Copyright	(c) Andrey Mokhov 2016-2018
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 Source #

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

Bounded Alphabet Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods minBound :: Alphabet # maxBound :: Alphabet #
Enum Alphabet Source #
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] #
Eq Alphabet Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods (==) :: Alphabet -> Alphabet -> Bool # (/=) :: Alphabet -> Alphabet -> Bool #
Ord Alphabet Source #
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 #
Show Alphabet Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods showsPrec :: Int -> Alphabet -> ShowS # show :: Alphabet -> String # showList :: [Alphabet] -> ShowS #

data State Source #

The state of the order.

Constructors

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

Instances

Bounded State Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods minBound :: State # maxBound :: State #
Enum State Source #
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] #
Eq State Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods (==) :: State -> State -> Bool # (/=) :: State -> State -> Bool #
Ord State Source #
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 #
Show State Source #
Instance details Defined in Algebra.Graph.Labelled.Example.Automaton Methods showsPrec :: Int -> State -> ShowS # show :: State -> String # showList :: [State] -> ShowS #

coffeeTeaAutomaton :: Automaton Alphabet State Source #

An example automaton for ordering coffee or tea.

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

reachability :: Map State [State] Source #

The map of State reachability.

reachability = Map.fromList $ map (s -> (s, reachable s order)) [Choice ..]

Or, when evaluated:

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