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FloatLib.Numerics.Representations.Boolean.Arithmetic

Executable Boolean numerical operations #

Boolean masks use their native Bool carrier. These definitions are direct inline operations, and their contracts expose the same functions through the representation-independent numerical API.

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@[inline]
def FloatLib.Numerics.Representations.Boolean.not (value : Bool) :
Bool

Boolean negation.

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    @[inline]
    def FloatLib.Numerics.Representations.Boolean.and (left right : Bool) :
    Bool

    Boolean conjunction.

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      @[inline]
      def FloatLib.Numerics.Representations.Boolean.or (left right : Bool) :
      Bool

      Boolean disjunction.

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        @[inline]
        def FloatLib.Numerics.Representations.Boolean.xor (left right : Bool) :
        Bool

        Boolean exclusive disjunction.

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          theorem FloatLib.Numerics.Representations.Boolean.not_refines :
          Operation.Finite1 numericalSystem numericalSystem not fun (x : numericalSystem.Scalar) => !x

          Native Boolean negation has exact Boolean semantics.

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          theorem FloatLib.Numerics.Representations.Boolean.and_refines :
          Operation.Finite2 numericalSystem numericalSystem numericalSystem and fun (x1 x2 : numericalSystem.Scalar) => x1 && x2

          Native Boolean conjunction has exact Boolean semantics.

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          theorem FloatLib.Numerics.Representations.Boolean.or_refines :
          Operation.Finite2 numericalSystem numericalSystem numericalSystem or fun (x1 x2 : numericalSystem.Scalar) => x1 || x2

          Native Boolean disjunction has exact Boolean semantics.

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          theorem FloatLib.Numerics.Representations.Boolean.xor_refines :
          Operation.Finite2 numericalSystem numericalSystem numericalSystem xor Bool.xor

          Native Boolean exclusive disjunction has exact Boolean semantics.