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12:06 AM

@Jeremygee Oh, yeah! The Curry-Howard-Lambek correspondence. Super cool stuff. Have you seen the nLab's article on this? ncatlab.org/nlab/show/computational+trilogy

I actually have some ideas for how we might directly leverage this in APL.

13 hours later…

Adám

1:00 PM

Welcome to APL Quest 2021-9! Today's quest is In the Long Run:

> Write a function that:
> • has a right argument that is a numeric vector of 2 or more elements representing daily prices of a stock.
> • returns an integer singleton that represents the highest number of consecutive days where the price increased, decreased, or remained the same, relative to the previous day.

The hint there is spot-on :-)

mitchell johnstone

This is what I had:⌈/¯2-/⍸1,⍨1,2≠/2×⍤-/⍵

Adám

That is very very good.

Really, my only remark here would be to break out × from the 2-/

mitchell johnstone

That makes sense. It was leftover from when I was trying to make it tacit.

Adám

Even so, you can do 2≠/∘×

There is a shorter, but less efficient solution too.

mitchell johnstone

My original approach was more straightforward: ⌈/∊(+⌿¨⊆⍨)¨↓⍉↑2(=,>,<)/⍵

Adám

1:06 PM

Right.

mitchell johnstone

Is that on the right track for the shorter solution? I couldn't see where to go from here.

Adám

Well, my thing was using ⊆⍨

The rest is basically the same as your good solution.

So, the whole thing I had was {1+⌈/0,≢¨⊆⍨2=/×2-/⍵}

Any other ideas on how to solve this?

I was thinking we could use ⊆ directly, but it'll be hard to map the input to a valid argument.

mitchell johnstone

@Adám I like that! I didn't catch the 2=/ operation on the first pass. And yeah, I couldn't see how to partition the original input well for ⊆.

Adám

Maybe we can use ⊂⍨ instead of ⊆ to avoid adding 1.

mitchell johnstone

{⌈/≢¨⊂⍨1,2≠/×2-/⍵} ?

Adám

1:20 PM

Yes!

I think that's it then. I'll be using your solutions for the video.

Btw, the videos I owe will be released daily at noon.

Then people can intertain themselves with those while I'm busy at the user meeting :-)

See you next week for 2021-10: On the Right Side!

mitchell johnstone

Thanks! There's a video? Also, I saw a similar solution using my original ⍸ approach on APLcart for "Lengths of subvectors of Yv having equal elements". Is the ⊂ approach not listed because it's less optimized?

Adám

Yes, see apl.wiki/APL_Quest and yes, that's why.

mitchell johnstone

Gotcha. Well, thanks @Adám!

Adám

2:15 PM