3 files changed, 247 insertions, 0 deletions
diff --git a/nfa/src/default/mod.rs b/nfa/src/default/mod.rs
new file mode 100644
index 0000000..805540b
--- /dev/null
+++ b/nfa/src/default/mod.rs
@@ -0,0 +1,123 @@
+//! This file provides a structure that implements the trait
+//! [`NFA`][super::Nfa].
+//!
+//! It is used as the default implementation.
+
+use graph::{error::Error as GError, DLGraph, Graph, GraphLabel, LabelGraph};
+
+use super::{error::Error, Nfa, Regex};
+
+// TODO: Store the regular expression in the NFA as well.
+//
+// The current focus of the project is to understand the growth rate
+// of the algorithm, to know whether I made a mistake in the previous
+// iteration of the implementation, or the algorithm is not as fast as
+// the author estimated, which is not quite likely, of course.
+//
+// Thus I shall establish a friendly interface that allows me to view
+// and debug the atomic languages and the languages, transparently.
+
+#[non_exhaustive]
+#[derive(Debug)]
+/// Default NFA implementation.
+pub struct DefaultNFA<T: GraphLabel> {
+    graph: DLGraph<T>,
+}
+
+impl<T: GraphLabel> Default for DefaultNFA<T> {
+    fn default() -> Self {
+        let graph = Default::default();
+        Self { graph }
+    }
+}
+
+impl<T: GraphLabel> Graph for DefaultNFA<T> {
+    type Iter<'a> = <DLGraph<T> as Graph>::Iter<'a> where T: 'a;
+
+    #[inline]
+    fn is_empty(&self) -> bool {
+        self.graph.is_empty()
+    }
+
+    #[inline]
+    fn nodes_len(&self) -> usize {
+        self.graph.nodes_len()
+    }
+
+    #[inline]
+    fn children_of(&self, node_id: usize) -> Result<Self::Iter<'_>, GError> {
+        self.graph.children_of(node_id)
+    }
+
+    #[inline]
+    fn degree(&self, node_id: usize) -> Result<usize, GError> {
+        self.graph.degree(node_id)
+    }
+
+    #[inline]
+    fn is_empty_node(&self, node_id: usize) -> Result<bool, GError> {
+        self.graph.is_empty_node(node_id)
+    }
+
+    #[inline]
+    fn has_edge(&self, source: usize, target: usize) -> Result<bool, GError> {
+        self.graph.has_edge(source, target)
+    }
+}
+
+impl<T: GraphLabel> LabelGraph<T> for DefaultNFA<T> {
+    type Iter<'a> = <DLGraph<T> as LabelGraph<T>>::Iter<'a> where T: 'a;
+
+    type LabelIter<'a> = <DLGraph<T> as LabelGraph<T>>::LabelIter<'a> where T: 'a;
+
+    // TODO: Return the label from the contained regular language.
+    #[inline]
+    fn vertex_label(&self, node_id: usize) -> Result<Option<T>, GError> {
+        if self.has_node(node_id) {
+            todo!()
+        } else {
+            Err(GError::IndexOutOfBounds(node_id, self.nodes_len()))
+        }
+    }
+
+    #[inline]
+    fn edge_label(&self, source: usize, target: usize) -> Result<Vec<T>, GError> {
+        self.graph.edge_label(source, target)
+    }
+
+    #[inline]
+    fn find_children_with_label(
+        &self,
+        node_id: usize,
+        label: &T,
+    ) -> Result<<Self as LabelGraph<T>>::Iter<'_>, GError> {
+        self.graph.find_children_with_label(node_id, label)
+    }
+
+    #[inline]
+    fn labels_of(&self, node_id: usize) -> Result<Self::LabelIter<'_>, GError> {
+        self.graph.labels_of(node_id)
+    }
+}
+
+impl<T: GraphLabel> Nfa<T> for DefaultNFA<T> {
+    #[allow(unused)]
+    fn to_nfa(regex: impl Regex<T>) -> Self {
+        todo!()
+    }
+
+    fn remove_epsilon(&mut self) -> Result<(), Error> {
+        todo!()
+    }
+
+    fn remove_dead(&mut self) -> Result<(), Error> {
+        todo!()
+    }
+
+    fn nulling(&mut self) -> Result<(), Error> {
+        todo!()
+    }
+}
+
+#[cfg(test)]
+mod default_nfa_test {}
diff --git a/nfa/src/error.rs b/nfa/src/error.rs
new file mode 100644
index 0000000..6112878
--- /dev/null
+++ b/nfa/src/error.rs
@@ -0,0 +1,30 @@
+//! This file implements the error type for the crate.
+
+use graph::error::Error as GError;
+
+use std::fmt::{Display, Formatter};
+
+#[derive(Debug, Clone, Eq, PartialEq, Ord, PartialOrd)]
+pub enum Error {
+    UnknownNode(usize),
+    UnsupportedOperation,
+    Graph(GError),
+}
+
+impl Display for Error {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Error::UnknownNode(id) => write!(f, "unknown node: {id}"),
+            Error::UnsupportedOperation => write!(f, "unsupported operation"),
+            Error::Graph(e) => write!(f, "graph error: {e}"),
+        }
+    }
+}
+
+impl std::error::Error for Error {}
+
+impl From<GError> for Error {
+    fn from(e: GError) -> Self {
+        Self::Graph(e)
+    }
+}
diff --git a/nfa/src/lib.rs b/nfa/src/lib.rs
new file mode 100644
index 0000000..ef207cf
--- /dev/null
+++ b/nfa/src/lib.rs
@@ -0,0 +1,94 @@
+#![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.
+
+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 will be needed later.
+}
+
+/// The expected behvaiour of a nondeterministic finite automaton.
+///
+/// Every NFA is a special labelled graph, so this trait extends the
+/// [`LabelGraph`][graph::LabelGraph] trait.
+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;
+
+#[cfg(test)]
+mod nfa_tests {}