File size: 2,979 Bytes
6fe30b6 | 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 | import OAI.Computability.FourierTransform.ChunkCompiler
import OAI.Computability.FourierTransform.WordCompilation
namespace OAI
namespace PowerSaving.RAM
open Ty Slant Slant.Stroke Spectral
noncomputable section
universe U
namespace Bench.Engrave
variable {m : Bool} {ι : Type U} {b : Bench m ι}
{n l k : ι→ℕ}
lemma strand (h : b.Digit n) (hk : b.Digit k) (hl : b.Digit l)
(r : ι→ℕ→Reel) (H : (b.scan l).Engrave (fun i => n i.i) (fun i => r i.i i.j))
(g : ∀ i, ∀ j<l i, (r i j).beats=k i) :
b.Engrave n fun i => Slant.strand (r i) (l i) := by
let R i j := Slant.strand (r i) j
have hb (i : ι) (j : ℕ) (hj : j ≤ l i) : (R i j).beats=j*k i :=
beat_strand j _ (fun t ht => g i t (ht.trans_le hj))
have hs (i : ι) (j : ℕ) (hj : j ≤ l i) : (R i j).Sound (n i) :=
sound_strand _ _ fun t ht => H.sound ⟨i,t,ht.trans_le hj⟩
refine ⟨fun i => hs i _ le_rfl, (hl.mul hk).congr (fun i => (hb i _ le_rfl).symm),h,?_⟩
let U i j := film (n i) (R i j)
refine loop (t:=filmTy) hl U ?_ ?_
· exact (Engrave.rest h (Digit.wc 0)).layers
· let P := b.climbs l filmTy U
have F := Feeds.climbs b l U
have hj := stepi hl U -- specify
have hg : P.Engrave (fun i => n i.i) (fun i => R i.i i.j) :=
⟨fun i => hs i.i i.j i.hj.le, ((hj.mul (draw F hk)).congr (fun i => (hb i.i i.j i.hj.le).symm)),
draw F h,stepsum b l U⟩
exact (hg.stack (H.transfer (inspect b l U))).layers
/-- nesting scans for 3 chunk coordinates. -/
abbrev double (b : Bench m ι) (l : ι→ℕ) :=
(b.scan l).scan fun i => l i.i
abbrev triple (b : Bench m ι) (l : ι→ℕ) :=
(double b l).scan fun i => l i.i.i
private lemma duoStrand (h : b.Digit n) (hk : b.Digit k) (hl : b.Digit l)
(r : ι→ℕ→ℕ→Reel)
(H : (double b l).Engrave (fun i => n i.i.i) (fun i => r i.i.i i.i.j i.j))
(g : ∀ i, ∀ j<l i, ∀ s<l i, (r i j s).beats=k i) :
b.Engrave n fun i => Slant.strand (fun j => Slant.strand (r i j) (l i)) (l i) := by
have F := Feeds.scan b l
apply strand h (hl.mul hk) hl (fun i j => Slant.strand (r i j) (l i))
· exact strand (draw F h) (draw F hk) (draw F hl) (fun i => r i.i i.j) H
(fun i => g i.i i.j i.hj)
· exact fun i j hj => beat_strand _ _ (g i j hj)
lemma riprap (h : b.Digit n) (hk : b.Digit k) (hl : b.Digit l)
(r : ι→ℕ→ℕ→ℕ→Reel)
(H : (triple b l).Engrave (fun i => n i.i.i.i) (fun i => r i.i.i.i i.i.i.j i.i.j i.j))
(g : ∀ i, ∀ j<l i, ∀ s<l i, ∀ t<l i, (r i j s t).beats=k i) :
b.Engrave n fun i => Slant.riprap (r i) (l i) := by
have F := Feeds.scan b l
exact strand h (hl.mul (hl.mul hk)) hl
(fun i j => Slant.strand (fun s => Slant.strand (r i j s) (l i)) (l i))
(duoStrand (draw F h) (draw F hk) (draw F hl) (fun i => r i.i i.j) H
(fun i => g i.i i.j i.hj)) (fun i j hj =>
beat_strand _ _ (fun s hs => beat_strand _ _ (g i j hj s hs)))
end Bench.Engrave
end
end PowerSaving.RAM
end OAI
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