


src  
test  
.ghci  
.gitignore  
changelog  
default.nix  
letslens.cabal  
letslens.nix  
LICENCE  
README.markdown  
Setup.hs  
shell.nix  
stack.yaml 
Let's Lens
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 viewupdate 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
module.
Exercises can be recognised by filling in a function body that has a placeholder
of error "todo: <functionname>"
.
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easily appeals to an intuition of "what a lens is", however, it is outdated.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
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 multiupdate 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