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object Naturals {
trait NAT {
type a[s[_ <: NAT] <: NAT, z <: NAT] <: NAT
type v = a[SUCC, ZERO]
}
final class ZERO extends NAT {
type a[s[_ <: NAT] <: NAT, z <: NAT] = z
}
final class SUCC[n <: NAT] extends NAT {
type a[s[_ <: NAT] <: NAT, z <: NAT] = s[n#a[s, z]]
}
type _0 = ZERO
type _1 = SUCC[_0]
type _2 = SUCC[_1]
type _3 = SUCC[_2]
type _4 = SUCC[_3]
type _5 = SUCC[_4]
type _6 = SUCC[_5]
// crashes scala-2.8.0 beta1
trait MUL[n <: NAT, m <: NAT] extends NAT {
trait curry[n[_[_], _], s[_]] { type f[z <: NAT] = n[s, z] }
type a[s[_ <: NAT] <: NAT, z <: NAT] = n#a[curry[m#a, s]#f, z]
}
}
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