Structuring Arrays with Algebraic Shapes [video] | Hacker News Reader

Structuring Arrays with Algebraic Shapes [video]

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41 pointssurprisetalk2 comments

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.

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

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