scala - How to implement parametric lenses that change type of state -

so in scala have typical lens signature as:

case class lens[o,v](get: o => v, set: (o,v) => o) 

but can see, updates , sets values of same type, not set 1 type another. have in mind more this:

case class lens[o[_],a,b](get: o[a] => a, set: (o[a],b) => o[b]) 

with a , b make sense o[_]my question is. stop being isomorphic? there simpler way without breaking rules?

i think figure out right lens abstraction, helpful have concrete lens-able type in mind.

however, particular example, there can say:

case class lens[o[_],v[_],a,b](get: o[a] => v[a], set: (o[a],v[b]) => o[b]) 

i not think kind of lens can composed. in order compose lenses, result of get has able feed set. here, result of get v[_], whereas set needs o[_].

as further explanation, here possible kind of polymorphic lens, not 1 fits needs:

trait lens[t[_]] {   def get[a](t: t[a]):   def set[a,b](t: t[a], x: b): t[b] } 

it can composed so:

def composelenses[t[_],u[_]](lens1: lens[t], lens2: lens[u]) =    new lens[({type x[a] = t[u[a]]})#x] {     def get[a](t: t[u[a]]): = lens2.get(lens1.get(t))     def set[a,b](t: t[u[a]], x: b): t[u[b]] = lens1.set(t, lens2.set(lens1.get(t), x))   } 

i wouldn't have been able figure out definition of lens abstractly -- in order had use concrete case:

case class box[a](x: a)  def boxboxget[a](b: box[box[a]]): = ??? def boxboxset[a,b](b: box[box[a]], x: b): box[box[b]] = ???