| import OAI.Computability.MatchingCount.IterateRoutine |
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| namespace OAI |
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| section |
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| namespace BinaryMatching.StackCode |
| open Polynomial |
| namespace Routine |
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| noncomputable def append : Routine (fun z : List Bool×List Bool => pairBits z.1 z.2) id |
| (fun z => z.1++z.2) where |
| scratch := 1 |
| block := (Block.decodeRev 0 1).seq (Block.reverseInto 1 0) |
| time := 10*X+10 |
| correct z := by |
| let s₀ : Store 2 := Function.update (fun _ => []) 0 (pairBits z.1 z.2) |
| let s₁ := Function.update (Function.update s₀ 0 z.2) 1 z.1.reverse |
| have h₁ : (Block.decodeRev 0 1).Runs s₀ s₁ (5*z.1.length+2) := by |
| simpa [s₁,s₀] using Block.decodeRev_runs (0:Fin 2) 1 (by decide) z.1 z.2 |
| s₀ (by simp [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 (z.1++z.2) := by |
| funext k |
| fin_cases k <;> simp [s₁,s₀] |
| rw [he] at h₂ |
| have hl : (s₁ 1).length=z.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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| noncomputable def pushBit (b : Bool) : Routine (id : List Bool → List Bool) id (List.cons b) where |
| scratch := 0 |
| block := Block.push 0 b |
| time := 1 |
| correct x := by |
| refine ⟨1,by simp,?_⟩ |
| simpa [Function.update_idem] using Block.push_runs (0:Fin 1) b (Function.update (fun _ => []) 0 x) |
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| noncomputable def tail : Routine (id : List Bool → List Bool) id List.tail where |
| scratch := 0 |
| block := Block.pop 0 |
| time := 1 |
| correct x := by |
| refine ⟨1,by simp,?_⟩ |
| simpa [Function.update_idem] using Block.pop_runs (0:Fin 1) (Function.update (fun _ => []) 0 x) |
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| noncomputable def isEmpty : Routine (id : List Bool → List Bool) (fun b : Bool => [b]) List.isEmpty where |
| scratch := 0 |
| block := Block.cases 0 (Block.push 0 true) |
| ((Block.clear 0).seq (Block.push 0 false)) ((Block.clear 0).seq (Block.push 0 false)) |
| time := 2*X+3 |
| correct x := by |
| let s : Store 1 := Function.update (fun _ => []) 0 x |
| have hfalse := Block.seq_runs _ _ (Block.clear_runs (0:Fin 1) s) |
| (Block.push_runs (0:Fin 1) false (Function.update s 0 [])) |
| have htrue := Block.push_runs (0:Fin 1) true s |
| cases x with |
| | nil => |
| have hh := Block.cases_runs_empty (0:Fin 1) (Block.push 0 true) |
| ((Block.clear 0).seq (Block.push 0 false)) ((Block.clear 0).seq (Block.push 0 false)) (by simp [s]) htrue |
| refine ⟨2,by simp,?_⟩ |
| simpa [s,Function.update_idem] using hh |
| | cons b l => |
| cases b with |
| | false => |
| have hh := Block.cases_runs_false (0:Fin 1) (Block.push 0 true) |
| ((Block.clear 0).seq (Block.push 0 false)) ((Block.clear 0).seq (Block.push 0 false)) |
| (by simp [s]) hfalse |
| refine ⟨2*(l.length+1)+3,?_,?_⟩ |
| · simp |
| · simpa [s,Function.update_idem,Nat.add_assoc] using hh |
| | true => |
| have hh := Block.cases_runs_true (0:Fin 1) (Block.push 0 true) |
| ((Block.clear 0).seq (Block.push 0 false)) ((Block.clear 0).seq (Block.push 0 false)) |
| (by simp [s]) hfalse |
| refine ⟨2*(l.length+1)+3,?_,?_⟩ |
| · simp |
| · simpa [s,Function.update_idem,Nat.add_assoc] using hh |
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| end Routine |
| end BinaryMatching.StackCode |
| end |
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| end OAI |
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