thesz a day ago

Arithmetic inside the types not necessarily introduces undecidability. One example is telescopes for indices:

  data N where
    Z :: N
    O :: N -> N
  data T (n :: N) where
    TZ :: T (O n)
    TO :: T n -> T (O n)
To safely access an element in array you have to provide a proof that a telescope can be constructed for given index range.
  • bgavran a day ago

    Indeed, the author seems to have a misunderstanding about both undecidability and complexity as they pertain to dependent types.

    Dependent types do not add complexity to our system, they reveal it.

    Case in point: here is a fully dependently-typed tensor processing framework written in Idris, which I believe matches most of the desiderata of his talk, capturing even a generalisation of arrays via Naperian functors that is mentioned at one point.

    https://github.com/bgavran/TypeSafe_Tensors