[Haskell-cafe] MonadPlus and Alternative folds

[Tom Ellis]

On Sat, Sep 19, 2015 at 06:13:18PM +0100, Tom Ellis wrote:
> On Sat, Sep 19, 2015 at 01:25:00AM -0400, David Feuer wrote:
> > It kind of seems like there should be fold-like things to match some and
> > many.
> > 
> > foldrAlt :: Alternative f => (a -> b -> b) -> b -> f a -> f b
> > foldrAlt c n m = foldr1Alt c n m <|> pure n
> > 
> > foldr1Alt :: Alternative f => (a -> b -> b) -> b -> f a -> f b
> > foldr1Alt c n m = c <$> m <*> foldrAlt c n m
> [...]
> 
> An Alternative allows list-like behaviour when it comes to *construction*,
> but offers no operation analogous to pattern-matching and therefore doesn't
> allow you to look inside it or do any sort of *destruction*.
> 
> I tried foldrAlt and it looped forever, as I expected.  I also expect the
> others to loop forever.

I now understand this can work for some Alternatives.  The operational reading
is

1. Try to read an a
2. If it fails, return the b
3. If it succeeds, update the b
4. Go to 1

However, since it doesn't work even for an Alternative as simple as Maybe
it's worth thinking about what class of Alternatives we really want it to
apply to.

Tom