# Proposal: add a foldable law

Gershom B gershomb at gmail.com
Sat May 5 22:13:51 UTC 2018

```Hmm… I think this works, and specifies the same law. Nice. Assuming I’m not wrong about that, I’m happy with either version, and will leave it to the committee to decide.

Best,
Gershom

On May 5, 2018 at 5:18:29 PM, David Feuer (david.feuer at gmail.com) wrote:

Let me take that back. Injectivity is necessary. And I meant

foldMap @t f = foldMapDefault f . toTrav

On Sat, May 5, 2018, 5:11 PM David Feuer <david.feuer at gmail.com> wrote:
Actually, requiring injectivity shouldn't be necessary.

On Sat, May 5, 2018, 5:09 PM David Feuer <david.feuer at gmail.com> wrote:
I have another idea that might be worth considering. I think it's a lot simpler than yours.

Law: If t is a Foldable instance, then there must exist:

1. A Traversable instance u and
2. An injective function
toTrav :: t a -> u a

Such that

foldMap @t = foldMapDefault . toTrav

I'm pretty sure this gets at the point you're trying to make.

On May 3, 2018 11:58 AM, "Gershom B" <gershomb at gmail.com> wrote:
This came up before (see the prior thread):

The thread at that time grew rather large, and only at the end did I
come up with what I continue to think is a satisfactory formulation of
the law.

However, at that point nobody really acted to do anything about it.

I would like to _formally request that the core libraries committee
review_ the final version of the law as proposed, for addition to
Foldable documentation:

==
Given a fresh newtype GenericSet = GenericSet Integer deriving (Eq,
Ord), where GenericSet is otherwise fully abstract:

forall (g :: forall a. f a -> Maybe a), (x :: f GenericSet).
maybe True (`Foldable.elem` x) (g x) =/= False
==

The intuition is: "there is no general way to get an `a` out of `f a`
which cannot be seen by the `Foldable` instance". The use of
`GenericSet` is to handle the case of GADTs, since even parametric
polymorphic functions on them may at given _already known_ types have
specific behaviors.

This law also works over infinite structures.

It rules out "obviously wrong" instances and accepts all the instances
we want to that I am aware of.

My specific motivation for raising this again is that I am rather
tired of people saying "well, Foldable has no laws, and it is in base,
so things without laws are just fine." Foldable does a have a law we
all know to obey. It just has been rather tricky to state. The above
provides a decent way to state it. So we should state it.

Cheers,
Gershom
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