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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 | import OAI.Computability.MatchingCount.SequenceRoutine
namespace OAI
section
namespace BinaryMatching.StackCode
open Polynomial
namespace Poly
variable {α β γ δ : Type} [Coding α] [Coding β] [Coding γ] [Coding δ]
theorem reindex {f : α → β} (hf : Poly f) (g : γ → δ) (i : γ → α)
(hin : ∀ x,encode x=encode (i x))
(hout : ∀ x,encode (f (i x))=encode (g x)) : Poly g :=
⟨hf.routine.reindex encode encode g i (fun x => (hin x).symm) hout⟩
theorem iterateFrom (step : α → α) (hs : Poly step) (count : β → ℕ) (initial : β → α)
(hc : Poly count) (hi : Poly initial) (P : Polynomial ℕ)
(hb : ∀ b j,j≤count b → (encode (step^[j] (initial b))).length≤
P.eval (encode (count b,initial b)).length) :
Poly (fun b => step^[count b] (initial b)) := by
let paired := (pair count initial hc hi).routine
let setup : Routine encode (fun b => encode (count b,initial b)) (id : β → β) :=
paired.reindex encode (fun b => encode (count b,initial b)) id id
(fun _ => rfl) (fun _ => rfl)
exact ⟨setup.comp (hs.routine.boundedIterate count initial P hb)⟩
end Poly
end BinaryMatching.StackCode
end
end OAI
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