Copyright | (c) Tom Harding 2020 |
---|---|

License | MIT |

Safe Haskell | Safe |

Language | Haskell2010 |

Simplistically, search problems are solved by running the computation with different input combinations, looking for any combinations that satisfy the constraints. In reality, we play some tricks to avoid running every possible input combination, but the principle is the same:

This module exposes the `Config`

type, which stores an initial assignment for
the input parameters (typically something close to `mempty`

), and a function
that generates possible refinements for those inputs.

For example, we might have a variable we know must be a number between `1`

and
`10`

. A good initial value for this might be a `mempty`

value such as
`Unknown`

, with the refinements being `Exactly`

the ten possible values.

The initial values are first fed into the computation *before* the propagators
are established. Sometimes, these initial propagators can produce new
information (such as advancing a few steps forward in a sudoku puzzle) before
we even start to refine the inputs. The benefit here is that we can sometimes
discover that a variable's search space is smaller than we realise, and so we
end up with much less work to do!

# Documentation

data Config (m :: Type -> Type) (x :: Type) Source #

An input configuration.

This stores both an `initial`

configuration of input parameters, as well as
a function that can look for ways to `refine`

an input. In other words, if
the initial value is an Data.JoinSemilattice.Intersect of `[1 .. 5]`

, the
refinements might be `singleton`

values of
every remaining possibility.

class Input (x :: Type) where Source #

The simplest way of generating an input configuration is to say that a
problem has `m`

variables that will all be one of `n`

possible values. For
example, a sudoku board is `81`

variables of `9`

possible values. This class
allows us to generate these simple input configurations like a game of
countdown: "`81`

from `1 .. 9`

, please, Carol!"

Different parameter types will have different representations for their
values. The `Raw`

type means that I can say `81 `

, and have
the parameter type determine how it will represent `from`

[1 .. 9]`1`

, for example. It's
a little bit of syntactic sugar for the benefit of the user, so they don't
need to know as much about how the parameter types work to use the
library.