Documentation

Lean.Meta.Tactic.Grind.Arith.Linear.Search

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def Lean.Meta.Grind.Arith.Linear.IneqCnstr.throwUnexpected {α : Type} (c : IneqCnstr) :
LinearM α
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    def Lean.Meta.Grind.Arith.Linear.DiseqCnstr.throwUnexpected {α : Type} (c : DiseqCnstr) :
    LinearM α
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      def Lean.Meta.Grind.Arith.Linear.EqCnstr.throwUnexpected {α : Type} (c : EqCnstr) :
      LinearM α
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        def Lean.Meta.Grind.Arith.Linear.getBestLower? (x : Var) :
        LinearM (Option (Rat × IneqCnstr))

        Assuming all variables smaller than x have already been assigned, returns the best lower bound for x using the given partial assignment and inequality constraints where x is the maximal variable.

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          def Lean.Meta.Grind.Arith.Linear.getBestUpper? (x : Var) :
          LinearM (Option (Rat × IneqCnstr))

          Assuming all variables smaller than x have already been assigned, returns the best upper bound for x using the given partial assignment and inequality constraints where x is the maximal variable.

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            def Lean.Meta.Grind.Arith.Linear.getDiseqValues (x : Var) :
            LinearM (Array (Rat × DiseqCnstr))

            Returns values we cannot assign x because of disequality constraints.

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              def Lean.Meta.Grind.Arith.Linear.findDiseq? (v : Rat) (dvals : Array (Rat × DiseqCnstr)) :
              Option DiseqCnstr
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                def Lean.Meta.Grind.Arith.Linear.inDiseqValues (v : Rat) (dvals : Array (Rat × DiseqCnstr)) :
                Bool
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                  partial def Lean.Meta.Grind.Arith.Linear.geAvoiding (v : Rat) (dvals : Array (Rat × DiseqCnstr)) :
                  Rat
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                  partial def Lean.Meta.Grind.Arith.Linear.leAvoiding (v : Rat) (dvals : Array (Rat × DiseqCnstr)) :
                  Rat
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                  def Lean.Meta.Grind.Arith.Linear.resolveLowerUpperConflict (c₁ c₂ : IneqCnstr) :
                  LinearM Unit
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                    def Lean.Meta.Grind.Arith.Linear.findInt? (lower : Rat) (lowerStrict : Bool) (upper : Rat) (upperStrict : Bool) (dvals : Array (Rat × DiseqCnstr)) :
                    Option Rat

                    Try to find integer between lower and upper bounds that is different for known disequalities

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                      partial def Lean.Meta.Grind.Arith.Linear.findRat (lower upper : Rat) (dvals : Array (Rat × DiseqCnstr)) :
                      Rat

                      Find rational value in the interval (lower, upper) that is different from all known disequalities.

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                      def Lean.Meta.Grind.Arith.Linear.DiseqCnstr.split (c : DiseqCnstr) :
                      SearchM IneqCnstr
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                        def Lean.Meta.Grind.Arith.Linear.resolveLowerDiseqConflict (c₁ : IneqCnstr) (c : DiseqCnstr) :
                        SearchM Unit

                        Given an inequality c₁ which is a lower bound, i.e., leading coefficient is negative, and a disequality c, splits c and resolve with c₁.

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                          def Lean.Meta.Grind.Arith.Linear.processVar (x : Var) :
                          SearchM Unit
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                            def Lean.Meta.Grind.Arith.Linear.hasAssignment :
                            LinearM Bool

                            Returns true if we already have a complete assignment / model.

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                              def Lean.Meta.Grind.Arith.Linear.resolveConflict (h : UnsatProof) :
                              SearchM Unit
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                                def Lean.Meta.Grind.Arith.Linear.check :
                                GoalM Bool

                                Returns true if work/progress has been done. There are two kinds of progress:

                                • An assignment for satisfying constraints was constructed.
                                • An inconsistency was detected.

                                The result is false if module for every structure already has an assignment.

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