#![warn(missing_docs)]
//! This crate implements non-deterministic finite automata.
//!
//! By default this uses the graph from the crate [`graph`].  To use
//! another external graph, add a module in which the external graph
//! implements the Graph trait from the [`graph`] crate, and then use
//! that external graph type as [`Graph`][graph::Graph] here.

pub mod error;

extern crate graph;

use core::fmt::Display;

use graph::{Graph, GraphLabel, LabelGraph};

use error::Error;

/// The expected behaviour of a regular language.
///
/// Nondeterministic finite automata are equivalent to regular
/// languages.  Since regular languages are easier to understand for a
/// human being, nondeterministic finite automata include the data for
/// the equivalent regular languages.
pub trait Regex<T: GraphLabel>: Graph + Display {
    /// Return the label of a vertex, or an error if the node is
    /// invalid.
    fn vertex_label(&self, node_id: usize) -> Result<T, Error>;

    #[inline]
    /// Return the root node of the regular language.
    ///
    /// Implementations can follow different conventions for the root
    /// node, and hence this function.
    ///
    /// If the regular language is empty, the implementation should
    /// return None.
    ///
    /// The default implementation uses the convention that the root
    /// node is always the first node.
    fn root(&self) -> Option<usize> {
        if self.is_empty() {
            None
        } else {
            Some(0)
        }
    }

    // TODO: add functions that determine if certain "positions" in a
    // regular language satisfy some special properties, like at the
    // end of a Kleene star, or at the end of a regular language, et
    // cetera.  These might be needed later.
}

/// The expected behvaiour of a nondeterministic finite automaton.
///
/// Every NFA is a special labelled graph.
pub trait Nfa<T: GraphLabel>: LabelGraph<T> {
    /// Remove all empty transitions from the nondeterministic finite
    /// automaton.
    fn remove_epsilon(&mut self) -> Result<(), Error>;

    /// Return a state-minimal NFA equivalent with the original one.
    ///
    /// This is not required.  It is just to allow me to experiment
    /// with NFA optimization algorithms.
    fn minimize(&self) -> Result<Self, Error> {
        Err(Error::UnsupportedOperation)
    }

    /// Build a nondeterministic finite automaton out of a regular
    /// language.
    fn to_nfa(regex: impl Regex<T>) -> Self;

    /// Remove all dead states from the nondeterministic finite
    /// automaton.
    ///
    /// A state is dead if there are no edges going to the state.
    fn remove_dead(&mut self) -> Result<(), Error>;

    /// For each empty transition from A to B, and for every edge from
    /// B to C, say, add an edge from A to C.
    ///
    /// This is needed specifically by the algorithm to produce a set
    /// of atomic languages that represent "null-closed" derived
    /// languages.
    fn nulling(&mut self) -> Result<(), Error>;
}

pub mod default;
pub mod desrec;

#[cfg(test)]
mod nfa_tests {}