| import OAI.Computability.MatchingCount.PairRoutine |
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| namespace OAI |
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| section |
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| namespace BinaryMatching.StackCode |
| open Polynomial |
| namespace Routine |
| variable {α β : Type} (ea : α → List Bool) (eb : β → List Bool) |
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| noncomputable def first : |
| Routine (fun z : α×β => pairBits (ea z.1) (eb z.2)) ea Prod.fst where |
| scratch := 1 |
| block := (Block.decodeRev 0 1).seq ((Block.clear 0).seq (Block.reverseInto 1 0)) |
| time := 10*X+10 |
| correct a := by |
| let s₀ : Store 2 := Function.update (fun _ => []) 0 (pairBits (ea a.1) (eb a.2)) |
| let s₁ := Function.update (Function.update s₀ 0 (eb a.2)) 1 (ea a.1).reverse |
| let s₂ := Function.update s₁ 0 [] |
| have h₁ : (Block.decodeRev 0 1).Runs s₀ s₁ (5*(ea a.1).length+2) := by |
| simpa [s₁,s₀] using Block.decodeRev_runs (0:Fin 2) 1 (by decide) (ea a.1) (eb a.2) |
| s₀ (by simp [s₀]) |
| have h₂ : (Block.clear 0).Runs s₁ s₂ (2*(eb a.2).length+1) := by |
| simpa [s₁] using Block.clear_runs (0:Fin 2) s₁ |
| have h₃ := Block.reverseInto_runs (1:Fin 2) 0 (by decide) s₂ |
| have he : Function.update (Function.update s₂ 1 []) 0 ((s₂ 1).reverse++s₂ 0)= |
| Function.update (fun _ => []) 0 (ea a.1) := by |
| funext k |
| fin_cases k <;> simp [s₂,s₁,s₀] |
| rw [he] at h₃ |
| have hl : (s₂ 1).length=(ea a.1).length := by simp [s₂,s₁] |
| rw [hl] at h₃ |
| refine ⟨_,?_,Block.seq_runs _ _ h₁ (Block.seq_runs _ _ h₂ h₃)⟩ |
| simp only [eval_add,eval_mul,eval_ofNat,eval_X,pairBits_length] |
| omega |
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| noncomputable def second : |
| Routine (fun z : α×β => pairBits (ea z.1) (eb z.2)) eb Prod.snd where |
| scratch := 1 |
| block := (Block.decodeRev 0 1).seq (Block.clear 1) |
| time := 10*X+10 |
| correct a := by |
| let s₀ : Store 2 := Function.update (fun _ => []) 0 (pairBits (ea a.1) (eb a.2)) |
| let s₁ := Function.update (Function.update s₀ 0 (eb a.2)) 1 (ea a.1).reverse |
| have h₁ : (Block.decodeRev 0 1).Runs s₀ s₁ (5*(ea a.1).length+2) := by |
| simpa [s₁,s₀] using Block.decodeRev_runs (0:Fin 2) 1 (by decide) (ea a.1) (eb a.2) |
| s₀ (by simp [s₀]) |
| have h₂ := Block.clear_runs (1:Fin 2) s₁ |
| have he : Function.update s₁ 1 []=Function.update (fun _ => []) 0 (eb a.2) := by |
| funext k |
| fin_cases k <;> simp [s₁,s₀] |
| rw [he] at h₂ |
| have hl : (s₁ 1).length=(ea a.1).length := by simp [s₁] |
| rw [hl] at h₂ |
| refine ⟨_,?_,Block.seq_runs _ _ h₁ h₂⟩ |
| simp only [eval_add,eval_mul,eval_ofNat,eval_X,pairBits_length] |
| omega |
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| end Routine |
| end BinaryMatching.StackCode |
| end |
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| end OAI |
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