foldl doesn't say it folds head to tail (which would be accurate). It says
it folds from the left ("to the right" is understood... where else are you
going to go from the left?).
I'm not going to quibble over what "left" is, nor what processing something
from the left to right means. If that's not understood between us, then we
don't have enough basis to discuss that aspect.
But I would like to point out that: the fact that it is a source of
confusion only brings to the surface the imprecision of its name.
On Thursday, December 15, 2016 at 1:05:14 PM UTC-6, Janis Voigtländer wrote:
>
> And I do get the mathematically wrong answer on foldl when using
>> mathematically non-associative operations (like subtraction). That's
>> provided we agree on the definition of which side of the list is the "left"
>> side.
>
> Well, still not quite for me. I’m sure we both agree what the “left” side
> of the list is. And still I don’t think there is an argument to make that
> hence Elm’ foldl‘s answer is mathematically wrong. The fact that we agree
> what the left side of the list is does not mean that foldl (-) 0 [1,2,3]
> needs to evaluate to ((0 - 1) - 2) -3. It can evaluate to 3 - (2 - (1 -
> 0)) without us disagreeing what is “left”. In other words, “leftiness” is
> not at issue here. Both ((0 - 1) - 2) -3 and 3 - (2 - (1 - 0)) do work
> “from the left”. They combine elements in the order in which they appear in
> the list *from left to right*. One could argue that the real thing at
> issue here is not what “left” means, but what “folding” means. You take it
> to mean to literally replace :: by (-) and you are only willing to argue
> about how the result is bracketed. But one can take “folding” to simply
> mean that stuff gets accumulated via an operator, and “left folding” then
> means that more-left-sitting elements get accumulated earlier. And Elm’s
> foldl is perfectly mathematically correct according to this meaning.
>
> Of course, that’s back to a point I made already the other day. There’s
> nothing “mathematically wrong” about Elm’s foldl unless one postulates
> “mathematically correct” to mean “ foldl needs to be the specific
> operation it is in Haskell etc.” But that’s not a mathematical argument.
>
>
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