Wrapper newtype for the whole family of optics.

The first parameter k identifies the particular optic kind (e.g. A_Lens or A_Traversal).

The parameter is is a list of types available as indices. This will typically be NoIx for unindexed optics, or WithIx for optics with a single index. See the "Indexed optics" section of the overview documentation in the Optics module of the main optics package for more details.

The parameters s and t represent the "big" structure, whereas a and b represent the "small" structure.

Common special case of Optic where source and target types are equal.

Here, we need only one "big" and one "small" type. For lenses, this means that in the restricted form we cannot do type-changing updates.

Explicit cast from one optic flavour to another.

The resulting optic kind is given in the first type argument, so you can use TypeApplications to set it. For example

 castOptic @A_Lens o

turns o into a Lens.

This is the identity function, modulo some constraint jiggery-pokery.

Subtyping relationship between kinds of optics.

An instance of Is k l means that any Optic k can be used as an Optic l. For example, we have an Is A_Lens A_Traversal instance, but not Is A_Traversal A_Lens.

This class needs instances for all possible combinations of tags.

Computes the least upper bound of two optics kinds.

Join k l represents the least upper bound of an Optic k and an Optic l. This means in particular that composition of an Optic k and an Optic k will yield an Optic (Join k l).

Compose two optics of compatible flavours.

Returns an optic of the appropriate supertype. If either or both optics are indexed, the composition preserves all the indices.

Compose two optics of the same flavour.

Normally you can simply use (%) instead, but this may be useful to help type inference if the type of one of the optics is otherwise under-constrained.

Flipped function application, specialised to optics and binding tightly.

Useful for post-composing optics transformations:

>>> toListOf (ifolded %& ifiltered (\i s -> length s <= i)) ["", "a","abc"]
["","a"]

An alias for an empty index-list

Singleton index list

Append two type-level lists together.

Check whether a list of indices is not empty and generate sensible error message if it's not.

Generate sensible error messages in case a user tries to pass either an unindexed optic or indexed optic with unflattened indices where indexed optic with a single index is expected.

Show useful error message when a function expects optics without indices.

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

Flipped version of <$>.

(<&>) = flip fmap

Examples

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0