#![warn(missing_docs)]
//! This package implements the core algorithm of the entire
//! workspace: parsing with derivatives by means of chain rule and
//! regular nulling languages.
//!
//! Since I shall not name my crate "core" to avoid collisions with
//! the Rust's own core, I decided to name this crate after what I
//! think is the essence of this algorithm, the chain-rule for
//! derivatives of languages.

pub mod atom;

pub mod item;

use graph::{error::Error as GError, LabelExtGraph};

use item::default::Error as ForestError;

use item::PaVi;

/// An edge in the Chain-Rule machine.
#[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash)]
pub struct Edge {
    /// The position in the atomic languages.
    label: usize,
    /// The source of the associated forest edge.
    forest_source: PaVi,
    /// The bottom source on which we shall perform reduction.
    ///
    /// If this equals `forest_source`, no extra reduction needs to be
    /// done.
    true_source: PaVi,
    /// Whether or not this edge is "accepting".
    accepting: bool,
}

impl Edge {
    /// Construct a new edge.
    pub fn new(label: usize, forest_source: PaVi, accepting: bool) -> Self {
        let true_source = forest_source;
        Self {
            label,
            forest_source,
            accepting,
            true_source,
        }
    }

    /// Return the label of the edge.
    pub fn label(&self) -> usize {
        self.label
    }

    /// Tell whether or not the edge is accepting.
    pub fn is_accepting(&self) -> bool {
        self.accepting
    }

    /// Return the associated forest edge of the edge.
    pub fn forest_source(&self) -> PaVi {
        self.forest_source
    }

    /// Set the associated forest edge of the edge of the edge.
    pub fn set_forest_source(&mut self, source: PaVi) {
        self.forest_source = source;
    }

    /// Set the associated bottom edge of the edge from which onwards
    /// we shall perform the reduction.
    pub fn set_true_source(&mut self, true_source: PaVi) {
        self.true_source = true_source;
    }

    /// Return the associated bottom edge of the edge from which
    /// onwards we shall perform the reduction.
    pub fn true_source(&self) -> PaVi {
        self.true_source
    }
}

impl core::fmt::Display for Edge {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        let label = self.label();
        let forest_source = self.forest_source();

        write!(f, "edge label {label} with item {}", forest_source)
    }
}

/// A Real Or Imaginary edge.
///
/// An imaginary edge will be ignored when adding edges.  The
/// imaginary edges will be used to determine the acceptance of a
/// node, when and only when that new node turns out to have no
/// children.
///
/// # Note
///
/// Non, je ne suis pas un roi.  Je ne sais pas qu'est-ce que vous
/// parlez.
#[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash)]
pub enum Roi {
    /// A real edge is an ordinary edge.
    Re(Edge),
    /// The label of an imaginary edge is not important, so we only
    /// record its target.
    Im(usize),
}

// Some convenient conversions

impl From<Edge> for Roi {
    fn from(edge: Edge) -> Self {
        Self::Re(edge)
    }
}

impl From<usize> for Roi {
    fn from(target: usize) -> Self {
        Self::Im(target)
    }
}

impl Roi {
    /// Return the real part if it is a real edge.
    fn real_part(self) -> Option<Edge> {
        if let Self::Re(edge) = self {
            Some(edge)
        } else {
            None
        }
    }

    /// Return the imaginary part if it is an imaginary edge.
    fn imaginary_part(self) -> Option<usize> {
        if let Self::Im(target) = self {
            Some(target)
        } else {
            None
        }
    }
}

/// Each derivation is a concatenation of two items, so there are two
/// layers.  But some items have no children and are accepting, in
/// which case we just skip that item completely, for performance
/// reasons, and hence there could be only one layer as well.
///
/// It might even happen that both layers have no children, in which
/// case we shall just put all previous edges here.
#[derive(Debug, Clone, Eq, PartialEq)]
pub enum TwoLayers {
    /// One layer has no children.
    One(Roi, usize),
    // REVIEW: Maybe we do not need to store an edge in the forest: we
    // only need the source of the edge?
    /// Both layers have children.
    ///
    /// The first element is the label of the second layer, the second
    /// the source of the associated forest edge of the second layer,
    /// and the third is a list of edges, which are the common first
    /// layers.
    Two(usize, PaVi, bool, Vec<(Roi, usize)>),
}

/// The type of a collapsed iterator.
pub struct Collapsed<'a, I, C>
where
    I: Iterator<Item = TwoLayers>,
    C: Chain<DerIter = I>,
{
    iter: I,
    chain: &'a mut C,
    stop: bool,
}

impl<'a, I, C> Collapsed<'a, I, C>
where
    I: Iterator<Item = TwoLayers>,
    C: Chain<DerIter = I>,
{
    /// Collapse an iterator.
    pub fn collapse(iter: I, chain: &'a mut C) -> Self {
        let stop = false;

        Self { iter, chain, stop }
    }
}

impl<'a, I, C> Iterator for Collapsed<'a, I, C>
where
    I: Iterator<Item = TwoLayers>,
    C: Chain<DerIter = I>,
{
    type Item = Result<(Roi, usize), <C as Chain>::Error>;

    fn next(&mut self) -> Option<Self::Item> {
        if self.stop {
            return None;
        }

        if let Some(two_layer) = self.iter.next() {
            match two_layer {
                TwoLayers::One(edge, to) => Some(Ok((edge, to))),
                TwoLayers::Two(label, forest_source, accepting, edges) => {
                    let new_index = match self.chain.extend(
                        edges
                            .into_iter()
                            .filter_map(|(roi, target)| roi.real_part().map(|edge| (edge, target))),
                    ) {
                        Ok(new) => new,
                        Err(error) => {
                            // Prevent further iterations.
                            self.stop = true;

                            return Some(Err(error.into()));
                        }
                    };

                    Some(Ok((
                        Edge::new(label, forest_source, accepting).into(),
                        new_index,
                    )))
                }
            }
        } else {
            None
        }
    }
}

/// The expected behaviours of a language which can take derivatives
/// by chain rule.
pub trait Chain: LabelExtGraph<Edge> {
    /// The implementations should choose a type to represent errors.
    type Error: std::error::Error + From<GError> + From<ForestError>;

    /// A type of atomic languages that is chosen for this chain rule
    /// machine.
    type Atom: atom::Atom;

    /// Represents the language that is present after we parse the
    /// empty string, that is the initial configuration of the
    /// language.
    fn unit(atom: Self::Atom) -> Result<Self, Self::Error>;

    /// Produce the underlying atom, so that we can produce an initial
    /// empty chain from the same atom again.
    fn atom(&self) -> &Self::Atom;

    /// Return true if and only if the language contains the empty
    /// string.
    fn epsilon(&self) -> Result<bool, Self::Error>;

    /// Update the history
    fn update_history(&mut self, new: usize);

    /// Update the acceptance of a node, when and only when that node
    /// turns out to have no children.
    fn update_epsilon(
        &mut self,
        node_id: usize,
        edges: impl Iterator<Item = (Roi, usize)>,
    ) -> Result<(), Self::Error>;

    /// An iterator that iterates all layers that need to be merged.
    type DerIter: Iterator<Item = TwoLayers>;

    /// Take the derivative by a terminal `t` at position `pos`.
    fn derive(&mut self, t: usize, pos: usize, no_item: bool)
        -> Result<Self::DerIter, Self::Error>;

    /// Take the union of all derivatives.
    fn union(&mut self, der_iter: Self::DerIter) -> Result<Vec<(Roi, usize)>, Self::Error> {
        // REVIEW: Think about the possibilities to avoid allocations.
        Collapsed::<_, Self>::collapse(der_iter, self)
            .collect::<Result<Vec<(Roi, usize)>, Self::Error>>()
            .map(|mut v| {
                v.retain(|(_, target)| {
                    *target == 0 || matches!(self.degree(*target), Ok(deg) if deg != 0)
                });
                v
            })
    }

    /// Use chain rule to compute the derivative with respect to a
    /// terminal.
    ///
    /// # Arguments
    ///
    /// The argument `t` is the terminal we computet the derivative
    /// with.
    ///
    /// The argument `pos` is the zero-based position within the
    /// input.
    ///
    /// The argument `no_item` determines whether we want the item
    /// derivation forest as well.
    fn chain(&mut self, t: usize, pos: usize, no_item: bool) -> Result<(), Self::Error> {
        let der_iter = self.derive(t, pos, no_item)?;

        let edges = self.union(der_iter)?;

        let new_index = self.extend(
            edges
                .iter()
                .filter_map(|(roi, target)| roi.real_part().map(|edge| (edge, *target))),
        )?;

        if self.is_empty_node(new_index)? {
            self.update_epsilon(new_index, edges.into_iter())?;
        }

        self.update_history(new_index);

        Ok(())
    }

    // FIXME: I shall probably not use the trait of forests for this
    // purpose, but I have not figured out yet wha the correct trait
    // should be.
    /// The type of output item that will be produced by this machine.
    type Item: item::Forest<grammar::GrammarLabel>;

    /// Signal to the parser that the end of the input is reached, so
    /// that the parser knows to generate suitable forests.
    ///
    /// This is not needed when recognizing instead of parsing.
    ///
    /// We also pass in the current position `pos` so that we have a
    /// little flexibility in the position of the end of input.  In
    /// addition, this makes it easier to produce the suitable
    /// forests.
    ///
    /// As a reminder, `pos` should be the position of the last
    /// terminal, so if there are three terminals in total, the `pos`
    /// should be `2` , instead of `3`.
    ///
    /// Similarly, we pass in the terminal at the position `pos` to
    /// aid the production of the forest.
    fn end_of_input(&mut self, pos: usize, ter: usize) -> Result<Self::Item, Self::Error>;
}

pub mod default;