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Not many people on HN mention APL. I programmed in APL professionally for almost ten years and know (knew?) the language well.

It's too late for me to go dig-up this old spreadsheet. Maybe I'll do it tomorrow. Excel does warn you when there are discrepancies between adjoining cells. If I remember correctly this was a cell that was copied down and used on a row. Thinking back I think the formula was entered once but replicated Dow a range of rows.

The problem with the APL comparison is that the language can become less elegant if the operations to be applied across the rows of a matrix are somewhat varied. I'm typing on an iPad right now so I can't even try to give you an APL example. Maybe tomorrow from my PC.

(I remembered your APL experience from some previous HN comment or other.) You're right that spreadsheets tend to be more heterogeneous than a chain of array operators. I'm not suggesting that APL as a language should be integrated into spreadsheets, but rather that there is a way to implement spreadsheet language (formulas and cells) that partially approaches how APL treats computation. This is possible because there is a lot of implicitly array-oriented computation in typical spreadsheets – that's what you're "declaring" when you drag a formula across a range of cells. What would a spreadsheet system be like if it really exploited this? The trick is to do it without breaking too much with the well-established mental model of Excel users.

Excel does have array formulas. Every time I used them I have to look up usage. From memory they work well for matrix transforms and such things. Again, my memory fails me because It's probably been five or more years since I've touched them.

I have a busy day today so I have to stay off HN. I'll look into some of the items requiring deeper answers later tonight or tomorrow.

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