[Haskell-cafe] Data.Foldable.all and empty list

[Kim-Ee Yeoh]

On Wed, Sep 30, 2015 at 4:33 AM, Lana Black <lanablack at amok.cc> wrote:

> Is there any particular reason why the 'all' function returns True when
> supplied with an empty list (or any other foldable)? I'm aware that it
> is implemented via All monoid instance, my question is whether this
> behaviour is intentional or it can be considered a bug.
>

Hi Lana, this is a good question, variants of which are actually asked
quite often.

The function 'all' has type signature (a -> Bool) -> [a] -> Bool.

Given a list of as that's split arbitrarily into bs and cs such that as ==
bs ++ cs,
'all' has the property that: all p as == all p bs && all p cs, for any
boolean predicate p.

So if bs or cs is the empty list, the property forces all f [] == True.

For a similar Q&A on related functions, see

https://groups.google.com/forum/#!msg/elm-discuss/sPS98RnV0Og/dSddTp8VXYcJ

-- Kim-Ee
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