Scala: Lenses 2

Looks like Lenses topic should not be closed without discussing compose method. This method decreases the count of lenses we have to produce. We called it M * N size issue in previous session.
This time it's hard to not jump into function programming math mess, but we will try.

Scala: Lenses 1

If U ever had a task on updating nested immutable structures - U might found it as non-clean code task, especially it's hard to guard solution from colleges :p

There is nice fitting solution coming from function programming theory, that shines in Scala as well.

Intro 

"Lenses are bidirectional transformations between pairs of connected structures. Asymmetric lenses —where one of those two connected structures is taken to be primary —have been extensively studied. Lenses were first proposed to solve the view- update problem of tree-like data structures by Foster et. al and have also been applied to the construction of a relational database query language."

Tony Morris