D,z.1.pow)),(z.2,selectedIndex z.1.k z.1.D z.1.pow z.2))) |
| pieceNumerator_poly (by fun_prop) |
| @[fun_prop] theorem scaledSlope_poly : Poly (fun z : Params×ℤ => scaledSlope z.1 z.2) := |
| Poly.comp _ (fun z : Params×ℤ => (z.1.k,selectedIndex z.1.k z.1.D z.1.pow z.2)) indexedSlope_poly (by fun_prop) |
| end BinaryMatching.Raw.Optimize.Compiler |
| end |
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| end OAI |
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