3 ms·

Assuming non-fixed width integers, how can you have an infinite sum type?

• tel 7y ago
  There’s nothing wrong with an infinite sum, in principle. You can’t usually define them unless you can use recursion. In the case of integers you can do data Int = Positive Nat | Negative Nat data Nat = Zero | Succ Nat
  • jolmg 7y ago
    Though, that has 2 zeros, a positive and a negative one, but zero should be neither. To avoid that, you can do: data Int = Zero | NonZero Sign PositiveInt data PositiveInt = One | Succ PositiveInt data Sign = Positive | Negative
    • tel 7y ago
      Good point.
• arianvanp 7y ago
  You can't. The Natural number definition combines a sum type with a recursive position. Or in other words, a finite tag (either zero or successors, 2 options) plus a pointer to the next value in the case of successor.