| import OAI.Computability.MatchingCount.RawRoutine |
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| namespace OAI |
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| section |
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| namespace BinaryMatching.StackCode |
| open Polynomial |
| namespace Block |
| variable {r : ℕ} |
| def lengthInto (src dst : Fin r) : Block r := loop src ((pop src).seq (push dst true)) |
| lemma lengthInto_runs (src dst : Fin r) (hne : src≠dst) (s : Store r) : |
| (lengthInto src dst).Runs s |
| (Function.update (Function.update s src []) dst (unary (s src).length++s dst)) |
| (3*(s src).length+1) := by |
| generalize hl : s src=l |
| induction l generalizing s with |
| | nil => |
| have he : Function.update (Function.update s src []) dst (unary 0++s dst)=s := by |
| simp only [unary_zero,List.nil_append] |
| rw [←hl,Function.update_eq_self,Function.update_eq_self] |
| change (lengthInto src dst).Runs s |
| (Function.update (Function.update s src []) dst (unary 0++s dst)) 1 |
| rw [he] |
| exact loop_runs_empty src _ s hl |
| | cons b l ih => |
| let s' := Function.update (Function.update s src l) dst (true::s dst) |
| have hp : (pop src).Runs s (Function.update s src l) 1 := by |
| simpa [hl] using pop_runs src s |
| have ht : (push dst true).Runs (Function.update s src l) s' 1 := by |
| simpa [s',hne.symm] using push_runs dst true (Function.update s src l) |
| have hi := ih s' (by simp [s',hne]) |
| have he : Function.update (Function.update s' src []) dst (unary l.length++s' dst)= |
| Function.update (Function.update s src []) dst (unary (b::l).length++s dst) := by |
| funext k |
| by_cases hk : k=dst |
| · subst k |
| simp only [Function.update_self,s',List.length_cons,unary] |
| simp only [List.replicate_succ',List.append_assoc,List.singleton_append] |
| · by_cases hks : k=src |
| · subst k; simp [s',hne] |
| · simp [s',Function.update_of_ne,hk,hks] |
| rw [he] at hi |
| have h := loop_runs_step src ((pop src).seq (push dst true)) (by simp [hl]) |
| (seq_runs _ _ hp ht) hi |
| have heq : 2+(3*l.length+1)+1=3*(b::l).length+1 := by simp; omega |
| rw [heq] at h |
| exact h |
| end Block |
| namespace Routine |
| variable {α : Type} |
| noncomputable def codeLength (ea : α → List Bool) : Routine ea unary (fun a => (ea a).length) where |
| scratch := 1 |
| block := (Block.lengthInto 0 1).seq (Block.reverseInto 1 0) |
| time := 7*X+2 |
| correct a := by |
| let s₀ : Store 2 := Function.update (fun _ => []) 0 (ea a) |
| let s₁ := Function.update (Function.update s₀ 0 []) 1 (unary (ea a).length) |
| have h₁ : (Block.lengthInto 0 1).Runs s₀ s₁ (3*(ea a).length+1) := by |
| simpa [s₀,s₁] using Block.lengthInto_runs (0:Fin 2) 1 (by decide) s₀ |
| have h₂ := Block.reverseInto_runs (1:Fin 2) 0 (by decide) s₁ |
| have he : Function.update (Function.update s₁ 1 []) 0 ((s₁ 1).reverse++s₁ 0)= |
| Function.update (fun _ => []) 0 (unary (ea a).length) := by |
| funext k |
| fin_cases k <;> simp [s₁,s₀] |
| rw [he] at h₂ |
| have hl : (s₁ 1).length=(ea a).length := by simp [s₁] |
| rw [hl] at h₂ |
| refine ⟨_,?_,Block.seq_runs _ _ h₁ h₂⟩ |
| simp only [eval_add,eval_mul,eval_ofNat,eval_X] |
| omega |
| end Routine |
| end BinaryMatching.StackCode |
| end |
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| end OAI |
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