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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 | import OAI.Computability.PerfectCompleteness.Repetition.CleanRecordChildBlocks
import OAI.Computability.PerfectCompleteness.Repetition.CutChildCleanLawLemmas
namespace OAI
section
namespace PerfectCompleteness.CleanRecordObservation
noncomputable section
open scoped Classical
open RecursiveSpaces TreeSourceSpaces SourceQuestionReconstruction
variable {branch : Nat → Nat} {h t v m : Nat} {C : Type*} [Fintype C]
(rows : Nat → Nat) (clauses : Fin m → SourceClause.NormalizedClause v)
(designated : Fin (branch h) → Slots branch h)
abbrev Record := CleanRecordChildBlocks.Record (C := C) (t := t) rows clauses designated
abbrev Sample := SourceChildKernel.Sample (C := C) (t := t) rows clauses designated
def observe (x : Sample (C := C) (t := t) rows clauses designated) :
Record (C := C) (t := t) rows clauses designated :=
UniformCleanSoundness.observations
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated)
(SourceChildKernel.zero (C := C) (t := t) rows clauses designated) x
theorem event_eq (record : Record (C := C) (t := t) rows clauses designated)
(x : Sample (C := C) (t := t) rows clauses designated) :
CleanRecordChildBlocks.event rows clauses designated record x =
decide (observe rows clauses designated x = record) :=
congrFun (UniformCleanSoundness.recordEvent_eq
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated)
(SourceChildKernel.zero (C := C) (t := t) rows clauses designated) record) x
@[simp] theorem event_observe (x : Sample (C := C) (t := t) rows clauses designated) :
CleanRecordChildBlocks.event rows clauses designated
(observe rows clauses designated x) x = true := by
rw [event_eq]
exact decide_eq_true rfl
def leftQuestions (record : Record (C := C) (t := t) rows clauses designated)
(x : Sample (C := C) (t := t) rows clauses designated) :
{i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} →
Fin t → Fin m :=
fun i k => ((x i.val).1 k).1
def rightQuestions (record : Record (C := C) (t := t) rows clauses designated)
(x : Sample (C := C) (t := t) rows clauses designated) :
{i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} →
Fin t → Fin v :=
fun i k => SourceClause.occurrenceVariable clauses ((x i.val).1 k)
theorem leftInside_eq (record : Record (C := C) (t := t) rows clauses designated)
(x : Sample (C := C) (t := t) rows clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) :
CleanEndpointSlots.leftInside clauses designated
(CleanRecordChildBlocks.clean rows clauses designated record)
(CleanRecordChildBlocks.visible rows clauses designated record)
(leftQuestions rows clauses designated record x) =
SourceChildKernel.parentLeftSlots clauses designated
(fun i => ((x i).1, (x i).2.1)) := by
have h := CleanSourceRecord.reconstructLeft_eq designated
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated)
(SourceChildKernel.zero (C := C) (t := t) rows clauses designated)
(v := v) record x hevent
funext s k
exact congrArg (fun f => SourceKeys.slot clauses (f s.1 s.2 k)) h
theorem rightInside_eq (record : Record (C := C) (t := t) rows clauses designated)
(x : Sample (C := C) (t := t) rows clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) :
CleanEndpointSlots.rightInside clauses designated
(CleanRecordChildBlocks.clean rows clauses designated record)
(CleanRecordChildBlocks.visible rows clauses designated record)
(CleanRecordChildBlocks.projected rows clauses designated record)
(rightQuestions rows clauses designated record x) =
SourceChildKernel.parentRightSlots rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2) := by
have h := CleanSourceRecord.reconstructRight_eq designated
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated)
(SourceChildKernel.zero (C := C) (t := t) rows clauses designated)
clauses record x hevent
funext s k
refine (congrArg (fun f => SourceKeys.slot clauses (f s.1 s.2 k)) h).trans ?_
have hflag : CleanSourceRecord.rawProjected designated
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated)
s.1 (x s.1).2.2 =
SourceChildKernel.rawProjected rows clauses designated s.1 (x s.1).2.2 := by
cases (x s.1).2.2 <;> rfl
exact (congrArg (fun projected : Bool => SourceKeys.slot clauses
(rightTuple clauses projected
(CleanSourceRecord.sourceTree designated
(D := SourceChildKernel.D (C := C) (t := t) rows clauses designated)
(SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) x s.1 s.2) k)) hflag).trans
(SourceChildKernel.mixedSlots_eq_rightTuple clauses designated s.1
((x s.1).1, (x s.1).2.1)
(SourceChildKernel.rawProjected rows clauses designated s.1 (x s.1).2.2) s.2 k).symm
end
end PerfectCompleteness.CleanRecordObservation
end
end OAI
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