Let's Lens presents a series of exercises, in a similar format to the Data61 functional programming course material. 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
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
Exercises can be recognised by filling in a function body that has a placeholder
error "todo: <function-name>".
This module presents a series of exercises, representing lenses as a traditional
pair of "
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easily appeals to an intuition of "what a lens is", however, it is outdated.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.
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
set operations into a data structure. This
representation is described in detail in
Morris, Tony. "Asymmetric Lenses in Scala." (2012).
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.
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
- Edward Kmett on the derivation of lenses