Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Lens
type Lens s t a b = forall (f :: * -> *). Functor f => (a -> f b) -> s -> f t #
A Lens
is actually a lens family as described in
http://comonad.com/reader/2012/mirrored-lenses/.
With great power comes great responsibility and a Lens
is subject to the
three common sense Lens
laws:
1) You get back what you put in:
view
l (set
l v s) ≡ v
2) Putting back what you got doesn't change anything:
set
l (view
l s) s ≡ s
3) Setting twice is the same as setting once:
set
l v' (set
l v s) ≡set
l v' s
These laws are strong enough that the 4 type parameters of a Lens
cannot
vary fully independently. For more on how they interact, read the "Why is
it a Lens Family?" section of
http://comonad.com/reader/2012/mirrored-lenses/.
There are some emergent properties of these laws:
1)
must be injective for every set
l ss
This is a consequence of law #1
2)
must be surjective, because of law #2, which indicates that it is possible to obtain any set
lv
from some s
such that set
s v = s
3) Given just the first two laws you can prove a weaker form of law #3 where the values v
that you are setting match:
set
l v (set
l v s) ≡set
l v s
Every Lens
can be used directly as a Setter
or Traversal
.
You can also use a Lens
for Getting
as if it were a
Fold
or Getter
.
Since every Lens
is a valid Traversal
, the
Traversal
laws are required of any Lens
you create:
lpure
≡pure
fmap
(l f).
l g ≡getCompose
.
l (Compose
.
fmap
f.
g)
typeLens
s t a b = forall f.Functor
f =>LensLike
f s t a b