basic-lens-0.0.1: Basic lens type and functions

Safe HaskellNone




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 Source #


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.


λ> data Person = Person Char Int deriving Show
λ> let _age f (Person x a) = fmap (\b -> Person x b) (f a)
λ> view _age (Person a 10)
λ> over _age (+1) (Person a 10)
Person a 11
λ> set _age 100 (Person a 10)
Person a 100


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


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

Get the a inside the s.

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

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

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

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