{-# LANGUAGE TypeFamilies #-}
-----------------------------------------------------------------------------
-- |
-- Module     : Algebra.Graph.Labelled.Example.Network
-- Copyright  : (c) Andrey Mokhov 2016-2022
-- License    : MIT (see the file LICENSE)
-- Maintainer : andrey.mokhov@gmail.com
-- Stability  : experimental
--
-- __Alga__ is a library for algebraic construction and manipulation of graphs
-- in Haskell. See <https://github.com/snowleopard/alga-paper this paper> for the
-- motivation behind the library, the underlying theory, and implementation details.
--
-- This module contains a simple example of using edge-labelled graphs defined
-- in the module "Algebra.Graph.Labelled" for working with networks, i.e. graphs
-- whose edges are labelled with distances.
-----------------------------------------------------------------------------
module Algebra.Graph.Labelled.Example.Network where

import Algebra.Graph.Labelled

-- | Our example networks have /cities/ as vertices.
data City = Aberdeen
          | Edinburgh
          | Glasgow
          | London
          | Newcastle
          deriving (City
City -> City -> Bounded City
forall a. a -> a -> Bounded a
$cminBound :: City
minBound :: City
$cmaxBound :: City
maxBound :: City
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City -> Int
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forall a.
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showsPrec :: Int -> City -> ShowS
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Show)

-- | For simplicity we measure /journey times/ in integer number of minutes.
type JourneyTime = Int

-- | A part of the EastCoast train network between 'Aberdeen' and 'London'.
--
-- @
-- eastCoast = 'overlays' [ 'Aberdeen'  '-<'&#49;50'>-' 'Edinburgh'
--                      , 'Edinburgh' '-<' 90'>-' 'Newcastle'
--                      , 'Newcastle' '-<'&#49;70'>-' 'London' ]
-- @
eastCoast :: Network JourneyTime City
eastCoast :: Network Int City
eastCoast = [Network Int City] -> Network Int City
forall e a. Monoid e => [Graph e a] -> Graph e a
overlays [ City
Aberdeen  City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-<Distance Int
150(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
Edinburgh
                     , City
Edinburgh City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-< Distance Int
90(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
Newcastle
                     , City
Newcastle City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-<Distance Int
170(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
London ]

-- | A part of the ScotRail train network between 'Aberdeen' and 'Glasgow'.
--
-- @
-- scotRail = 'overlays' [ 'Aberdeen'  '-<'&#49;40'>-' 'Edinburgh'
--                     , 'Edinburgh' '-<' 50'>-' 'Glasgow'
--                     , 'Edinburgh' '-<' 70'>-' 'Glasgow' ]
-- @
scotRail :: Network JourneyTime City
scotRail :: Network Int City
scotRail = [Network Int City] -> Network Int City
forall e a. Monoid e => [Graph e a] -> Graph e a
overlays [ City
Aberdeen  City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-<Distance Int
140(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
Edinburgh
                    , City
Edinburgh City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-< Distance Int
50(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
Glasgow
                    , City
Edinburgh City -> Distance Int -> (City, Distance Int)
forall a e. a -> e -> (a, e)
-< Distance Int
70(City, Distance Int) -> City -> Network Int City
forall a e. (a, e) -> a -> Graph e a
>- City
Glasgow ]

-- TODO: Add an illustration.
-- | An example train network.
--
-- @
-- network = 'overlay' 'scotRail' 'eastCoast'
-- @
network :: Network JourneyTime City
network :: Network Int City
network = Network Int City -> Network Int City -> Network Int City
forall e a. Monoid e => Graph e a -> Graph e a -> Graph e a
overlay Network Int City
scotRail Network Int City
eastCoast