Documentation

Lean.Elab.Tactic.BVDecide.LRAT.Trim

This module implements the LRAT trimming algorithm described in section 4 of "Faster LRAT Checking Than Solving with CaDiCaL" (https://drops.dagstuhl.de/storage/00lipics/lipics-vol271-sat2023/LIPIcs.SAT.2023.21/LIPIcs.SAT.2023.21.pdf).

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structure Lean.Elab.Tactic.BVDecide.LRAT.trim.Context :
Type

The context used for trimming LRAT proofs.

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    structure Lean.Elab.Tactic.BVDecide.LRAT.trim.State :
    Type
    • used : ByteArray

      For each proof step i contains at index i - initialId 0 if i is unused, 1 if it is used.

    • mapped : Array Nat

      For each proof step i contains at index i - initialId the step that i maps to in the new proof or 0 if that step is not yet set. Used such that the proof remains a sequence without gaps.

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      @[reducible, inline]
      abbrev Lean.Elab.Tactic.BVDecide.LRAT.trim.M :
      Type → Type
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        partial def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.findInitialId (proof : Array Std.Tactic.BVDecide.LRAT.IntAction) (curr : Nat := 0) :
        Except String Nat
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        def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.findEmptyId (proof : Array Std.Tactic.BVDecide.LRAT.IntAction) :
        Except String Nat
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          def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.run {α : Type} (proof : Array Std.Tactic.BVDecide.LRAT.IntAction) (x : M α) :
          Except String α
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            @[inline]
            def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.getInitialId :
            M Nat
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              @[inline]
              def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.getEmptyId :
              M Nat
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                @[inline]
                def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.getProofStep (id : Nat) :
                M (Option Std.Tactic.BVDecide.LRAT.IntAction)
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                  @[inline]
                  def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.isUsed (id : Nat) :
                  M Bool
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                    @[inline]
                    def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.markUsed (id : Nat) :
                    M Unit
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                      @[inline]
                      def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.registerIdMap (oldId newId : Nat) :
                      M Unit
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                        def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.mapStep (step : Std.Tactic.BVDecide.LRAT.IntAction) :
                        M Std.Tactic.BVDecide.LRAT.IntAction
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                          @[inline]
                          def Lean.Elab.Tactic.BVDecide.LRAT.trim.M.mapStep.mapIdent (ident : Nat) :
                          M Nat
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                            def Lean.Elab.Tactic.BVDecide.LRAT.trim.useAnalysis :
                            M Unit

                            Perform a use-def analysis of LRAT proof steps, starting at the empty clause and working its way up with DFS.

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                              partial def Lean.Elab.Tactic.BVDecide.LRAT.trim.useAnalysis.go (worklist : Array Nat) :
                              M Unit
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                              def Lean.Elab.Tactic.BVDecide.LRAT.trim.mapping :
                              M (Array Std.Tactic.BVDecide.LRAT.IntAction)

                              Map the set of used proof steps to a new LRAT proof that has no holes in the sequence of proof identifiers.

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                                def Lean.Elab.Tactic.BVDecide.LRAT.trim.go :
                                M (Array Std.Tactic.BVDecide.LRAT.IntAction)
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                                  def Lean.Elab.Tactic.BVDecide.LRAT.trim (proof : Array Std.Tactic.BVDecide.LRAT.IntAction) :
                                  Except String (Array Std.Tactic.BVDecide.LRAT.IntAction)

                                  Trim the LRAT proof by removing all steps that are not used in reaching the empty clause conclusion.

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