Joachim Breitner

Drawing foldl and foldr

Published 2019-05-02 in sections English, Haskell.

Often, someone wants to exhaling the difference between a left-fold and a right-fold, i.e. foldl and foldr in Haskell, you see a picture like the following

foldl and foldr

foldl and foldr

This is taken from the recently published and very nice “foldilocks” tutorial by Ayman Nadeem, but I have seen similar pictures before.

I always thought that something is not quite right about them, in particular the foldr. I mean, they are correct, and while the foldl one clearly conveys the right intuition, the foldr doesn’t quite: it looks as if the computer would fast forward to the end of the list, and then start processing it. But that does not capture the essence of foldr, which also starts at the beginning of the list, by applying its argument lazily.

And therefore, this is how I would draw this graph:

foldl and foldr

foldl and foldr

This way (at least to people from a left-to-right top-to-bottom culture), it becomes more intuitive that with foldr, you are first looking at an application of the combinator to the first element, and then possibly more.

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