openAI-math-dataset / lean /OAI /Computability /PerfectCompleteness /Machines /CleanRecordDecoderInput.lean
| 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 | |