I would like write a function which turns a function (a -> b) into a function (s -> t) with the help of a Lens s t a b (edit: I realised that this function already exists with Setter s t a b and is called over or %~, but it doesn't answer the question below of using a Lens to get a value). It seems simple, but I'm getting a confusing type error. To make an even more minimal example, consider the following function which simply returns the value extracted from the second argument by the lens:
f :: Lens s t a b -> s -> a
f l s = s ^. l
This doesn't compile. There are 2 errors, both in the second argument of ^. (namely l):
However, the following compiles:
f :: Getter s a -> s -> a
f l s = s ^. l
Then, I realised that in the hierarchy of lens types, the arrow between Lens and Getter specifies s=t, a=b. Is there no way to use a general Lens s t a b to get a value of type a from a value of type s?
The problem with using ^. isn't its implementation, but its type signature. If we lift its definition, we can use it for f:
f :: Lens s t a b -> s -> a
f l s = getConst $ l Const s
This is most easily understood if you expand the definition of Lens : forall (f :: * -> *). Functor f => (a -> f b) -> s -> f t.