Control.Lens.Basic

Basic lens type and functions.

The lens package should be a drop-in replacement for this.

Lens type

type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t

Purpose

A value of type Lens s t a b provides the following:

• A reference into the structure s to read and update the value a inside it.
• The possibility to change the type of s to t and the type of a to b.

The Functor constraint

Operations may do something more interesting inside the f functor. For the purpose of this module and package, all the functions below (view, over, set) use a no-op functor and therefore the above type is equivalent to:

type Lens s t a b = (a -> b) -> (s -> t)

But it is left generic for forward compatibilty with the lens package.

Example

λ> data Person = Person { personChar :: Char, personAge :: Int } deriving Show
λ> view $(field 'personChar) (Person a 10)
a
λ> over $(field 'personAge) (*2) (Person a 10)
Person {personChar = a, personAge = 20}
λ>

Laws

1) Get-Put: You get back what you put in.

view l (set l v s) ≡ v

2) Put-Get: Putting back what you got doesn't change anything.

set l (view l s) s ≡ s

3) Put-Put: Setting is idempotent.

set l v (set l v s) ≡ set l v s

Functions

view :: Lens s t a b -> s -> a

Get the a inside the s.

set :: Lens s t a b -> b -> s -> t

Set the a inside the s, optionally changing the types to b and t.

over :: Lens s t a b -> (a -> b) -> s -> t

Modify the a inside the s, optionally changing the types to b and t.

field :: Name -> Q Exp

Make a lens from a field name.

Example: over $(field 'foo) (*2)