On Sat, Feb 11, 2017 at 21:04, David Menendez wrote:
On Fri, Feb 10, 2017 at 7:53 PM, Anthony Clayden wrote:
Certainly (.) for lenses works 'backwards' (i.e. suffix style) compared to function-prefix style. (As any Lens tutorial will say.)
Those tutorials are oversimplifying.
Thank you David, ho hum I'm not getting much feedback about ecosystem/ co-existence; nor a specialised composition operator.
Lenses (and their relatives) transform operations, not values.
So it must be a stubborn superstition on my part that getting/putting from/to structures is about values. I'm not here to 'knock' lenses (of whichever model), but every time I scratch the surface, the answers wander off into category theory and higher-order types. I'll draw a comparison with another place in Haskell where category theory has huge benefits: monads. There's less than a handful of operators for monads, and those are conveniently handled behind some elegant syntactic sugar (do-notation). So a newbie doesn't really need to grok monads. They can get on and use them; learn the theory later. Can that be said of lenses? I guess part of the trouble is that H98 record operations have gobbled up so much of the syntactic design space. Nevertheless I don't see what syntactic sugar could help with lenses.
Composition of lenses is exactly like composition of functions, with the inner-most operation on the right.
That doesn't seem to say more than "it's composition". If I want to get a foo out of a bar out of a baz in a s, I'd (perhaps naievely) go foo (bar (baz s)) -- i.e. (foo . bar . baz) s And I'm using function application all the way through. I'd only think of doing s.baz.bar.foo If I was trying to mimic OO style methods. And anyway with lenses, that's exactly what I _can't_ do. Lenses do not use function application of the lens to the structure. You need an extra operator (view, over). Then I'm not seeing the syntactic merit of using composition (.) for lenses. It's certainly making the mental machinery incompatible for lenses vs records, even if they can co-exist semantically.
A lens foo :: Lens O I transforms an operation on I into an operation on O. A composition outer.inner turns an operation on the target of inner into an operation on the source of outer.
This is demonstrated by the way over distributes with (.):
over (outer . inner) = over outer . over inner
What confuses people is view, which is contravariant:
view (outer . inner) = view inner . view outer
but you can't avoid having one of over and view be contravariant.
OK. (Why did it need so much category theory to explain that?) And why do those nifty equivalences have to intrude so much into the surface syntax, just to get a value out of a structure? AntC