Lazy vectors of 1s and 0s

[jlperla]

This is a placeholder issue with the hope of implementing something like https://discourse.julialang.org/t/possibility-of-a-generically-sized-vector-of-1s-and-0s-similar-to-the-uniformscalingoperator-in-juila-v0-7/10297

In order to have the bold 1 notation, JuliaLang/julia#26808 would be required, but that can wait.

Any thoughts on what the vector of 1s and the vector of 0s should be called?

[dlfivefifty]

Here’s a thought along the same lines as InfiniteArrays.jl:

struct UnknownSize <: Number end

Ones(UnknownSize())

[jlperla]

Sounds good to me. When I find an RA who I want to play around with an implementation, I will tell her or him to look at the dispatching in InfiniteArrays.jl as a starting point.

Do you think it is useful to try to push a PR for JuliaLang/julia#26808 ? I am not sure what is involved, but I suspect it is not a huge amount of work... the problem is getting someone who knows Scheme might be tricky.

[dlfivefifty]

I think making that PR happen is a good idea, though I'm not able to do it so I'll leave it to you.

Note InfiniteArrays.jl is Julia v0.7 only, so it might be wise to wait for UnknownSize as well.

What do you think of a unicode synonym, like Ones(⍰) or Ones(❓)?

[jlperla]

Yeah, I think it may make sense to target v0.7 then. I wouldn't want to teach with this until the fall anyways. I will try to figure out a way to get the PR for the unicode in the next few months.

I am not sure about using ⍰ = UnknownSize() I like unicode symbols when they clearly represent concise mathematical notation, but I think it may be confusing when it doesn't. But I don't have a very strong opinion.

If we were able to go

const 𝟏 = Ones(UnknownSize())
const 𝟎 = Zeros(UnknownSize())

then I think that may be sufficient for now.

[jlperla]

cc: @arnavsood and @Nosferican
Here is the issue I mentioned, which is intended to implement that discourse discussion. The plan is to chip away at this (as a v0.7 only solution)

• Use https://github.com/JuliaApproximation/InfiniteArrays.jl and https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/uniformscaling.jl as a starting point
• Add tests to https://github.com/JuliaArrays/FillArrays.jl/blob/master/test/runtests.jl perhaps using https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/test/uniformscaling.jl for some inspiration
• Call it Ones(UnknownSize()) and Zeros(UnknownSize()) as discussed here, where you can dispatch on the UnknownSize structure.
• Start off with test cases and implementation of these as column vectors only. That would get us through some of the key examples in the lecture notes.
• Separately we will figure out the unicode change to julia's parsing.