forest seems to be completed

I seem to have finished the implementation of forests.  Now it remains
the implementation of the chain-rule machine, of which I have a rough
plan now.

3 files changed, 498 insertions, 73 deletions

diff --git a/forest/Cargo.toml b/forest/Cargo.toml
index b88451d..c51bf36 100644
--- a/forest/Cargo.toml
+++ b/forest/Cargo.toml
@@ -5,5 +5,11 @@ edition = "2021"
 
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
+[features]
+default = []
+
+# This flag controls whether to print GraphViz files during testing.
+test-print-viz = []
+
 [dependencies]
 graph = { path = "../graph" }
diff --git a/forest/src/default.rs b/forest/src/default.rs
index d3970e9..d79c1c7 100644
--- a/forest/src/default.rs
+++ b/forest/src/default.rs
@@ -1,21 +1,471 @@
 //! This file provides a default implementation for the
 //! [`Forest`][crate::Forest] trait.
 
-#[allow(unused_imports)]
 use super::*;
-#[allow(unused_imports)]
-use graph::{error::Error as GraphError, ALGraph, Graph};
-
-#[allow(unused_imports)]
-use std::collections::{hash_set::Iter, HashMap, HashSet};
-
-// TODO: Use PLGraph instead.
-
-// #[derive(Debug, Clone)]
-// pub struct DefaultForest<NodeLabel: GraphLabel, EdgeLabel: GraphLabel> {
-//     graph: ALGraph,
-//     vertex_labels: HashMap<usize, NodeLabel>,
-//     edge_labels: HashMap<(usize, usize), EdgeLabel>,
-//     plugins: HashSet<usize>,
-//     plugouts: HashSet<usize>,
-// }
+use graph::{
+    builder::BuilderMut, labelled::binary::PLGBuilderMut, Graph, LabelGraph, PLGraph, RedirectGraph,
+};
+
+use core::fmt::Display;
+
+/// The type of errors for forest operations.
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Ord, PartialOrd)]
+pub enum Error {
+    /// An index is out of bounds.
+    ///
+    /// The first component is the index that is out of bounds, and
+    /// the second component is the current length of nodes.
+    IndexOutOfBounds(usize, usize),
+    /// The forest does not permit duplicate nodes but encounters a
+    /// repeated node.
+    DuplicatedNode(usize),
+    /// A node has no labels while it is required to have one.
+    NodeNoLabel(usize),
+    /// Encounter an invalid error in converting from an error of
+    /// graphs.
+    InvalidGraphError(GError),
+}
+
+impl Display for Error {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Error::IndexOutOfBounds(index, bound) => {
+                write!(f, "index {index} is out of bound {bound}")
+            }
+            Error::DuplicatedNode(n) => write!(f, "node {n} is duplicated"),
+            Error::InvalidGraphError(ge) => write!(f, "invalid error: {ge}"),
+            Error::NodeNoLabel(n) => write!(f, "node {n} has no labels, but it should have one"),
+        }
+    }
+}
+
+impl std::error::Error for Error {}
+
+impl From<GError> for Error {
+    fn from(ge: GError) -> Self {
+        match ge {
+            GError::IndexOutOfBounds(index, bound) => Self::IndexOutOfBounds(index, bound),
+            GError::DuplicatedNode(n) => Self::DuplicatedNode(n),
+            _ => Self::InvalidGraphError(ge),
+        }
+    }
+}
+
+/// A default implementation of forest.
+#[derive(Debug, Clone)]
+pub struct DefaultForest<T: GraphLabel> {
+    graph: PLGraph<T>,
+    root: Option<usize>,
+}
+
+impl<T: GraphLabel> Default for DefaultForest<T> {
+    fn default() -> Self {
+        let graph = Default::default();
+        let root = None;
+
+        Self { graph, root }
+    }
+}
+
+impl<T: GraphLabel> AsRef<DefaultForest<T>> for DefaultForest<T> {
+    fn as_ref(&self) -> &DefaultForest<T> {
+        &self
+    }
+}
+
+impl<T: GraphLabel> Graph for DefaultForest<T> {
+    type Iter<'a> = <PLGraph<T> 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 edges_len(&self) -> Option<usize> {
+        self.graph.edges_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)
+    }
+
+    fn replace_by_builder(&mut self, _builder: impl graph::Builder<Result = Self>) {
+        unimplemented!()
+    }
+}
+
+impl<T: GraphLabel> ParentsGraph for DefaultForest<T> {
+    type Iter<'a>= <PLGraph<T> as ParentsGraph>::Iter<'a>
+    where
+        Self:'a;
+
+    fn parents_of(&self, node_id: usize) -> Result<<Self as ParentsGraph>::Iter<'_>, GError> {
+        self.graph.parents_of(node_id)
+    }
+}
+
+impl<T: GraphLabel> LabelGraph<T> for DefaultForest<T> {
+    type Iter<'a> = std::iter::Empty<usize>
+    where
+        Self: 'a;
+
+    type LabelIter<'a> = std::iter::Empty<(&'a T, <Self as LabelGraph<T>>::Iter<'a>)>
+    where
+        Self: 'a,
+        T: 'a;
+
+    type EdgeLabelIter<'a> = std::iter::Empty<T>
+    where
+        Self: 'a,
+        T: 'a;
+
+    #[inline]
+    fn query_label(&self, label: T) -> Option<usize> {
+        self.graph.query_label(label)
+    }
+
+    #[inline]
+    fn vertex_label(&self, node_id: usize) -> Result<Option<T>, GError> {
+        self.graph.vertex_label(node_id)
+    }
+
+    fn edge_label(
+        &self,
+        _source: usize,
+        _target: usize,
+    ) -> Result<Self::EdgeLabelIter<'_>, GError> {
+        unimplemented!("edges have no labels")
+    }
+
+    fn find_children_with_label(
+        &self,
+        _node_id: usize,
+        _label: &T,
+    ) -> Result<<Self as LabelGraph<T>>::Iter<'_>, GError> {
+        unimplemented!("edges have no labels")
+    }
+
+    fn labels_of(&self, _node_id: usize) -> Result<Self::LabelIter<'_>, GError> {
+        unimplemented!("edges have no labels")
+    }
+
+    fn has_edge_label(&self, _node_id: usize, _label: &T, _target: usize) -> Result<bool, GError> {
+        unimplemented!("edges have no labels")
+    }
+}
+
+impl<T: GraphLabel> Forest<T> for DefaultForest<T> {
+    type Error = Error;
+
+    fn root(&self) -> Option<usize> {
+        self.root
+    }
+
+    fn new_leaf(label: T) -> Self {
+        let mut graph = PLGraph::default();
+
+        let mut builder = PLGBuilderMut::from_graph_mut(&mut graph);
+
+        let root = Some(builder.add_vertex(label));
+
+        Self { graph, root }
+    }
+
+    fn is_prefix<F>(&self, node_id: usize, fragment: F) -> Result<bool, Self::Error>
+    where
+        F: AsRef<Self>,
+    {
+        if !self.has_node(node_id) {
+            return Err(Error::IndexOutOfBounds(node_id, self.nodes_len()));
+        }
+
+        // We do a depth-first traversal to determine if every node
+        // encountered has the same set of children (labels taken into
+        // the consideration).
+
+        let fragment = fragment.as_ref();
+
+        let mut frag_stack = Vec::with_capacity(fragment.nodes_len());
+
+        let mut self_stack = Vec::with_capacity(fragment.nodes_len());
+
+        let frag_root = if let Some(root) = fragment.root() {
+            root
+        } else {
+            // an empty forest is a prefix of any forest.
+            return Ok(true);
+        };
+
+        frag_stack.push(frag_root);
+        self_stack.push(node_id);
+
+        // defer popping
+        while let (Some(frag_top), Some(self_top)) =
+            (frag_stack.last().copied(), self_stack.last().copied())
+        {
+            frag_stack.pop();
+            self_stack.pop();
+
+            if fragment.vertex_label(frag_top)? != self.vertex_label(self_top)? {
+                // not a prefix
+                return Ok(false);
+            }
+
+            let mut self_children = self.children_of(self_top)?;
+
+            for child in fragment.children_of(frag_top)? {
+                if let Some(self_child) = self_children.next() {
+                    frag_stack.push(child);
+                    self_stack.push(self_child);
+                } else {
+                    // too few children
+                    return Ok(false);
+                }
+            }
+        }
+
+        // Check both stacks are empty at the end.
+        Ok(frag_stack.is_empty() && self_stack.is_empty())
+    }
+
+    fn plant<F>(&mut self, node_id: usize, fragment: F) -> Result<(), Self::Error>
+    where
+        F: AsRef<Self>,
+    {
+        // Convert self to a builder_mut, and traverse fragment in a
+        // depth-first manner and adjoin corresponding nodes along the
+        // way.
+
+        if !self.has_node(node_id) {
+            return Err(Error::IndexOutOfBounds(node_id, self.nodes_len()));
+        }
+
+        let fragment = fragment.as_ref();
+
+        let mut builder = PLGBuilderMut::from_graph_mut(&mut self.graph);
+
+        let root = if let Some(root) = fragment.root() {
+            root
+        } else {
+            // Nothing to do to plant an empty forest.
+            return Ok(());
+        };
+
+        // Just a dummy label for use in adding edges.
+        //
+        // REVIEW: I probably should refactor the API for builder_mut.
+        let root_label = fragment
+            .vertex_label(root)?
+            .ok_or(Error::NodeNoLabel(root))?;
+
+        let nodes_len = fragment.nodes_len();
+
+        // First adjoin those nodes and join the edges later.
+
+        for node in 0..nodes_len {
+            let label = fragment
+                .vertex_label(node)?
+                .ok_or(Error::NodeNoLabel(node))?;
+
+            builder.add_vertex(label);
+        }
+
+        // If the fragment root has a duplicate label, the forest will
+        // not grow, so we use the label to find the adjoined node
+        // index.
+
+        // the nodes hava already been added to the forest, so it is
+        // safe to call unwrap.
+        macro_rules! conversion (
+            ($node:expr) => {
+                {
+                    builder
+                        .query_label(
+                            fragment
+                                .vertex_label($node)?
+                                .ok_or(Error::NodeNoLabel($node))?
+                        ).unwrap()
+                }
+            }
+        );
+
+        // Don't forget to join the new sub-forest to the original
+        // forest, at the specified position.
+
+        builder.add_edge(node_id, conversion!(root), root_label)?;
+
+        // We can try to calculate the depth of fragments, if we need
+        // to lower the memory usage.  But in our use cases, we
+        // usually deal with fragments where each node has at most one
+        // child, so the depth is supposed to be equal to the length
+        // in this case.
+        let mut stack = Vec::with_capacity(fragment.nodes_len());
+
+        stack.push(root);
+
+        while let Some(top) = stack.pop() {
+            for child in fragment.children_of(top)? {
+                builder.add_edge(conversion!(top), conversion!(child), root_label)?;
+            }
+        }
+
+        Ok(())
+    }
+
+    fn clone_node<F>(&mut self, node_id: usize, clone_transform: F) -> Result<usize, Self::Error>
+    where
+        F: Fn(T) -> T,
+    {
+        let mut builder = PLGBuilderMut::from_graph_mut(&mut self.graph);
+
+        let old_label = builder
+            .vertex_label(node_id)?
+            .ok_or(Error::NodeNoLabel(node_id))?;
+
+        let new_label = clone_transform(old_label);
+
+        // Make a new node
+        let new_index = builder.add_vertex(new_label);
+
+        // Re-direct parents to the new node.
+        //
+        // This must be done before pointing the new node to the old
+        // node, otherwise that edge will be redirected as well.
+
+        // Unfortunately I cannot loop through parents and mutate them
+        // at the same time, so I first collect them into a vector.
+        let parents: Vec<_> = builder.parents_of(node_id)?.collect();
+
+        for parent in parents.into_iter() {
+            builder.redirect(parent.node(), parent.edge(), new_index)?;
+        }
+
+        // Point the new node to the old node.  OLD_LABEL is just a
+        // place holder.
+
+        builder.add_edge(new_index, node_id, old_label)?;
+
+        Ok(new_index)
+    }
+}
+
+#[cfg(test)]
+mod forest_test {
+    use super::*;
+
+    macro_rules! leaf (
+        ($label:expr, $type:tt) =>{
+            DefaultForest::<$type>::new_leaf($label)
+        };
+        ($label:expr) => {
+            DefaultForest::<usize>::new_leaf($label)
+        }
+    );
+
+    #[test]
+    fn test_forest_api() -> Result<(), Box<dyn std::error::Error>> {
+        let forest: DefaultForest<usize> = Default::default();
+
+        // empty forest
+
+        assert!(forest.is_empty());
+
+        // leaf forest
+
+        let mut forest = leaf!(0, usize);
+
+        assert_eq!(forest.nodes_len(), 1);
+        assert_eq!(forest.root(), Some(0));
+
+        // add some child
+
+        forest.plant(0, leaf!(1))?;
+
+        assert_eq!(forest.nodes_len(), 2);
+        let mut children = forest.children_of(0)?;
+        assert_eq!(children.next(), Some(1));
+        assert_eq!(children.next(), None);
+
+        // add more children
+
+        forest.plant(0, leaf!(2))?;
+        forest.plant(0, leaf!(3))?;
+        forest.plant(0, leaf!(4))?;
+        forest.plant(2, leaf!(5))?;
+
+        assert_eq!(forest.nodes_len(), 6);
+        let mut children = forest.children_of(0)?;
+        assert_eq!(children.next(), Some(1));
+        assert_eq!(children.next(), Some(2));
+        assert_eq!(children.next(), Some(3));
+        assert_eq!(children.next(), Some(4));
+        let mut children = forest.children_of(2)?;
+        assert_eq!(children.next(), Some(5));
+        assert_eq!(children.next(), None);
+
+        let mut test_forest = leaf!(0);
+        test_forest.plant(0, leaf!(1))?;
+        test_forest.plant(0, leaf!(2))?;
+        test_forest.plant(0, leaf!(3))?;
+        test_forest.plant(2, leaf!(5))?;
+
+        assert!(forest.is_prefix(0, &test_forest)?);
+
+        let mut test_forest = leaf!(0);
+        test_forest.plant(0, leaf!(1))?;
+        test_forest.plant(0, leaf!(2))?;
+        // this child of the root should have label 3 in order to be a
+        // prefix.
+        test_forest.plant(0, leaf!(4))?;
+        test_forest.plant(2, leaf!(5))?;
+
+        assert!(!forest.is_prefix(0, &test_forest)?);
+
+        let mut test_forest = leaf!(2);
+        test_forest.plant(0, leaf!(5))?;
+
+        assert!(forest.is_prefix(2, &test_forest)?);
+
+        // now test cloning
+
+        // add a duplicate label
+        forest.plant(3, leaf!(5))?;
+
+        let len = forest.nodes_len();
+
+        let clone_transform = |label| label + len;
+
+        forest.clone_node(5, clone_transform)?;
+
+        assert_eq!(forest.nodes_len(), 7);
+
+        #[cfg(feature = "test-print-viz")]
+        forest.print_viz("forest.gv")?;
+
+        Ok(())
+    }
+}
diff --git a/forest/src/lib.rs b/forest/src/lib.rs
index c2f4988..f843bc1 100644
--- a/forest/src/lib.rs
+++ b/forest/src/lib.rs
@@ -11,57 +11,7 @@
 //! out-coming and in-coming plugs.  These plugs are used to join
 //! different fragments of forests together.
 
-use graph::{GraphLabel, LabelGraph, ParentsGraph};
-
-use core::fmt::Display;
-
-// TODO: move this to default
-
-/// The type of errors for forest operations.
-#[derive(Debug)]
-pub enum Error {
-    /// An index is out of bounds.
-    IndexOutOfBounds(usize, usize),
-}
-
-impl Display for Error {
-    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        match self {
-            Error::IndexOutOfBounds(index, bound) => {
-                write!(f, "index {index} is out of bound {bound}")
-            }
-        }
-    }
-}
-
-impl std::error::Error for Error {}
-
-// /// A builder of a forest.
-// pub trait ForestBuilder<NodeLabel: GraphLabel, EdgeLabel: GraphLabel> {
-//     /// The type of the resulting forest.
-//     type Output: Forest<NodeLabel, EdgeLabel>;
-
-//     /// Construct a new builder with only one node with the given
-//     /// label.
-//     fn new_leaf(label: NodeLabel) -> Self;
-
-//     /// Add a child to the builder the given labels for the new node
-//     /// and the added edge.
-//     ///
-//     /// All plug-out nodes within the builder should have a new child
-//     /// with the specified labels, and hence multiple children might
-//     /// be added, and the plug-out nodes should be modified
-//     /// accordingly.
-//     fn add_children(&mut self, vertex_label: NodeLabel, edge_labe: EdgeLabel);
-
-//     /// Build the forest.
-//     fn build(self) -> Self::Output;
-
-//     /// Build the forest from a reference.
-//     fn build_ref(&self) -> Self::Output;
-// }
-
-// FIXME: The trait should be re-designed.
+use graph::{error::Error as GError, GraphLabel, LabelGraph, ParentsGraph};
 
 /// The expected behaviours of a forest.
 ///
@@ -69,19 +19,38 @@ impl std::error::Error for Error {}
 /// labelled graphs.
 pub trait Forest<T: GraphLabel>: ParentsGraph + LabelGraph<T> {
     /// The type of errors for operations on the forest.
-    type Error: std::error::Error + From<graph::error::Error>;
+    type Error: std::error::Error + From<GError>;
+
+    /// Return the root of the forest.
+    ///
+    /// A forest without a root is regarded as empty.
+    fn root(&self) -> Option<usize>;
+
+    /// Construct a forest consisting of one leaf node with the given
+    /// label.
+    fn new_leaf(label: T) -> Self;
 
     /// Detect if the fragment is a prefix of the sub-forest rooted at
     /// `node_id`.
-    fn is_prefix<F: AsRef<Self>>(&self, node_id: usize, fragment: F) -> Result<bool, Self::Error>;
+    fn is_prefix<F>(&self, node_id: usize, fragment: F) -> Result<bool, Self::Error>
+    where
+        F: AsRef<Self>;
 
     /// Extend the forest by adjoining another forest at a given node.
-    fn plant<F: AsRef<Self>>(&mut self, node_id: usize, fragment: F) -> Result<(), Self::Error>;
+    fn plant<F>(&mut self, node_id: usize, fragment: F) -> Result<(), Self::Error>
+    where
+        F: AsRef<Self>;
 
     /// Clone a node by making a new node and making all the nodes
     /// that previously pointed to the old node now point to the new
-    /// node, and the new node points to the old node.
-    fn clone(&mut self, node_id: usize) -> Result<(), Self::Error>;
+    /// node, and the new node points to the old node.  Return the
+    /// index of the new node.
+    ///
+    /// The label of the new node will be given by the label
+    /// transformer.
+    fn clone_node<F>(&mut self, node_id: usize, clone_transform: F) -> Result<usize, Self::Error>
+    where
+        F: Fn(T) -> T;
 }
 
 pub mod default;