Smt: remove inner nodes when removing value

src/merkle/smt/full/mod.rs

@@ -232,6 +232,10 @@ impl SparseMerkleTree<SMT_DEPTH> for Smt {
         self.inner_nodes.insert(index, inner_node);
     }
 
+    fn remove_inner_node(&mut self, index: NodeIndex) {
+        let _ = self.inner_nodes.remove(&index);
+    }
+
     fn insert_value(&mut self, key: Self::Key, value: Self::Value) -> Option<Self::Value> {
         // inserting an `EMPTY_VALUE` is equivalent to removing any value associated with `key`
         if value != Self::EMPTY_VALUE {

src/merkle/smt/full/tests.rs

@@ -25,7 +25,7 @@ fn test_smt_insert_at_same_key() {
 
     // Insert value 1 and ensure root is as expected
     {
-        let leaf_node = build_single_leaf_node(key_1, value_1);
+        let leaf_node = build_empty_or_single_leaf_node(key_1, value_1);
         let tree_root = store.set_node(smt.root(), key_1_index, leaf_node).unwrap().root;
 
         let old_value_1 = smt.insert(key_1, value_1);
@@ -36,7 +36,7 @@ fn test_smt_insert_at_same_key() {
 
     // Insert value 2 and ensure root is as expected
     {
-        let leaf_node = build_single_leaf_node(key_1, value_2);
+        let leaf_node = build_empty_or_single_leaf_node(key_1, value_2);
         let tree_root = store.set_node(smt.root(), key_1_index, leaf_node).unwrap().root;
 
         let old_value_2 = smt.insert(key_1, value_2);
@@ -64,7 +64,7 @@ fn test_smt_insert_at_same_key_2() {
     let mut store: MerkleStore = {
         let mut store = MerkleStore::default();
 
-        let leaf_node = build_single_leaf_node(key_already_present, value_already_present);
+        let leaf_node = build_empty_or_single_leaf_node(key_already_present, value_already_present);
         store
             .set_node(*EmptySubtreeRoots::entry(SMT_DEPTH, 0), key_already_present_index, leaf_node)
             .unwrap();
@@ -109,10 +109,29 @@ fn test_smt_insert_at_same_key_2() {
     }
 }
 
-/// This test ensures that the root of the tree is as expected when we add 3 items at 3 different
-/// keys. This also tests that the merkle paths produced are as expected.
+/// This test ensures that the root of the tree is as expected when we add/remove 3 items at 3
+/// different keys. This also tests that the merkle paths produced are as expected.
 #[test]
-fn test_smt_insert_multiple_values() {
+fn test_smt_insert_and_remove_multiple_values() {
+    fn insert_values_and_assert_path(
+        smt: &mut Smt,
+        store: &mut MerkleStore,
+        key_values: &[(RpoDigest, Word)],
+    ) {
+        for &(key, value) in key_values {
+            let key_index: NodeIndex = LeafIndex::<SMT_DEPTH>::from(key).into();
+
+            let leaf_node = build_empty_or_single_leaf_node(key, value);
+            let tree_root = store.set_node(smt.root(), key_index, leaf_node).unwrap().root;
+
+            let _ = smt.insert(key, value);
+
+            assert_eq!(smt.root(), tree_root);
+
+            let expected_path = store.get_path(tree_root, key_index).unwrap();
+            assert_eq!(smt.open(&key).0, expected_path.path);
+        }
+    }
     let mut smt = Smt::default();
     let mut store: MerkleStore = MerkleStore::default();
 
@@ -140,22 +159,20 @@ fn test_smt_insert_multiple_values() {
     let value_2 = [ONE + ONE; WORD_SIZE];
     let value_3 = [ONE + ONE + ONE; WORD_SIZE];
 
+    // Insert values in the tree
     let key_values = [(key_1, value_1), (key_2, value_2), (key_3, value_3)];
+    insert_values_and_assert_path(&mut smt, &mut store, &key_values);
 
-    for (key, value) in key_values {
-        let key_index: NodeIndex = LeafIndex::<SMT_DEPTH>::from(key).into();
+    // Remove values from the tree
+    let key_empty_values = [(key_1, EMPTY_WORD), (key_2, EMPTY_WORD), (key_3, EMPTY_WORD)];
+    insert_values_and_assert_path(&mut smt, &mut store, &key_empty_values);
 
-        let leaf_node = build_single_leaf_node(key, value);
-        let tree_root = store.set_node(smt.root(), key_index, leaf_node).unwrap().root;
+    let empty_root = *EmptySubtreeRoots::entry(SMT_DEPTH, 0);
+    assert_eq!(smt.root(), empty_root);
 
-        let old_value = smt.insert(key, value);
-        assert_eq!(old_value, EMPTY_WORD);
-
-        assert_eq!(smt.root(), tree_root);
-
-        let expected_path = store.get_path(tree_root, key_index).unwrap();
-        assert_eq!(smt.open(&key).0, expected_path.path);
-    }
+    // an empty tree should have no leaves or inner nodes
+    assert!(smt.leaves.is_empty());
+    assert!(smt.inner_nodes.is_empty());
 }
 
 /// This tests that inserting the empty value does indeed remove the key-value contained at the
@@ -309,8 +326,12 @@ fn test_smt_entries() {
 // HELPERS
 // --------------------------------------------------------------------------------------------
 
-fn build_single_leaf_node(key: RpoDigest, value: Word) -> RpoDigest {
-    SmtLeaf::Single((key, value)).hash()
+fn build_empty_or_single_leaf_node(key: RpoDigest, value: Word) -> RpoDigest {
+    if value == EMPTY_WORD {
+        SmtLeaf::Empty.hash()
+    } else {
+        SmtLeaf::Single((key, value)).hash()
+    }
 }
 
 fn build_multiple_leaf_node(kv_pairs: &[(RpoDigest, Word)]) -> RpoDigest {

src/merkle/smt/mod.rs

@@ -5,7 +5,7 @@ use crate::{
     Word,
 };
 
-use super::{MerkleError, MerklePath, NodeIndex, Vec};
+use super::{EmptySubtreeRoots, MerkleError, MerklePath, NodeIndex, Vec};
 
 mod full;
 pub use full::{Smt, SmtLeaf, SMT_DEPTH};
@@ -118,16 +118,27 @@ pub(crate) trait SparseMerkleTree<const DEPTH: u8> {
         mut index: NodeIndex,
         node_hash_at_index: RpoDigest,
     ) {
-        let mut value = node_hash_at_index;
-        for _ in 0..index.depth() {
+        let mut node_hash = node_hash_at_index;
+        for node_depth in (0..index.depth()).rev() {
             let is_right = index.is_value_odd();
             index.move_up();
             let InnerNode { left, right } = self.get_inner_node(index);
-            let (left, right) = if is_right { (left, value) } else { (value, right) };
-            self.insert_inner_node(index, InnerNode { left, right });
-            value = Rpo256::merge(&[left, right]);
+            let (left, right) = if is_right {
+                (left, node_hash)
+            } else {
+                (node_hash, right)
+            };
+            node_hash = Rpo256::merge(&[left, right]);
+
+            if node_hash == *EmptySubtreeRoots::entry(DEPTH, node_depth) {
+                // If a subtree is empty, when can remove the inner node, since it's equal to the
+                // default value
+                self.remove_inner_node(index)
+            } else {
+                self.insert_inner_node(index, InnerNode { left, right });
+            }
         }
-        self.set_root(value);
+        self.set_root(node_hash);
     }
 
     // REQUIRED METHODS
@@ -145,6 +156,9 @@ pub(crate) trait SparseMerkleTree<const DEPTH: u8> {
     /// Inserts an inner node at the given index
     fn insert_inner_node(&mut self, index: NodeIndex, inner_node: InnerNode);
 
+    /// Removes an inner node at the given index
+    fn remove_inner_node(&mut self, index: NodeIndex);
+
     /// Inserts a leaf node, and returns the value at the key if already exists
     fn insert_value(&mut self, key: Self::Key, value: Self::Value) -> Option<Self::Value>;
 

src/merkle/smt/simple/mod.rs

@@ -275,6 +275,10 @@ impl<const DEPTH: u8> SparseMerkleTree<DEPTH> for SimpleSmt<DEPTH> {
         self.inner_nodes.insert(index, inner_node);
     }
 
+    fn remove_inner_node(&mut self, index: NodeIndex) {
+        let _ = self.inner_nodes.remove(&index);
+    }
+
     fn insert_value(&mut self, key: LeafIndex<DEPTH>, value: Word) -> Option<Word> {
         self.leaves.insert(key.value(), value)
     }