algebraic-graphs-0.7: A library for algebraic graph construction and transformation

Copyright | (c) Andrey Mokhov 2016-2022
License | MIT (see the file LICENSE)
Maintainer | andrey.mokhov@gmail.com
Stability | experimental
Safe Haskell | None
Language | Haskell2010

Algebra.Graph.Labelled.Example.Automaton

Description

Alga is a library for algebraic construction and manipulation of graphs in Haskell. See 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 finite automata.

Synopsis

- data Alphabet
  - = Coffee
  - | Tea
  - | Cancel
  - | Pay
- data State
  - = Choice
  - | Payment
  - | Complete
- coffeeTeaAutomaton :: Automaton Alphabet State
- reachability :: Map State [State]

# Documentation

data Alphabet #

The alphabet of actions for ordering coffee or tea.

Constructors

Coffee | Order coffee
Tea | Order tea
Cancel | Cancel payment or order
Pay | Pay for the order

#### Instances

Instances details

Bounded Alphabet # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods minBound :: Alphabet # maxBound :: Alphabet #
Enum Alphabet # |

Instance details

Defined in Algebra.Graph.Labelled.Example.Automaton

Methods

succ :: Alphabet -> Alphabet #

pred :: Alphabet -> Alphabet #

toEnum :: Int -> Alphabet #

fromEnum :: Alphabet -> Int #

enumFrom :: Alphabet -> [Alphabet] #

enumFromThen :: Alphabet -> Alphabet -> [Alphabet] #

enumFromTo :: Alphabet -> Alphabet -> [Alphabet] #

enumFromThenTo :: Alphabet -> Alphabet -> Alphabet -> [Alphabet] #

Show Alphabet # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods showsPrec :: Int -> Alphabet -> ShowS # show :: Alphabet -> String # showList :: [Alphabet] -> ShowS #
Eq Alphabet # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods (==) :: Alphabet -> Alphabet -> Bool # (/=) :: Alphabet -> Alphabet -> Bool #
Ord Alphabet # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods compare :: Alphabet -> Alphabet -> Ordering # (<) :: Alphabet -> Alphabet -> Bool # (<=) :: Alphabet -> Alphabet -> Bool # (>) :: Alphabet -> Alphabet -> Bool # (>=) :: Alphabet -> Alphabet -> Bool # max :: Alphabet -> Alphabet -> Alphabet # min :: Alphabet -> Alphabet -> Alphabet #

data State #

The state of the order.

Constructors

Choice | Choosing what to order
Payment | Making the payment
Complete | The order is complete

#### Instances

Instances details

Bounded State # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods minBound :: State # maxBound :: State #
Enum State # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods succ :: State -> State # pred :: State -> State # toEnum :: Int -> State # fromEnum :: State -> Int # enumFrom :: State -> [State] # enumFromThen :: State -> State -> [State] # enumFromTo :: State -> State -> [State] # enumFromThenTo :: State -> State -> State -> [State] #
Show State # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods showsPrec :: Int -> State -> ShowS # show :: State -> String # showList :: [State] -> ShowS #
Eq State # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods (==) :: State -> State -> Bool # (/=) :: State -> State -> Bool #
Ord State # |
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods compare :: State -> State -> Ordering # (<) :: State -> State -> Bool # (<=) :: State -> State -> Bool # (>) :: State -> State -> Bool # (>=) :: State -> State -> Bool # max :: State -> State -> State # min :: State -> State -> State #

coffeeTeaAutomaton :: Automaton Alphabet State #

An example automaton for ordering coffee or tea.

    coffeeTeaAutomaton = overlays [ Choice  -<[Coffee, Tea]>- Payment
                                  , Payment -<[Pay        ]>- Complete
                                  , Choice  -<[Cancel     ]>- Complete
                                  , Payment -<[Cancel     ]>- Choice ]

reachability :: Map State [State] #

The map of `State` reachability.

    reachability = Map.fromList $ map (id &&& reachable skeleton) [Choice ..]
      where
        skeleton = emap (Any . not . isZero) coffeeTeaAutomaton

Or, when evaluated:

    reachability = Map.fromList [ (Choice  , [Choice  , Payment, Complete])
                                , (Payment , [Payment , Choice , Complete])
                                , (Complete, [Complete                   ]) ]