The optics Haskell package is an alternative to the famous lens package.
lens uses a van Laarhoven encoding, encoding lenses as functions. This means than not only do lens lenses form a category, but they actually compose using standard function composition. In other words, they can compose using the old-fashioned . operator, even before the Category typeclass.
optics, in contrast, defines lenses using opaque newtypes. It should still be possible to get access to composition via the . operator by defining a Category instance. However, optics doesn't do that, but instead defines a new % composition operator. The docs have this to say:
The (.) operator from Control.Category cannot be used to compose optics [..] because it would not support type-changing optics or composing optics of different kinds.
and
optics must use a different composition operator (%). Optic does not quite form a Category, thanks to type-changing optics.
This leaves me very puzzled. It is well known that lens' van Laarhoven lenses do support type-changing (polymorphic update), whilst still being a category by construction, via their underlying function type.
Can someone explain why it's impossible for optics lenses to form a category, even though they are functionally equivalent to van Laarhoven?
Is it possible to define lenses more opaque than lens whilst still forming a lawful category?
