69 lines
2.7 KiB
Markdown
69 lines
2.7 KiB
Markdown
# Let's Lens
|
|
|
|
|
|
|
|
### Abstract
|
|
|
|
Let's Lens presents a series of exercises, in a similar format to
|
|
[the NICTA functional programming course material](http://github.com/NICTA/course).
|
|
The subject of the exercises is around the concept of lenses, initially proposed
|
|
by Foster et al., to solve the view-update problem of relational databases.
|
|
|
|
The theories around lenses have been advanced significantly in recent years,
|
|
resulting in a library, implemented in Haskell, called `lens`.
|
|
|
|
http://hackage.haskell.org/package/lens
|
|
|
|
The exercises take into account various possible goals. For example, if you wish
|
|
to study the history of lenses, then build up to the most recent theories, it is
|
|
best to start at the `Lets.GetSetLens` module. If you wish to derive the
|
|
structure of lenses from first principles, then derive the more modern theories,
|
|
start at the `Lets.Lens.Lens` module.
|
|
|
|
Exercises can be recognised by filling in a function body that has a placeholder
|
|
of `error "todo: <function-name>"`.
|
|
|
|
----
|
|
|
|
### Exercise modules
|
|
|
|
##### `Lets.GetSetLens`
|
|
|
|
This module presents a series of exercises, representing lenses as a traditional
|
|
pair of "`get` and `set`" functions. This representation may be beneficial as it
|
|
easily appeals to an intuition of "what a lens is", however, it is outdated.
|
|
|
|
These exercises are useful to gain an initial understanding of the problems that
|
|
lenses solve, as well as to gain an insight into the history of lenses and how
|
|
the theories have developed over time.
|
|
|
|
##### `Lets.StoreLens`
|
|
|
|
This series of exercises is similar to `Lets.GetSetLens`, however, using a
|
|
slightly altered representation of a lens, based on the `Store` comonad, which
|
|
fuses the typical `get` and `set` operations into a data structure. This
|
|
representation is described in detail in
|
|
*Morris, Tony. "Asymmetric Lenses in Scala." (2012).*
|
|
|
|
##### `Lets.OpticPolyLens`
|
|
|
|
This series of exercises introduces a new representation of lenses, first
|
|
described by Twan van Laarhoven. This representation also introduces a
|
|
generalisation of lenses to permit *polymorphic update* of structures.
|
|
|
|
##### `Lets.Lens.Lens`
|
|
|
|
This series of exercises starts at first principles to derive the concept of a
|
|
lens, as it was first described by Twan van Laarhoven. The derivation then goes
|
|
on to described other structures to solve various practical problems such as
|
|
*multi-update* and *partial update*.
|
|
|
|
This representation presents a generalisation, permitting *polymorphic update*
|
|
over structures. After lenses are derived, further concepts are introduced, such
|
|
as `Fold`s, `Traversal`s and `Prism`s.
|
|
|
|
----
|
|
|
|
### Credits
|
|
|
|
* Edward Kmett on the [derivation of lenses](https://github.com/ekmett/lens/wiki/Derivation)
|