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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 | import OAI.Computability.PerfectCompleteness.Decoding.CleanLeftDecoderLemmas
import OAI.Computability.PerfectCompleteness.Repetition.CleanPhysicalReplay
import OAI.Computability.PerfectCompleteness.Repetition.CleanRecordObservation
namespace OAI
section
namespace PerfectCompleteness.CleanRecordDecoderInput
noncomputable section
open scoped Classical
open RecursiveSpaces DescendantSpaces TreeSourceSpaces HierarchicalArrays
variable {branch : Nat → Nat} {n h t v m : Nat} [NeZero m]
(rows repeats : Nat → Nat) (upper : Nodes branch n)
(d : HierarchicalFrozenTables.LowerNodes upper (h + 1))
(cut : OwnInputReference.Cut upper (HierarchicalLeftDecoder.LowerNode upper (h + 1) d))
abbrev path := CleanRightDecoder.fullPath upper
(HierarchicalLeftDecoder.LowerNode upper (h + 1) d) cut
(CleanDecoderContext.lowerHeight upper d)
variable (outside : Slots branch n → 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 Record := CleanPhysicalReplay.Record (t := t) rows repeats (path upper d cut) clauses designated
abbrev Sample := CleanPhysicalReplay.Sample (t := t) rows repeats (path upper d cut) clauses designated
abbrev Exterior := CleanPhysicalReplay.Exterior rows repeats (path upper d cut) outside placeholder
def exposed (record : Record (t := t) rows repeats upper d cut clauses designated)
(external : Exterior rows repeats upper d cut outside placeholder) :
CleanDecoderContext.Exposed branch rows repeats n h t v m upper d where
clauses := clauses
designated := designated
clean := CleanRecordChildBlocks.clean rows clauses designated record
visible := CleanRecordChildBlocks.visible rows clauses designated record
projected := CleanRecordChildBlocks.projected rows clauses designated record
cleanProjected := CleanSourceRecord.clean_projected designated
(SourceChildKernel.Factors (C := WholeCutCalls.Index rows repeats (path upper d cut))
(t := t) rows clauses designated) record
cut := cut
outside := outside
leftTape := CleanPhysicalReplay.leftRecord rows repeats (path upper d cut) outside placeholder
clauses designated record external
rightTape := CleanPhysicalReplay.rightRecord rows repeats (path upper d cut) outside placeholder
clauses designated record external
abbrev observe (x : Sample (t := t) rows repeats upper d cut clauses designated) :
Record (t := t) rows repeats upper d cut clauses designated :=
CleanRecordObservation.observe rows clauses designated x
omit [NeZero m] in
@[simp] theorem event_observe (x : Sample (t := t) rows repeats upper d cut clauses designated) :
CleanRecordChildBlocks.event rows clauses designated
(observe rows repeats upper d cut clauses designated x) x = true :=
CleanRecordObservation.event_observe rows clauses designated x
def leftQuestions (record : Record (t := t) rows repeats upper d cut clauses designated)
(x : Sample (t := t) rows repeats upper d cut clauses designated) :=
CleanRecordObservation.leftQuestions rows clauses designated record x
def rightQuestions (record : Record (t := t) rows repeats upper d cut clauses designated)
(x : Sample (t := t) rows repeats upper d cut clauses designated) :=
CleanRecordObservation.rightQuestions rows clauses designated record x
def sources (record : Record (t := t) rows repeats upper d cut clauses designated)
(x : Sample (t := t) rows repeats upper d cut clauses designated) :
{i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} →
SourceOddLists.Occurrences m t := fun i => (x i.val).1
omit [NeZero m] in
theorem leftQuestions_sources (record : Record (t := t) rows repeats upper d cut clauses designated)
(x : Sample (t := t) rows repeats upper d cut clauses designated) :
leftQuestions rows repeats upper d cut clauses designated record x =
fun i => SourceOddLists.left (sources rows repeats upper d cut clauses designated record x i) := rfl
omit [NeZero m] in
theorem rightQuestions_sources (record : Record (t := t) rows repeats upper d cut clauses designated)
(x : Sample (t := t) rows repeats upper d cut clauses designated) :
rightQuestions rows repeats upper d cut clauses designated record x =
fun i => SourceOddLists.right clauses
(sources rows repeats upper d cut clauses designated record x i) := rfl
theorem leftSlots_eq (record : Record (t := t) rows repeats upper d cut clauses designated)
(external : Exterior rows repeats upper d cut outside placeholder)
(x : Sample (t := t) rows repeats upper d cut clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) :
CleanDecoderContext.leftSlots
(exposed rows repeats upper d cut outside placeholder clauses designated record external)
(leftQuestions rows repeats upper d cut clauses designated record x) =
CutSlotAssembly.fill (path upper d cut) outside
(CleanPhysicalReplay.leftInside rows repeats (path upper d cut) clauses designated x) := by
exact congrArg (CutSlotAssembly.fill (path upper d cut) outside)
(CleanRecordObservation.leftInside_eq rows clauses designated record x hevent)
theorem rightSlots_eq (record : Record (t := t) rows repeats upper d cut clauses designated)
(external : Exterior rows repeats upper d cut outside placeholder)
(x : Sample (t := t) rows repeats upper d cut clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) :
CleanDecoderContext.rightSlots
(exposed rows repeats upper d cut outside placeholder clauses designated record external)
(rightQuestions rows repeats upper d cut clauses designated record x) =
CutSlotAssembly.fill (path upper d cut) outside
(CleanPhysicalReplay.rightInside rows repeats (path upper d cut) clauses designated x) := by
exact congrArg (CutSlotAssembly.fill (path upper d cut) outside)
(CleanRecordObservation.rightInside_eq rows clauses designated record x hevent)
end
end PerfectCompleteness.CleanRecordDecoderInput
end
end OAI
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