Modulealgebraic-graphs-0.8Haskell2010

Algebra.Graph.Labelled.Example.Automaton

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
data State
value coffeeTeaAutomaton
value reachability

Packagealgebraic-graphs-0.8
Exports4
LanguageHaskell2010
LicenceMIT
SourceAutomaton.hs

datadata 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

Instances5Bounded, Enum, Eq, Ord, Show

Bounded AlphabetDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Enum AlphabetDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Eq AlphabetDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Ord AlphabetDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Show AlphabetDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton

datadata State

Source#

The state of the order.

Constructors

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

Instances5Bounded, Enum, Eq, Ord, Show

Bounded StateDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Enum StateDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Eq StateDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Ord StateDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton
Show StateDefined in algebraic-graphs-0.8 · Algebra.Graph.Labelled.Example.Automaton

valuecoffeeTeaAutomaton :: Automaton Alphabet State

Source#

An example automaton for ordering coffee or tea.

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

valuereachability :: Map State [State]

Source#

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                   ]) ]