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| 1 | + |
| 2 | +trait Nat |
| 3 | +case object Z extends Nat |
| 4 | +case class S[N <: Nat](pred: N) extends Nat |
| 5 | + |
| 6 | +type Z = Z.type |
| 7 | +given zero: Z = Z |
| 8 | +given succ[N <: Nat](using n: N): S[N] = S(n) |
| 9 | + |
| 10 | +case class Sum[N <: Nat, M <: Nat, R <: Nat](result: R) |
| 11 | + |
| 12 | +given sumZ[N <: Nat](using n: N): Sum[Z, N, N] = Sum(n) |
| 13 | +given sumS[N <: Nat, M <: Nat, R <: Nat]( |
| 14 | + using sum: Sum[N, M, R] |
| 15 | +): Sum[S[N], M, S[R]] = Sum(S(sum.result)) |
| 16 | + |
| 17 | +def add[N <: Nat, M <: Nat, R <: Nat](n: N, m: M)( |
| 18 | + using sum: Sum[N, M, R] |
| 19 | +): R = sum.result |
| 20 | + |
| 21 | +case class Prod[N <: Nat, M <: Nat, R <: Nat](result: R) |
| 22 | + |
| 23 | + |
| 24 | +@main def Test: Unit = |
| 25 | + |
| 26 | + val n1: S[Z] = add(Z, S(Z)) |
| 27 | + summon[n1.type <:< S[Z]] // OK |
| 28 | + |
| 29 | + val n3: S[S[S[Z]]] = add(S(S(Z)), S(Z)) |
| 30 | + summon[n3.type <:< S[S[S[Z]]]] // Ok |
| 31 | + |
| 32 | + val m3_2 = add(S(Z), S(S(Z))) |
| 33 | + summon[m3_2.type <:< S[S[S[Z]]]] // Error before changes: Cannot prove that (m3_2 : S[S[Nat]]) <:< S[S[S[Z]]] |
| 34 | + |
| 35 | + val m4_2 = add(S(Z), S(S(S(Z)))) |
| 36 | + summon[m4_2.type <:< S[S[S[S[Z]]]]] |
| 37 | + |
| 38 | + |
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