path: root/nfa/src/default/regex.rs

//! This file provides a default implementation of Regex.

use graph::{error::Error as GError, ALGraph, ExtGraph, Graph, GraphLabel};

use crate::{desrec::DesRec, error::Error, Regex};

use receme::{algebra::Algebra, catana::Cata};

use std::fmt::{Debug, Display};

/// The type of a node in a regular expression.
///
/// # Example
///
/// If a node has type "Kleene", this means it represents a star
/// construct in a regular expression, and its children are the
/// contents of the star.
///
/// # Note
///
/// There is no "concatenation" node type.  A concatenation of two
/// nodes is represented as the two nodes being successive children in
/// their common parent node.
///
/// This is possible because a regular expression has a root node.
/// For the sake of convenience, the root node has type "Or".
#[derive(Debug, Hash, Default, Eq, PartialEq, Clone, Copy, Ord, PartialOrd)]
pub enum RegexType<T: GraphLabel + Display> {
    /// A star node is a node with an arbitrary number of repetitions.
    Kleene,
    /// A plus node is a node with at least one repetition: a+ equals
    /// aa*
    Plus,
    /// An optional node
    Optional,
    /// An or node means an alternation of its children.
    Or,
    /// A paren node represents a parenthesis.
    Paren,
    /// An empty node
    #[default]
    Empty,
    /// A literal node
    Lit(T),
}

/// A default implementation of regular expressions.
#[derive(Debug)]
pub struct DefaultRegex<T: GraphLabel + Display> {
    /// The underlying graph is stored using adjacency lists.
    graph: ALGraph,
    /// The types of the underlying nodes.
    types: Vec<RegexType<T>>,
}

impl<T: GraphLabel + Display> Default for DefaultRegex<T> {
    fn default() -> Self {
        Self {
            graph: Default::default(),
            types: Default::default(),
        }
    }
}

impl<T: GraphLabel + Display> DefaultRegex<T> {
    /// Return the number of elements in this regular expression,
    /// counting nodes.
    pub fn len(&self) -> usize {
        self.types.len()
    }

    /// Return true if and only if this regular expression has no
    /// nodes.
    pub fn is_empty(&self) -> bool {
        self.types.is_empty()
    }

    /// Add a node as the child of an existing node or as a root.
    pub fn add_node(
        &mut self,
        label: RegexType<T>,
        parent: Option<usize>,
    ) -> Result<(), ParseError> {
        self.graph.extend(parent.iter().copied())?;
        self.types.push(label);

        Ok(())
    }
}

// REVIEW: This may not be needed.
impl<S: GraphLabel + Display, T, A> Cata<T, Vec<T>, A> for &DefaultRegex<S>
where
    A: Algebra<T, Vec<T>>,
{
    fn cata(self, mut alg: A) -> T {
        let mut results: Vec<Option<T>> = std::iter::repeat_with(Default::default)
            .take(self.len())
            .collect();

        for index in 0..=self.len() {
            let algebra_result = {
                let results_of_children: Vec<T> = self
                    .graph
                    .children_of(index)
                    .unwrap()
                    .map(|child_index| std::mem::replace(&mut results[child_index], None).unwrap())
                    .collect();

                alg(results_of_children)
            };

            // Artificially use this value to satisfy the compiler.
            let _ = std::mem::replace(&mut results[index], Some(algebra_result));
        }

        std::mem::replace(&mut results[0], None).unwrap()
    }
}

impl<T: GraphLabel + Display> Display for DefaultRegex<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        #[derive(Copy, Clone)]
        enum StackElement {
            Seen(usize),
            Unseen(usize),
        }

        impl StackElement {
            fn index(&self) -> usize {
                match self {
                    Seen(index) => *index,
                    Unseen(index) => *index,
                }
            }

            fn is_seen(&self) -> bool {
                match self {
                    Seen(_) => true,
                    Unseen(_) => false,
                }
            }
        }

        use StackElement::{Seen, Unseen};

        let mut stack: Vec<StackElement> = Vec::new();
        let mut types = self.types.clone();
        types.push(RegexType::Paren);

        stack.push(Unseen(0));

        while let Some(top) = stack.pop() {
            let node_type = types[top.index()];

            // TODO: Do not use unwrap here.

            match node_type {
                RegexType::Kleene => {
                    if !top.is_seen() {
                        stack.push(Seen(top.index()));
                        stack.extend(
                            self.graph
                                .children_of(top.index())
                                .unwrap()
                                .map(Unseen)
                                .rev(),
                        );
                    } else {
                        write!(f, "*")?;
                    }
                }
                RegexType::Plus => {
                    if !top.is_seen() {
                        stack.push(Seen(top.index()));
                        stack.extend(
                            self.graph
                                .children_of(top.index())
                                .unwrap()
                                .map(Unseen)
                                .rev(),
                        );
                    } else {
                        write!(f, "+")?;
                    }
                }
                RegexType::Optional => {
                    if !top.is_seen() {
                        stack.push(Seen(top.index()));
                        stack.extend(
                            self.graph
                                .children_of(top.index())
                                .unwrap()
                                .map(Unseen)
                                .rev(),
                        );
                    } else {
                        write!(f, "?")?;
                    }
                }
                RegexType::Or => {
                    if !top.is_seen() {
                        write!(f, "(")?;

                        let len = self.len();

                        stack.push(Unseen(types.len() - 1));

                        for (child_index, child) in self
                            .graph
                            .children_of(top.index())
                            .unwrap()
                            .enumerate()
                            .rev()
                        {
                            if child_index != len - 1 && child_index != 0 {
                                stack.push(Unseen(child));
                                stack.push(Seen(top.index()));
                            } else {
                                stack.push(Unseen(child));
                            }
                        }
                    } else {
                        write!(f, "|")?;
                    }
                }
                RegexType::Paren => {
                    write!(f, ")")?;
                }
                RegexType::Empty => {
                    stack.extend(
                        self.graph
                            .children_of(top.index())
                            .unwrap()
                            .map(Unseen)
                            .rev(),
                    );
                }
                RegexType::Lit(label) => write!(f, "{label}")?,
            }
        }

        Ok(())
    }
}

impl<T: GraphLabel + Display> Graph for DefaultRegex<T> {
    type Iter<'a> = <ALGraph as Graph>::Iter<'a>
    where
        Self: '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 + Display> Regex<RegexType<T>> for DefaultRegex<T> {
    #[inline]
    fn vertex_label(&self, node_id: usize) -> Result<RegexType<T>, Error> {
        self.types
            .get(node_id)
            .copied()
            .ok_or(Error::UnknownNode(node_id))
    }
}

/// An error type for holding parsing errors.
#[derive(Debug)]
pub enum ParseError {
    /// Encounter an invalid state.
    Invalid,
    /// An error from graph operations.
    Graph(GError),
    /// Encounter an empty stack.
    EmptyStack,
    /// Encounter a non-single stack at the end.
    NonSingleStack,
    /// Encounter a stack whose element is out of bounds.
    ///
    /// The first component is the stack element, while the second the
    /// bound.
    InvalidStack(usize, usize),
    /// Encounter a repetition construct without a preceding element.
    InvalidRepetition(usize),
    /// Invalid character
    InvalidCharacter(char),
}

impl Display for ParseError {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{self:?}")
    }
}

impl std::error::Error for ParseError {}

impl From<GError> for ParseError {
    fn from(ge: GError) -> Self {
        Self::Graph(ge)
    }
}

/// The direction of parsing.
///
/// This means whether we want to stay at the same level of
/// parent-child hierarchy, or to become the child, or to climb back
/// to the last parent.
#[derive(Debug, Copy, Clone, Default)]
pub enum ParseDirection {
    /// Climb back to the last parent.
    Up,
    /// Stay at the same level in the hierarchy.
    #[default]
    Right,
    /// Become the child.
    Down,
}

impl Display for ParseDirection {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        let direction = match self {
            ParseDirection::Up => "↑",
            ParseDirection::Right => "→",
            ParseDirection::Down => "↓",
        };

        write!(f, "{direction}")
    }
}

impl<T: GraphLabel + Display + Debug> DesRec for DefaultRegex<T> {
    type Label = RegexType<T>;

    type Regex = Self;

    type Error = ParseError;

    type Aux = ParseDirection;

    type Scanner<'a> =
        Box<dyn FnMut(&'a str) -> Result<Option<(usize, Self::Label, Self::Aux)>, Self::Error>>;

    fn parse<'a>(
        mut input: &'a str,
        mut scanner: Self::Scanner<'a>,
        post_p: bool,
    ) -> Result<Option<(DefaultRegex<T>, &'a str)>, Self::Error> {
        use ParseDirection::*;
        use RegexType::*;

        let mut intermediate_stack: Vec<(RegexType<T>, ParseDirection)> =
            Vec::with_capacity(input.len());

        // Classifies the input into a sequence of tokens with
        // directions.
        while !input.is_empty() {
            if let Some((len, label, direction)) = scanner(input)? {
                if len == 0 {
                    break;
                }

                input = &input[len..];

                intermediate_stack.push((label, direction));

                // If we encounter an opening parenthesis, we add
                // another auxiliary instruction.
                if matches!((label, direction), (Or, Down)) {
                    intermediate_stack.push((Empty, Down));
                }
            } else {
                break;
            }
        }

        let inter_len = intermediate_stack.len();

        let mut parents_stack: Vec<usize> = Vec::with_capacity(inter_len + 2);

        parents_stack.push(0);
        parents_stack.push(1);

        let mut list_of_children: Vec<Vec<usize>> = std::iter::repeat_with(Vec::new)
            .take(inter_len + 2)
            .collect();

        list_of_children[0].push(1);

        let mut types: Vec<RegexType<T>> = vec![Or, Empty];

        types.extend(intermediate_stack.iter().map(|(label, _direction)| *label));

        // Converts the sequence of tokens and directions into a
        // regular expression.
        for (index, (label, direction)) in intermediate_stack.iter().copied().enumerate() {
            let mut parent: usize;
            let mut parent_children: &mut Vec<usize>;

            if let Some(parent_stack_parent) = parents_stack.last().copied() {
                parent = parent_stack_parent;

                match list_of_children.get_mut(parent) {
                    Some(stack_parent_children) => {
                        parent_children = stack_parent_children;

                        match (label, direction) {
                            (Paren, Up) => {
                                // a closing parenthesis does not need
                                // to be counted as a child
                                parents_stack.pop();
                                // a closing parenthesis jumps out of
                                // two levels at once
                                parents_stack.pop();
                            }
                            (Empty, Up) => {
                                // an upwards pipe

                                // first add the current node to the parent of the parent
                                parents_stack.pop();

                                if let Some(parent_stack_parent) = parents_stack.last().copied() {
                                    parent = parent_stack_parent;

                                    if let Some(stack_parent_children) =
                                        list_of_children.get_mut(parent)
                                    {
                                        parent_children = stack_parent_children;

                                        parent_children.push(index + 2);
                                    } else {
                                        return Err(ParseError::InvalidStack(
                                            parent,
                                            inter_len + 2,
                                        ));
                                    }
                                } else {
                                    return Err(ParseError::EmptyStack);
                                }

                                // then make the current node the new parent
                                parents_stack.push(index + 2);
                            }
                            (_, Up) => {
                                parents_stack.pop();
                                parent_children.push(index + 2);
                            }
                            (_, Right) => {
                                parent_children.push(index + 2);
                            }
                            (_, Down) => {
                                parents_stack.push(index + 2);
                                parent_children.push(index + 2);
                            }
                        }
                    }
                    None => return Err(ParseError::InvalidStack(parent, inter_len)),
                }
            } else {
                // There are unbalanced closing parentheses.
                return Err(ParseError::EmptyStack);
            }

            // A special handling of repetition constructs as postfix
            // operators: it swaps with the preceding element.
            if post_p {
                match label {
                    Kleene | Plus | Optional => {
                        // remove the current node from the parent
                        parent_children.pop();

                        if let Some(preceding) = parent_children.last().copied() {
                            list_of_children.swap(preceding, index + 2);

                            types.swap(preceding, index + 2);

                            match list_of_children.get_mut(preceding) {
                                Some(preceding_children) => {
                                    preceding_children.push(index + 2);
                                }
                                None => {
                                    return Err(ParseError::InvalidStack(preceding, inter_len + 2))
                                }
                            }
                        } else {
                            return Err(ParseError::InvalidRepetition(index));
                        }
                    }
                    _ => {}
                }
            }
        }

        // There are unbalanced opening parentheses.
        if parents_stack.len() != 2 {
            return Err(ParseError::NonSingleStack);
        }

        let graph = list_of_children.into();

        let result = DefaultRegex { graph, types };

        Ok(Some((result, input)))
    }
}

#[cfg(test)]
mod test_des_rec {
    use super::*;

    fn test_scanner(
        input: &str,
    ) -> Result<Option<(usize, RegexType<char>, ParseDirection)>, ParseError> {
        use ParseDirection::*;
        use RegexType::*;

        if let Some(first) = input.chars().next() {
            match first {
                '*' => Ok(Some((1, Kleene, Right))),
                '+' => Ok(Some((1, Plus, Right))),
                '?' => Ok(Some((1, Optional, Right))),
                '|' => Ok(Some((1, Empty, Up))),
                '(' => Ok(Some((1, Or, Down))),
                ')' => Ok(Some((1, Paren, Up))),
                ' '..='~' => Ok(Some((1, Lit(first), Right))),
                _ => Err(ParseError::InvalidCharacter(first)),
            }
        } else {
            Ok(None)
        }
    }

    #[test]
    fn test_des_rec() -> Result<(), Box<dyn std::error::Error>> {
        let input_string = "a*b?c+|(d*| +)?".to_owned();

        if let Some((regex, remain)) =
            DefaultRegex::<char>::parse(&input_string, Box::new(test_scanner), true)?
        {
            println!("regex = {regex}");
            println!("remain = {remain}");

            println!("regex length = {}", regex.len());

            Ok(())
        } else {
            unreachable!()
        }
    }
}