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92416a2 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 | import OAI.Computability.WLIdentification.CircuitPresentation
namespace OAI
namespace WLIdentification
namespace FinitePresentation
open WordExpressions
attribute [local instance] Classical.propDecidable Classical.decEq
namespace Number
variable {A : Word → Type} {P : Presented A}
def sigmaSnd {d : ∀ w,A w → ℕ} (D : Number P d) : Number (P.finSigma D) (fun _ x => x.2.val) where
eval _ i := (Nat.unpair i).2
correct w x := by change (Nat.unpair (Nat.pair _ _)).2=_; rw [Nat.unpair_pair]; rfl
poly := NatPoly.unpair_snd (NatPoly.var 1)
end Number
namespace CircuitRealizer
variable {P E Z T : Word → Type} {PP : Presented P} {EP : Presented E}
{ZP : Presented Z} {TP : Presented T} {r : Word → ℕ}
{rp : NatPoly (fun X : Fin 1 → Word => r (X 0))}
{C : ∀ w, ProductCircuit (r w) (P w) (E w) (Z w) (T w)}
(F : CircuitRealizer PP EP ZP TP r rp C)
noncomputable def primaryIndex : Number F.primaryP (fun w p => NaturalCode.option (C w).pointIndex p) :=
((F.pointIndex.add (Number.const PP 1)).optionCases (fun _ => 0) (NatPoly.const 0)).congr (by intro w p; cases p <;> rfl)
noncomputable def connectionIndex : Number F.connectionP (fun w l => (C w).connectionIndex l) := by
apply F.casesNumber
· exact (Number.const EP 0).pair F.edgeIndex
· exact (Number.const TP 1).pair F.testIndex
· exact (Number.const F.rowP 2).pair (Number.code F.rowP)
· exact (Number.const F.broadcastP 3).pair ((F.pointIndex.comp (Map.sigmaFst PP F.dimension)).pair (Number.sigmaSnd F.dimension))
· exact (Number.const F.selfP 4).pair ((F.primaryIndex.comp (Map.sigmaFst F.primaryP F.primaryDim)).pair (Number.sigmaSnd F.primaryDim))
· exact Number.const Presented.unit (Nat.pair 5 0)
noncomputable def realIndex : Number F.realP (fun w p => (C w).realIndex p) :=
((Number.sumCases ((Number.const F.primaryP 0).pair F.primaryIndex)
(Number.sumCases ((Number.const F.connectionP 1).pair F.connectionIndex) (Number.const Presented.unit (Nat.pair 2 0)))).retype
(realEquiv (C := C))).congr (by intro w p; cases p <;> rfl)
noncomputable def comparisonIndex : Number F.comparisonP (fun w e => (C w).comparisonIndex e) := by
apply F.comparisonCases
· exact (Number.const ZP 0).pair F.seedIndex
· exact (Number.const F.connectionP 1).pair F.connectionIndex
· exact (Number.const F.connectionP 2).pair F.connectionIndex
· exact (Number.const F.connectionP 3).pair F.connectionIndex
noncomputable def realDim : Number F.realP (fun w p => (C w).realDimension p) :=
((Number.sumCases F.primaryDim (Number.sumCases (Number.const F.connectionP 2) (Number.const Presented.unit 1))).retype
(realEquiv (C := C))).congr (by intro w p; cases p <;> rfl)
noncomputable def toPrimary : Map F.primaryP F.realP (fun _ => ProductCircuit.RealType.primary) :=
(Map.untype F.realBase (realEquiv (C := C))).comp (Map.inl F.primaryP (F.connectionP.sum Presented.unit))
noncomputable def toBuffer : Map F.connectionP F.realP (fun _ => ProductCircuit.RealType.buffer) :=
(Map.untype F.realBase (realEquiv (C := C))).comp
((Map.inr F.primaryP (F.connectionP.sum Presented.unit)).comp (Map.inl F.connectionP Presented.unit))
noncomputable def toDummy {A : Word → Type} (AP : Presented A) : Map AP F.realP (fun _ _ => .dummy) :=
Map.const AP F.realP (fun _ => .dummy) (NatPoly.const 3)
noncomputable def comparisonSource : Map F.comparisonP F.realP (fun w => (C w).comparisonSource) := by
apply F.comparisonCases
· exact F.toPrimary.comp ((Map.some PP).comp F.seedType)
· exact F.toPrimary.comp F.connectionSource
· exact F.toPrimary.comp F.connectionSource
· exact F.toBuffer
noncomputable def comparisonTarget : Map F.comparisonP F.realP (fun w => (C w).comparisonTarget) := by
apply F.comparisonCases
· exact F.toDummy ZP
· exact F.toBuffer
· exact F.toBuffer
· exact F.toPrimary.comp F.connectionTarget
noncomputable def connectionDomain : Test (F.connectionP.prod (F.rowP.prod Presented.bool))
(fun w x => decide (x.2.2∈((C w).connectionMap x.1).domain x.2.1)) := by
apply F.casesTestFst
· exact F.edgeDomain
· exact F.testDomain
all_goals exact (Test.const _ true).congr (by intro w x; simp only [ProductCircuit.connectionMap,ProductMap.flip,ProductMap.identity,Finset.mem_univ,decide_true])
noncomputable def rightBit {A : Word → Type} (AP : Presented A) :
Map (AP.prod (F.rowP.prod Presented.bool)) Presented.bool (fun _ x => x.2.2) :=
(Map.snd F.rowP Presented.bool).comp (Map.snd AP (F.rowP.prod Presented.bool))
noncomputable def flipMapping : Map (F.rowP.prod (F.rowP.prod Presented.bool)) Presented.bool
(fun _w x => (ProductMap.flip x.1).mapping x.2.1 x.2.2) := by
let H : Test (F.rowP.prod (F.rowP.prod Presented.bool)) (fun _ x => decide (x.2.1=x.1)) :=
Test.eq ((Map.fst F.rowP Presented.bool).comp (Map.snd F.rowP (F.rowP.prod Presented.bool))) (Map.fst _ _)
let B := Test.ofBoolMap (F.rightBit F.rowP)
exact (Map.boolOfTest (Test.ite H B.not B)).congr (by intro w x; simp only [decide_eq_true_eq]; rfl)
noncomputable def connectionMapping : Map (F.connectionP.prod (F.rowP.prod Presented.bool)) Presented.bool
(fun w x => ((C w).connectionMap x.1).mapping x.2.1 x.2.2) := by
apply F.casesNumberFst
· exact F.edgeMapping
· exact F.rightBit TP
· exact F.flipMapping
· exact F.rightBit F.broadcastP
· exact F.rightBit F.selfP
· exact F.rightBit Presented.unit
noncomputable def comparisonDomain : Test (F.comparisonP.prod (F.rowP.prod Presented.bool))
(fun w x => decide (x.2.2∈((C w).comparisonMap x.1).domain x.2.1)) := by
apply F.comparisonTestFst
· exact F.seedDomain
· exact F.connectionDomain
· exact F.connectionDomain
· exact F.connectionDomain
noncomputable def comparisonMapping : Map (F.comparisonP.prod (F.rowP.prod Presented.bool)) Presented.bool
(fun w x => ((C w).comparisonMap x.1).mapping x.2.1 x.2.2) := by
apply F.comparisonNumberFst
· exact F.rightBit ZP
· exact F.rightBit F.connectionP
· exact F.rightBit F.connectionP
· exact F.connectionMapping
end CircuitRealizer
end FinitePresentation
end WLIdentification
end OAI
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