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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 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 | import Mathlib
import OAI.Computability.MinUncut.Graphs.DemandQueryEffectivity
namespace OAI
section
noncomputable section
namespace MinUncut.Preprocess
open MinUncut.Inner MinUncut.Outer MinUncut.Outer.LocalTemplate MinUncut.FiniteGaussian
open MinUncutGames.Foundations.Hastad.SourceOccurrences UEncoding
open MinUncut.Costed MinUncut.Costed.SourceWords MinUncut.FiniteProof
lemma c_replicate {X : Type} [Primcodable X] : Computable₂ (fun n (x : X)=>List.replicate n x) := by
have hf : Computable₂ (fun (x : X) (_ : ℕ)=>x) := Computable.fst
have hh : Computable (fun p : ℕ × X=>(List.range p.1).map (fun _=>p.2)) :=
(c_rangeMap hf).comp Computable.snd Computable.fst
change Computable (fun p : ℕ × X=>List.replicate p.1 p.2)
simpa using hh
attribute [local irreducible] rationalScoreTable MinUncut.FiniteGaussian.midpoint
namespace DemandBody
variable {P : Type} [Primcodable P] {p : P}
variable (t : P → ℕ) (ht : Computable t) (h : ∀p,Fin (t p) → Bool)
variable (hc : Computable (fun p=>(((Encoding.fin (t p)).function Encoding.bool).code (h p)).val))
variable (m n : P → ℕ) (hm : Computable m) (hn : Computable n) (hnpos : ∀p,0<n p)
variable (g : P → GridData) (hg : Computable g)
def samples := ((Weights.localSamples t ht h hc m n hm hn hnpos g hg).prod (tests P)).prod
(Alphabet.positionsList t ht)
def bodyQuery (σ η : ℚ) (x : (LocalSample (Alphabet (h p)) (m p) (n p) (g p) × Test) × (Fin (t p) → Fin 3)) :=
query (h p) x.1.1.1 x.1.1.2.1 x.1.1.2.2.1
(rationalScoreTable σ η (fun i=>midpoint (g p).T (g p).L (x.1.1.2.2.2 i))) x.1.2
lemma map_bodyScores (σ η : P → ℚ) (hσ : Computable σ) (hη : Computable η) :
(samples t ht h hc m n hm hn hnpos g hg).Map
((Grid.indices m n hm hn hnpos).function UEncoding.bool)
(fun p x=>rationalScoreTable (σ p) (η p) (fun i=>midpoint (g p).T (g p).L (x.1.1.2.2.2 i))) := by
let s:=Weights.localSamples t ht h hc m n hm hn hnpos g hg
let c:=(s.prod (tests P)).prod (Alphabet.positionsList t ht)
have hs : c.Map s (fun _ x=>x.1.1) := (map_fst _ _).first
have hq : c.Map (Grid.samples m n hm hn hnpos g hg) (fun _ x=>x.1.1.2.2.2) :=
map_comp (map_comp (map_comp hs (map_snd _ _)) (map_snd _ _)) (map_snd _ _)
have htable : (Grid.samples m n hm hn hnpos g hg).Map
((Grid.indices m n hm hn hnpos).function UEncoding.bool)
(fun p q=>rationalScoreTable (σ p) (η p) (fun i=>midpoint (g p).T (g p).L (q i))) :=
map_lambda (Grid.map_scoreTable m n hm hn hnpos g hg σ η hσ hη)
exact map_comp (a:=c) (b:=Grid.samples m n hm hn hnpos g hg)
(c:=(Grid.indices m n hm hn hnpos).function UEncoding.bool)
(f:=fun _ x=>x.1.1.2.2.2)
(g:=fun p q=>rationalScoreTable (σ p) (η p) (fun i=>midpoint (g p).T (g p).L (q i))) hq htable
lemma map_bodyQuery (σ η : P → ℚ) (hσ : Computable σ) (hη : Computable η) :
(samples t ht h hc m n hm hn hnpos g hg).Map (Queries.queries t ht h hc)
(fun p x=>bodyQuery t h m n g (σ p) (η p) x) := by
let s:=Weights.localSamples t ht h hc m n hm hn hnpos g hg
let c:=(s.prod (tests P)).prod (Alphabet.positionsList t ht)
let ar:=Alphabet.arrays t ht h hc m n hm hn hnpos
have hs : c.Map s (fun _ x=>x.1.1) := (map_fst _ _).first
have hB : c.Map ar (fun _ x=>x.1.1.1) := map_comp hs (map_fst _ _)
have hC : c.Map ar (fun _ x=>x.1.1.2.1) := map_comp (map_comp hs (map_snd _ _)) (map_fst _ _)
have hz : c.Map (Face.codes m n hm hn hnpos) (fun _ x=>x.1.1.2.2.1) :=
map_comp (map_comp (map_comp hs (map_snd _ _)) (map_snd _ _)) (map_fst _ _)
have hj : c.Map (tests P) (fun _ x=>x.1.2) := (map_snd _ _).first
exact Queries.map_query t ht h hc m n hm hn hnpos hB hC hz
(map_bodyScores t ht h hc m n hm hn hnpos g hg σ η hσ hη) hj
lemma out_bodyExpressions (σ η : P → ℚ) (hσ : Computable σ) (hη : Computable η) :
(samples t ht h hc m n hm hn hnpos g hg).Out (fun p x=>
([leftExpr (bodyQuery t h m n g (σ p) (η p) x) x.2,
rightExpr (bodyQuery t h m n g (σ p) (η p) x) x.2,
signExpr (bodyQuery t h m n g (σ p) (η p) x) x.2]).map (fun e=>e.program.code)) :=
Syntax.out_queryExpressions t ht h hc (map_bodyQuery t ht h hc m n hm hn hnpos g hg σ η hσ hη)
(map_snd _ _)
lemma out_bodyWeight (a : P → ℚ) (ha : Computable a)
(b : P → Test → ℚ) (hb : (tests P).Out (fun p j=>b p j)) :
(samples t ht h hc m n hm hn hnpos g hg).Out
(fun p x=>localWeight (g p) (a p) (b p x.1.2) x.1.2 x.1.1) := by
have hw:=(Weights.out_localWeight t ht h hc m n hm hn hnpos g hg a (fun _=>1) ha (ca_const 1)).first (b:=Alphabet.positionsList t ht)
have hj : (samples t ht h hc m n hm hn hnpos g hg).Map (tests P) (fun _ x=>x.1.2) :=
(map_snd _ _).first
have hbud:=hb.comp hj
apply (hw.ratDiv hbud).ofEq
intro p x
simp only [localWeight,div_one]
lemma out_bodyRepetitions (a : P → ℚ) (ha : Computable a)
(b : P → Test → ℚ) (hb : (tests P).Out (fun p j=>b p j)) :
(samples t ht h hc m n hm hn hnpos g hg).Out (fun p x=>
multiplicity (innerDenominator (t p) (m p) (n p) (g p) (a p) (b p))
(localWeight (g p) (a p) (b p x.1.2) x.1.2 x.1.1)) := by
have hw := out_bodyWeight t ht h hc m n hm hn hnpos g hg a ha b hb
have hd := out_const (samples t ht h hc m n hm hn hnpos g hg)
(Denominator.c_innerDenominator t m n ht hm hn hnpos g hg a ha b hb)
exact ((hw.map primrec_ratNum.to_comp).map primrec_intToNat.to_comp).map₂
(hd.map₂ (hw.map primrec_ratDen.to_comp) Primrec.nat_div.to_comp) Primrec.nat_mul.to_comp
lemma out_repeatedExpressions (a : P → ℚ) (ha : Computable a)
(b : P → Test → ℚ) (hb : (tests P).Out (fun p j=>b p j))
(σ η : P → ℚ) (hσ : Computable σ) (hη : Computable η) :
(samples t ht h hc m n hm hn hnpos g hg).Out (fun p x=>
(List.replicate (multiplicity (innerDenominator (t p) (m p) (n p) (g p) (a p) (b p))
(localWeight (g p) (a p) (b p x.1.2) x.1.2 x.1.1))
(([leftExpr (bodyQuery t h m n g (σ p) (η p) x) x.2,
rightExpr (bodyQuery t h m n g (σ p) (η p) x) x.2,
signExpr (bodyQuery t h m n g (σ p) (η p) x) x.2]).map (fun e=>e.program.code))).flatten) := by
exact ((out_bodyRepetitions t ht h hc m n hm hn hnpos g hg a ha b hb).map₂
(out_bodyExpressions t ht h hc m n hm hn hnpos g hg σ η hσ hη)
c_replicate).map Primrec.list_flatten.to_comp
end DemandBody
end MinUncut.Preprocess
end
end
end OAI
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