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Scala Type Level Programming: The Natural Numbers: First Assertions
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| // 1 = O + 1 | |
| implicitly[MsbOne =:= MsbZero#inc] | |
| // 2 = O + 1 + 1 | |
| implicitly[B0[MsbOne] =:= MsbZero#inc#inc] | |
| // 3 = O + 1 + 1 + 1 | |
| implicitly[B1[MsbOne] =:= MsbZero#inc#inc#inc] | |
| // 4 = O + 1 + 1 + 1 + | |
| implicitly[B0[B0[MsbOne]] =:= MsbZero#inc#inc#inc#inc] | |
| // etc | |
| implicitly[B1[B0[MsbOne]] =:= MsbZero#inc#inc#inc#inc#inc] | |
| implicitly[B0[B1[MsbOne]] =:= MsbZero#inc#inc#inc#inc#inc#inc] | |
| implicitly[B1[B1[MsbOne]] =:= MsbZero#inc#inc#inc#inc#inc#inc#inc] | |
| implicitly[B0[B0[B0[MsbOne]]] =:= MsbZero#inc#inc#inc#inc#inc#inc#inc#inc] | |
| implicitly[B1[B0[B0[MsbOne]]] =:= MsbZero#inc#inc#inc#inc#inc#inc#inc#inc#inc] | |
| // 0 = 0 * 2 | |
| implicitly[MsbZero =:= MsbZero#dbl] | |
| // 2 = 1 * 2 | |
| implicitly[B0[MsbOne] =:= MsbOne#dbl] | |
| // 4 = 2 * 2 | |
| implicitly[B0[B0[MsbOne]] =:= B0[MsbOne]#dbl] | |
| // 6 = 3 * 2 | |
| implicitly[B0[B1[MsbOne]] =:= B1[MsbOne]#dbl] | |
| type T0 = MsbZero | |
| type T1 = T0#inc | |
| type T2 = T1#inc | |
| type T3 = T2#inc | |
| type T4 = T3#inc | |
| type T5 = T4#inc | |
| type T6 = T5#inc | |
| type T7 = T6#inc | |
| type T8 = T7#inc | |
| type T9 = T8#inc | |
| type T10 = T9#inc | |
| type T11 = T10#inc | |
| type T12 = T11#inc | |
| type T13 = T12#inc | |
| type T14 = T13#inc | |
| type T15 = T14#inc | |
| type T16 = T15#inc | |
| type T17 = T16#inc | |
| implicitly[T17 =:= MsbZero#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc#inc] | |
| // 17 = 1 * 2 * 2 * 2 * 1 + 1 | |
| implicitly[T17 =:= MsbOne#dbl#dbl#dbl#dbl#inc] | |
| type T20 = T10#add[T10] | |
| type T27 = T20#add[T7] |
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