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2f887db | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 | import OAI.Computability.PerfectCompleteness.Decoding.WholeCutGroupedProjection
import OAI.Computability.PerfectCompleteness.Foundations.HierarchicalProjectedSliceLemmas
namespace OAI
section
namespace PerfectCompleteness.CleanPhysicalCanonicalQuery
open scoped Classical
open RecursiveSpaces DescendantSpaces TreeSourceSpaces HierarchicalArrays
noncomputable section
variable {branch : Nat → Nat} {root h t v m : Nat} [NeZero m]
(rows repeats : Nat → Nat) (p : Path branch root (h + 1))
(outside : Slots branch root → Fin t → MixedSupport.Slot)
(placeholder : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clauses : Fin m → SourceClause.NormalizedClause v)
(designated : Fin (branch h) → Slots branch h)
abbrev Sample := CleanPhysicalReplay.Sample (t := t) rows repeats p clauses designated
def leftSlots (x : Sample (t := t) rows repeats p clauses designated) :
Slots branch root → Fin t → MixedSupport.Slot :=
CutSlotAssembly.fill p outside (CleanPhysicalReplay.leftInside rows repeats p clauses designated x)
def rightSlots (x : Sample (t := t) rows repeats p clauses designated) :
Slots branch root → Fin t → MixedSupport.Slot :=
CutSlotAssembly.fill p outside (CleanPhysicalReplay.rightInside rows repeats p clauses designated x)
def projection (x : Sample (t := t) rows repeats p clauses designated) :
∀ s k, MixedSupport.Projection
(leftSlots rows repeats p outside clauses designated x s k)
(rightSlots rows repeats p outside clauses designated x s k) :=
CutProjectionAssembly.fillProjection p outside _ _
(SourceChildKernel.parentProjection rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2))
def leftArrays (x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder) :
Arrays (leftSlots rows repeats p outside clauses designated x) rows :=
WholeCutSampler.evaluate rows repeats p _
(CleanPhysicalReplay.leftTape rows repeats p outside placeholder clauses designated x external)
def rightArrays (x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder) :
Arrays (rightSlots rows repeats p outside clauses designated x) rows :=
WholeCutSampler.evaluate rows repeats p _
(CleanPhysicalReplay.rightTape rows repeats p outside placeholder clauses designated x external)
omit [NeZero m] in
theorem arrays_pullback (x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder) :
leftArrays rows repeats p outside placeholder clauses designated x external =
ChildBlockProjection.arraysPullback rows
(projection rows repeats p outside clauses designated x)
(rightArrays rows repeats p outside placeholder clauses designated x external) :=
WholeCutGroupedProjection.physicalTape_pullback rows repeats p outside placeholder
(CleanPhysicalReplay.leftInside rows repeats p clauses designated x)
(CleanPhysicalReplay.rightInside rows repeats p clauses designated x)
(SourceChildKernel.parentProjection rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2)) external
(CleanPhysicalReplay.rightBlocks rows repeats p clauses designated x)
omit [NeZero m] in
theorem query_pullback {Y : Type*}
(x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y) :
WholeCutKeyLocality.query rows repeats p
(leftSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.leftTape rows repeats p outside placeholder clauses designated x external) post =
WholeCutKeyLocality.query rows repeats p
(rightSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.rightTape rows repeats p outside placeholder clauses designated x external) post ∘
MixedSupport.projectionMap (TreeCanonical.numberedProjection
(projection rows repeats p outside clauses designated x)) := by
change SourceProjectedCanonicalQuery.query rows
(leftArrays rows repeats p outside placeholder clauses designated x external) post =
SourceProjectedCanonicalQuery.query rows
(rightArrays rows repeats p outside placeholder clauses designated x external) post ∘ _
rw [arrays_pullback]
exact SourceProjectedCanonicalQuery.query_pullback rows
(projection rows repeats p outside clauses designated x)
(rightArrays rows repeats p outside placeholder clauses designated x external) post
omit [NeZero m] in
theorem key_eq {Y : Type*}
(x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y) (side : CanonicalKeys.Side) :
CanonicalKeys.key side (TreeCanonical.numberedSlots
(leftSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(leftSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.leftTape rows repeats p outside placeholder clauses designated x external) post) =
CanonicalKeys.key side (TreeCanonical.numberedSlots
(rightSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(rightSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.rightTape rows repeats p outside placeholder clauses designated x external) post) := by
rw [query_pullback]
exact CanonicalKeys.key_projection side
(TreeCanonical.numberedProjection (projection rows repeats p outside clauses designated x)) _
omit [NeZero m] in
theorem label_val_eq {Y : Type*}
(x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y)
(labeling : KeyStrategy.Strategy (TreeCanonical.locationCount branch root t))
(side : CanonicalKeys.Side) :
(KeyStrategy.label labeling side (TreeCanonical.numberedSlots
(leftSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(leftSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.leftTape rows repeats p outside placeholder clauses designated x external) post)).val =
(KeyStrategy.label labeling side (TreeCanonical.numberedSlots
(rightSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(rightSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.rightTape rows repeats p outside placeholder clauses designated x external) post)).val :=
KeyStrategy.label_val_eq_of_key_eq labeling side side _ _ _ _
(key_eq rows repeats p outside placeholder clauses designated x external post side)
omit [NeZero m] in
theorem response_eq {Y : Type*}
(x : Sample (t := t) rows repeats p clauses designated)
(external : CleanPhysicalReplay.Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y)
(labeling : KeyStrategy.Strategy (TreeCanonical.locationCount branch root t))
(side : CanonicalKeys.Side) :
KeyStrategy.response labeling side (TreeCanonical.numberedSlots
(leftSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(leftSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.leftTape rows repeats p outside placeholder clauses designated x external) post) =
KeyStrategy.response labeling side (TreeCanonical.numberedSlots
(rightSlots rows repeats p outside clauses designated x))
(WholeCutKeyLocality.query rows repeats p
(rightSlots rows repeats p outside clauses designated x)
(CleanPhysicalReplay.rightTape rows repeats p outside placeholder clauses designated x external) post) := by
rw [query_pullback]
exact KeyStrategy.response_projection labeling side
(TreeCanonical.numberedProjection (projection rows repeats p outside clauses designated x)) _
end
end PerfectCompleteness.CleanPhysicalCanonicalQuery
end
end OAI
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