Arithmetic inside the types not necessarily introduces undecidability. One example is telescopes for indices:
To safely access an element in array you have to provide a proof that a telescope can be constructed for given index range.data N where Z :: N O :: N -> N data T (n :: N) where TZ :: T (O n) TO :: T n -> T (O n)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.