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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 53 54 55 56 57 58 59 60 61 62 63 64 65 | import OAI.Computability.MatchingCount.PairRoutine
namespace OAI
section
namespace BinaryMatching.StackCode
open Polynomial
namespace Routine
variable {α β : Type} (ea : α → List Bool) (eb : β → List Bool)
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
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
end Routine
end BinaryMatching.StackCode
end
end OAI
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