User talk:⊂⍺m: Difference between revisions

Equivalently from a slightly different angle, if we use the model <syntaxhighlight lang=apl inline>X⊂⍤(f/)⍤g⍤1⍤1 99⊢Y⍉⍨¯1⌽⍳≢⍴Y</syntaxhighlight>, the collapsing of dimensions is due more generally to <syntaxhighlight lang=apl inline>⊂⍤…⍤g⍤1</syntaxhighlight> mapping two vectors to a scalar. Clearly the same holds for <syntaxhighlight lang=apl inline>⊂⍤g⍤1</syntaxhighlight>, i.e., the same expression with the reduction removed.

:Iverson's model may have been more like <syntaxhighlight lang=apl inline>f⌿⍤(1-≢⍴X)⊢ X g⍤¯1⍤1 99⊢ Y</syntaxhighlight>, so that the flat intermediate result does have this extra axis. Maybe with a transpose like your second example, who knows. In a nested APL, <syntaxhighlight lang=apl inline>g¨</syntaxhighlight> should be used instead of <syntaxhighlight lang=apl inline>g</syntaxhighlight>, but I think with this modification it correctly describes the semantics other than maybe evaluation order. I would say even in your examples there is an extra axis, but it's hidden away by a layer of nesting; forcing everything to be flat makes it literally an array axis at some point. --[[User:Marshall|Marshall]] ([[User talk:Marshall|talk]]) 01:05, 26 June 2023 (UTC)

::You’re right, he may have described it in some different way conceptually—after all, the notation for it preceded any implementation. I was trying to save other APL novices the bit of confusion this had caused me, but upon reflection, the description is pretty vague anyway.

:::Yep, I can see how you'd get to that point. Thanks for taking the time to edit, I see lots of improvements! --[[User:Marshall|Marshall]] ([[User talk:Marshall|talk]]) 19:11, 27 June 2023 (UTC)