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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 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | import OAI.Computability.MatchingCount.IterateRoutine
namespace OAI
section
namespace BinaryMatching.StackCode
open Polynomial
namespace Routine
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
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)
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)
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
end Routine
end BinaryMatching.StackCode
end
end OAI
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