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| 1 | +/* |
| 2 | +sealed trait Nat |
| 3 | +case object Z extends Nat |
| 4 | +case class S[N <: Nat](pred: N) extends Nat |
| 5 | +type Z = Z.type |
| 6 | +
|
| 7 | +given [N <: Nat](using n: N): S[N] = S(n) |
| 8 | +given zero: Z = Z |
| 9 | +
|
| 10 | +case class Sum[N <: Nat, M <: Nat, R <: Nat](r: R) |
| 11 | +
|
| 12 | +given [N <: Nat](using n: N): Sum[Z, N, N] = Sum(n) |
| 13 | +given [N <: Nat, M <: Nat, R <: Nat]( |
| 14 | + using sum: Sum[N, M, R] |
| 15 | +): Sum[S[N], M, S[R]] = Sum(S(sum.r)) |
| 16 | +
|
| 17 | +def add[N <: Nat, M <: Nat, R <: Nat](n: N, m: M)(using sum: Sum[N, M, R]): R = sum.r |
| 18 | +*/ |
| 19 | + |
| 20 | + |
| 21 | +trait Nat |
| 22 | +case object Z extends Nat |
| 23 | +case class S[N <: Nat](pred: N) extends Nat |
| 24 | + |
| 25 | +type Z = Z.type |
| 26 | +given zero: Z = Z |
| 27 | +given succ[N <: Nat](using n: N): S[N] = S(n) |
| 28 | + |
| 29 | +case class Sum[N <: Nat, M <: Nat, R <: Nat](result: R) |
| 30 | + |
| 31 | +given sumZ[N <: Nat](using n: N): Sum[Z, N, N] = Sum(n) |
| 32 | +given sumS[N <: Nat, M <: Nat, R <: Nat]( |
| 33 | + using sum: Sum[N, M, R] |
| 34 | + ): Sum[S[N], M, S[R]] = Sum(S(sum.result)) |
| 35 | + |
| 36 | +def add[N <: Nat, M <: Nat, R <: Nat](n: N, m: M)( |
| 37 | + using sum: Sum[N, M, R] |
| 38 | +): R = sum.result |
| 39 | + |
| 40 | +case class Prod[N <: Nat, M <: Nat, R <: Nat](result: R) |
| 41 | + |
| 42 | + |
| 43 | +@main def Test: Unit = |
| 44 | + |
| 45 | + val n1 = add(Z, S(Z)) |
| 46 | + summon[n1.type <:< S[Z]] |
| 47 | + |
| 48 | + val n3 = add(S(S(Z)), S(Z)) |
| 49 | + summon[n3.type <:< S[S[S[Z]]]] |
| 50 | + |
| 51 | + val n3_2 = add(S(Z), S(S(Z))) |
| 52 | + summon[n3_2.type <:< S[S[S[Z]]]] |
| 53 | + |
| 54 | + |
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