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| Language.HaLex.Dfa | | Portability | portable | | Stability | provisional | | Maintainer | jas@di.uminho.pt |
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| Description |
Deterministic Finite Automata in Haskell.
Code Included in the Lecture Notes on
Language Processing (with a functional flavour).
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| Synopsis |
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| data Dfa st sy = Dfa [sy] [st] st [st] (st -> sy -> st) | | | dfaaccept :: Eq st => Dfa st sy -> [sy] -> Bool | | | dfawalk :: (st -> sy -> st) -> st -> [sy] -> st | | | ttDfa2Dfa :: (Eq st, Eq sy) => ([sy], [st], st, [st], [(st, sy, st)]) -> Dfa st sy | | | dfa2tdfa :: (Eq st, Ord sy) => Dfa st sy -> TableDfa st | | | transitionsFromTo :: Eq st => (st -> sy -> st) -> [sy] -> st -> st -> [sy] | | | destinationsFrom :: (st -> sy -> st) -> [sy] -> st -> [st] | | | transitionTableDfa :: (Ord st, Ord sy) => Dfa st sy -> [(st, sy, st)] | | | reachedStatesFrom :: (Eq [st], Ord st) => (st -> sy -> st) -> [sy] -> st -> [st] | | | beautifyDfa :: (Ord st, Ord sy) => Dfa st sy -> Dfa Int sy | | | renameDfa :: (Ord st, Ord sy) => Dfa st sy -> Int -> Dfa Int sy | | | showDfaDelta :: (Show st, Show sy) => [st] -> [sy] -> (st -> sy -> st) -> [Char] -> [Char] | | | beautifyDfaWithSyncSt :: Eq st => Dfa [st] sy -> Dfa [Int] sy | | | dfaIO :: (Show st, Show sy) => Dfa st sy -> String -> IO () | | | sizeDfa :: Dfa st sy -> Int | | | dfadeadstates :: Ord st => Dfa st sy -> [st] | | | isStDead :: Ord st => (st -> sy -> st) -> [sy] -> [st] -> st -> Bool | | | isStSync :: Eq st => (st -> sy -> st) -> [sy] -> [st] -> st -> Bool | | | numberOutgoingArrows :: (st -> sy -> st) -> [sy] -> st -> Int | | | numberIncomingArrows :: Eq st => (st -> sy -> st) -> [sy] -> [st] -> st -> Int |
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| Data type |
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| data Dfa st sy |
| The type of Deterministic Finite Automata parameterized with
the type st of states and sy of symbols. | | Constructors | | Dfa [sy] [st] st [st] (st -> sy -> st) | |
| | Instances | | (Show st, Show sy) => Show (Dfa st sy) | | (Show st, Show sy, Ord st, Ord sy) => Fa Dfa st sy |
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| Acceptance |
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| dfaaccept |
| :: Eq st | | | => Dfa st sy | Automaton | | -> [sy] | Input symbols | | -> Bool | | | Test whether the given automaton accepts the given list of
input symbols (expressed as a fold). |
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| dfawalk |
| :: (st -> sy -> st) | Transition function | | -> st | Initial state | | -> [sy] | Input symbols | | -> st | Final state | | Execute the transition function of a Dfa on an initial state
and list of input symbol. Return the final state when all input
symbols have been consumed. |
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| Transformation |
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| ttDfa2Dfa |
| :: (Eq st, Eq sy) | | | => ([sy], [st], st, [st], [(st, sy, st)]) | Tuple-based Automaton | | -> Dfa st sy | Automaton | | Reconstruct a Dfa from a transition table.
Given an automaton expressed by a transition table
(ie a list of triples of the form
(Origin,Symbol,Destination)
it constructs a Dfa. The other elements of the
input tuple are the vocabulary, a set of
states, an initial state, and a set of
final states. |
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| dfa2tdfa |
| :: (Eq st, Ord sy) | | | => Dfa st sy | Automaton | | -> TableDfa st | Transition table | | Dfa to a Table-based Dfa
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| Transitions |
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| transitionsFromTo |
| :: Eq st | | | => (st -> sy -> st) | Transition function | | -> [sy] | Vocabulary | | -> st | Origin | | -> st | Destination | | -> [sy] | Labels | | Compute the labels with the same (giving) origin and destination states |
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| destinationsFrom |
| :: (st -> sy -> st) | Tansition Function | | -> [sy] | Vocabulary | | -> st | Origin | | -> [st] | Destination States | | Compute the destination states giving the origin state |
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| transitionTableDfa |
| :: (Ord st, Ord sy) | | | => Dfa st sy | Automaton | | -> [(st, sy, st)] | Transition table | | Produce the transition table of a given Dfa.
Given a Dfa, it returns a list of triples of the form
(Origin,Symbol,Destination)
defining all the transitions of the Dfa.
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| reachedStatesFrom |
| :: (Eq [st], Ord st) | | | => (st -> sy -> st) | Transition function | | -> [sy] | Vocabulary | | -> st | Origin | | -> [st] | Reached states | | Compute the states that can be reached from a state
according to a given transition function and vocabulary |
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| Printing |
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| beautifyDfa :: (Ord st, Ord sy) => Dfa st sy -> Dfa Int sy |
| Beautify a Dfa by assigning (natural) numbers to states. |
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| renameDfa |
| :: (Ord st, Ord sy) | | | => Dfa st sy | Automaton | | -> Int | Initial state ID | | -> Dfa Int sy | Renamed automaton | | Renames a Dfa.
It renames a DFA in such a way that the renaming of two isomorphic DFA
returns the same DFA.
It is the basis for the equivalence test for minimized DFA.
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| showDfaDelta :: (Show st, Show sy) => [st] -> [sy] -> (st -> sy -> st) -> [Char] -> [Char] |
| Helper function to show the transition function of a Dfa. |
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| beautifyDfaWithSyncSt |
| :: Eq st | | | => Dfa [st] sy | Original Automaton | | -> Dfa [Int] sy | Beautified Automaton (states as integers) |
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| dfaIO |
| :: (Show st, Show sy) | | | => Dfa st sy | Automaton | | -> String | Haskell module name | | -> IO () | | | Write a Dfa to a Haskell module in a file. |
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| Properties of Dfa |
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| sizeDfa :: Dfa st sy -> Int |
| Compute the size of a deterministic finite automaton.
The size of an automaton is the number of its states. |
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| dfadeadstates |
| :: Ord st | | | => Dfa st sy | Automaton | | -> [st] | Dead states | | Compute the dead states of a Dfa
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| Properties of States |
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| isStDead |
| :: Ord st | | | => (st -> sy -> st) | Transition Function | | -> [sy] | Vocabulary | | -> [st] | Set of Final States | | -> st | State | | -> Bool | | Checks whether a state is dead or not.
One state is dead when it is not possible to reach a final state from it.
(probably we should consider that it has to be reachable from the
initial state, as well) |
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| isStSync |
| :: Eq st | | | => (st -> sy -> st) | Transition Function | | -> [sy] | Vocabulary | | -> [st] | Set of Final States | | -> st | State | | -> Bool | | Checks whether a state is a sync state or not
A sync state is a state that has transitions to itself for all
symbols of the vocabulary |
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| numberOutgoingArrows |
| :: (st -> sy -> st) | Transition Function | | -> [sy] | Vocabulary | | -> st | Origin | | -> Int | Number of Arrows | | Compute the number of outgoing arrows for a given state |
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| numberIncomingArrows |
| :: Eq st | | | => (st -> sy -> st) | Transition Function | | -> [sy] | Vocabulary | | -> [st] | Set of States | | -> st | Destination | | -> Int | Number of Arrows | | Compute the number of incoming arrows for a given state
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| Produced by Haddock version 0.6 |
