Answers

Here are the answers to this chapter’s questions:

1. A lens is a first-class data accessor. In its standard form, it focuses on a particular field in a data structure and allows you to both retrieve and modify the value of that field.

   Packages such as lens and microlens use the following function-based representation for (monomorphic) lenses:

   type Lens' s v =
     forall f. Functor f => (v -> f v) -> (s -> f s)

   Here, the s type parameter denotes the source type (the data structure) and the v parameter denotes the view type (the field).

   A key property that makes working with lenses convenient is that they compose. The preceding function-based representation lens composition is simply function composition, (.).

2. A polymorphic lens is a lens that allows you to modify the value of a view in a way that changes its type, from v to w. As a consequence, the type of the source changes as well, from s to t.

   Packages such as lens and microlens use the...