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Scala Type Level Programming: The Natural Numbers: Addition
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sealed trait Nat { | |
type half <: Nat | |
type add[That <: Nat] <: Nat | |
// TODO: Better name | |
type coreT[That <: Nat] <: Nat | |
} | |
sealed trait MsbZero extends Nat { | |
override type half = MsbZero | |
override type add[That <: Nat] = That | |
override type coreT[That <: Nat] = B0[That] | |
} | |
sealed trait MsbOne extends Nat { | |
override type half = MsbZero | |
override type add[That <: Nat] = That#inc | |
override type coreT[That <: Nat] = B1[That] | |
} | |
sealed trait B0[HigherBits <: Nat] extends Nat { | |
override type half = HigherBits | |
override type add[That <: Nat] = That#coreT[That#half#add[HigherBits]] | |
override type coreT[That <: Nat] = B0[That] | |
} | |
sealed trait B1[HigherBits <: Nat] extends Nat { | |
override type half = HigherBits | |
override type add[That <: Nat] = That#inc#coreT[That#inc#half#add[HigherBits]] | |
override type coreT[That <: Nat] = B1[That] | |
} |
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