Safe Haskell	Safe-Inferred
Language	Haskell2010

Haal.BlackBox

Description

This module defines the BlackBox type class as well as the Automaton and SUL sub classes.

Synopsis

class SUL (aut s) Identity => Automaton (aut :: Type -> Type -> Type -> Type) s where
- transitions :: (FiniteOrd i, FiniteOrd s) => aut s i o -> Map (s, i) (s, o)
- states :: FiniteOrd s => aut s i o -> Set s
- current :: aut s i o -> s
- update :: aut s i o -> s -> aut s i o
class Monad m => SUL (sul :: Type -> Type -> Type) (m :: Type -> Type) where
- step :: sul i o -> i -> m (sul i o, o)
- reset :: sul i o -> m (sul i o)
type StateID = Int
type Finite i = (Enum i, Bounded i)
type FiniteEq i = (Eq i, Finite i)
type FiniteOrd i = (Ord i, Finite i)
inputs :: FiniteOrd i => sul i o -> Set i
outputs :: FiniteOrd o => sul i o -> Set o
walk :: SUL sul m => sul i o -> [i] -> m (sul i o, [o])
stepPure :: SUL sul Identity => sul i o -> i -> (sul i o, o)
walkPure :: SUL sul Identity => sul i o -> [i] -> (sul i o, [o])
resetPure :: SUL sul Identity => sul i o -> sul i o
initial :: Automaton aut s => aut s i o -> s
distinguish :: (Automaton aut s, FiniteOrd i, Ord s, Eq o) => aut s i o -> s -> s -> [i]
accessSequences :: forall s i o aut. (Automaton aut s, FiniteOrd i, Ord s) => aut s i o -> Map s [i]
localCharacterizingSet :: (Automaton aut s, FiniteOrd i, FiniteOrd s, Eq o) => aut s i o -> s -> Set [i]
globalCharacterizingSet :: (Automaton aut s, FiniteOrd i, FiniteOrd s, Eq o) => aut s i o -> Set [i]
reachable :: forall s i o aut. (Automaton aut s, Ord s, FiniteOrd i) => aut s i o -> Set s

Documentation

class SUL (aut s) Identity => Automaton (aut :: Type -> Type -> Type -> Type) s where Source #

The Automaton type class extends the SUL type class and adds support for automata operations. Automatons are models, not programs, so they are pure and operate in the Identity monad.

Methods

transitions :: (FiniteOrd i, FiniteOrd s) => aut s i o -> Map (s, i) (s, o) Source #

states :: FiniteOrd s => aut s i o -> Set s Source #

current :: aut s i o -> s Source #

update :: aut s i o -> s -> aut s i o Source #

Instances

Instances details

Automaton MealyAutomaton s Source #
Instance details Defined in Haal.Automaton.MealyAutomaton Methods transitions :: (FiniteOrd i, FiniteOrd s) => MealyAutomaton s i o -> Map (s, i) (s, o) Source # states :: FiniteOrd s => MealyAutomaton s i o -> Set s Source # current :: MealyAutomaton s i o -> s Source # update :: MealyAutomaton s i o -> s -> MealyAutomaton s i o Source #
Automaton MooreAutomaton s Source #
Instance details Defined in Haal.Automaton.MooreAutomaton Methods transitions :: (FiniteOrd i, FiniteOrd s) => MooreAutomaton s i o -> Map (s, i) (s, o) Source # states :: FiniteOrd s => MooreAutomaton s i o -> Set s Source # current :: MooreAutomaton s i o -> s Source # update :: MooreAutomaton s i o -> s -> MooreAutomaton s i o Source #

class Monad m => SUL (sul :: Type -> Type -> Type) (m :: Type -> Type) where Source #

The SUL type class defines the basic interface for a black box automaton. It provides methods to step through the automaton and retrieve the current state. It also requires a monad m, that may be Identity in case of a pure SUL, or IO in case of an external program that performs IO.

Methods

step :: sul i o -> i -> m (sul i o, o) Source #

reset :: sul i o -> m (sul i o) Source #

Instances

Instances details

SUL (MealyAutomaton s) Identity Source #
Instance details Defined in Haal.Automaton.MealyAutomaton Methods step :: MealyAutomaton s i o -> i -> Identity (MealyAutomaton s i o, o) Source # reset :: MealyAutomaton s i o -> Identity (MealyAutomaton s i o) Source #
SUL (MooreAutomaton s) Identity Source #
Instance details Defined in Haal.Automaton.MooreAutomaton Methods step :: MooreAutomaton s i o -> i -> Identity (MooreAutomaton s i o, o) Source # reset :: MooreAutomaton s i o -> Identity (MooreAutomaton s i o) Source #

type StateID = Int Source #

The StateID type is an alias for an integer that represents the state of the automaton. - It is used as a default type for the state of learned automata.

type Finite i = (Enum i, Bounded i) Source #

Finite is an alias for (Enum, Bounded).

type FiniteEq i = (Eq i, Finite i) Source #

FiniteEq is an alias for (Eq, Finite).

type FiniteOrd i = (Ord i, Finite i) Source #

FiniteOrd is an alias for (Ord, Bounded).

inputs :: FiniteOrd i => sul i o -> Set i Source #

Return a Set containing only the valid inputs of the SUL.

outputs :: FiniteOrd o => sul i o -> Set o Source #

Return a Set containing only the valid outputs of the SUL.

walk :: SUL sul m => sul i o -> [i] -> m (sul i o, [o]) Source #

Generalization of step that operates on a list of inputs.

stepPure :: SUL sul Identity => sul i o -> i -> (sul i o, o) Source #

Pure instance of step.

walkPure :: SUL sul Identity => sul i o -> [i] -> (sul i o, [o]) Source #

Pure instance of walk.

resetPure :: SUL sul Identity => sul i o -> sul i o Source #

Pure instance of reset.

initial :: Automaton aut s => aut s i o -> s Source #

Return the initial state of an automaton.

distinguish :: (Automaton aut s, FiniteOrd i, Ord s, Eq o) => aut s i o -> s -> s -> [i] Source #

Returns an input sequence that distinguishes the given states in the given automaton.

accessSequences :: forall s i o aut. (Automaton aut s, FiniteOrd i, Ord s) => aut s i o -> Map s [i] Source #

Returns a map containing the shortest sequence to access each reachable state from the initial state.

localCharacterizingSet :: (Automaton aut s, FiniteOrd i, FiniteOrd s, Eq o) => aut s i o -> s -> Set [i] Source #

Returns a set of lists of inputs that can be used to distinguish between the given state and - any other state of the automaton.

globalCharacterizingSet :: (Automaton aut s, FiniteOrd i, FiniteOrd s, Eq o) => aut s i o -> Set [i] Source #

Returns a set of lists of inputs that can be used to distinguish between any two different states of the automaton.

reachable :: forall s i o aut. (Automaton aut s, Ord s, FiniteOrd i) => aut s i o -> Set s Source #

Return the set of reachable states of an automaton.