feat(smt): impl constructing leaves that don't yet exist

This commit implements 'prospective leaf construction' -- computing
sparse Merkle tree leaves for a key-value insertion without actually
performing that insertion.

For SimpleSmt, this is trivial, since the leaf type is simply the value
being inserted.

For the full Smt, the new leaf payload depends on the existing payload
in that leaf. Since almost all leaves are very small, we can just clone
the leaf and modify a copy.

This will allow us to perform more general prospective changes on Merkle
trees.

src/merkle/smt/full/leaf.rs

@@ -350,7 +350,7 @@ impl Deserializable for SmtLeaf {
 // ================================================================================================
 
 /// Converts a key-value tuple to an iterator of `Felt`s
-fn kv_to_elements((key, value): (RpoDigest, Word)) -> impl Iterator<Item = Felt> {
+pub(crate) fn kv_to_elements((key, value): (RpoDigest, Word)) -> impl Iterator<Item = Felt> {
     let key_elements = key.into_iter();
     let value_elements = value.into_iter();
 
@@ -359,7 +359,7 @@ fn kv_to_elements((key, value): (RpoDigest, Word)) -> impl Iterator<Item = Felt>
 
 /// Compares two keys, compared element-by-element using their integer representations starting with
 /// the most significant element.
-fn cmp_keys(key_1: RpoDigest, key_2: RpoDigest) -> Ordering {
+pub(crate) fn cmp_keys(key_1: RpoDigest, key_2: RpoDigest) -> Ordering {
     for (v1, v2) in key_1.iter().zip(key_2.iter()).rev() {
         let v1 = v1.as_int();
         let v2 = v2.as_int();

src/merkle/smt/full/mod.rs

@@ -263,6 +263,28 @@ impl SparseMerkleTree<SMT_DEPTH> for Smt {
         leaf.hash()
     }
 
+    fn construct_prospective_leaf(
+        &self,
+        mut existing_leaf: SmtLeaf,
+        key: &RpoDigest,
+        value: &Word,
+    ) -> SmtLeaf {
+        debug_assert_eq!(existing_leaf.index(), Self::key_to_leaf_index(key));
+
+        match existing_leaf {
+            SmtLeaf::Empty(_) => SmtLeaf::new_single(*key, *value),
+            _ => {
+                if *value != EMPTY_WORD {
+                    existing_leaf.insert(*key, *value);
+                } else {
+                    existing_leaf.remove(*key);
+                }
+
+                existing_leaf
+            },
+        }
+    }
+
     fn key_to_leaf_index(key: &RpoDigest) -> LeafIndex<SMT_DEPTH> {
         let most_significant_felt = key[3];
         LeafIndex::new_max_depth(most_significant_felt.as_int())

src/merkle/smt/full/tests.rs

@@ -2,7 +2,7 @@ use alloc::vec::Vec;
 
 use super::{Felt, LeafIndex, NodeIndex, Rpo256, RpoDigest, Smt, SmtLeaf, EMPTY_WORD, SMT_DEPTH};
 use crate::{
-    merkle::{EmptySubtreeRoots, MerkleStore},
+    merkle::{smt::SparseMerkleTree, EmptySubtreeRoots, MerkleStore},
     utils::{Deserializable, Serializable},
     Word, ONE, WORD_SIZE,
 };
@@ -258,6 +258,119 @@ fn test_smt_removal() {
     }
 }
 
+/// This tests that we can correctly calculate prospective leaves -- that is, we can construct
+/// correct [`SmtLeaf`] values for a theoretical insertion on a Merkle tree without mutating or
+/// cloning the tree.
+#[test]
+fn test_prospective_hash() {
+    let mut smt = Smt::default();
+
+    let raw = 0b_01101001_01101100_00011111_11111111_10010110_10010011_11100000_00000000_u64;
+
+    let key_1: RpoDigest = RpoDigest::from([ONE, ONE, ONE, Felt::new(raw)]);
+    let key_2: RpoDigest =
+        RpoDigest::from([2_u32.into(), 2_u32.into(), 2_u32.into(), Felt::new(raw)]);
+    // Sort key_3 before key_1, to test non-append insertion.
+    let key_3: RpoDigest =
+        RpoDigest::from([0_u32.into(), 0_u32.into(), 0_u32.into(), Felt::new(raw)]);
+
+    let value_1 = [ONE; WORD_SIZE];
+    let value_2 = [2_u32.into(); WORD_SIZE];
+    let value_3: [Felt; 4] = [3_u32.into(); WORD_SIZE];
+
+    // insert key-value 1
+    {
+        let prospective =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_1), &key_1, &value_1).hash();
+        smt.insert(key_1, value_1);
+
+        let leaf = smt.get_leaf(&key_1);
+        assert_eq!(
+            prospective,
+            leaf.hash(),
+            "prospective hash for leaf {leaf:?} did not match actual hash",
+        );
+    }
+
+    // insert key-value 2
+    {
+        let prospective =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_2), &key_2, &value_2).hash();
+        smt.insert(key_2, value_2);
+
+        let leaf = smt.get_leaf(&key_2);
+        assert_eq!(
+            prospective,
+            leaf.hash(),
+            "prospective hash for leaf {leaf:?} did not match actual hash",
+        );
+    }
+
+    // insert key-value 3
+    {
+        let prospective =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_3), &key_3, &value_3).hash();
+        smt.insert(key_3, value_3);
+
+        let leaf = smt.get_leaf(&key_3);
+        assert_eq!(
+            prospective,
+            leaf.hash(),
+            "prospective hash for leaf {leaf:?} did not match actual hash",
+        );
+    }
+
+    // remove key 3
+    {
+        let old_leaf = smt.get_leaf(&key_3);
+        let old_value_3 = smt.insert(key_3, EMPTY_WORD);
+        assert_eq!(old_value_3, value_3);
+        let prospective_leaf =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_3), &key_3, &old_value_3);
+
+        assert_eq!(
+            old_leaf.hash(),
+            prospective_leaf.hash(),
+            "removing and prospectively re-adding a leaf didn't yield the original leaf:\
+            \n  original leaf:    {old_leaf:?}\
+            \n  prospective leaf: {prospective_leaf:?}",
+        );
+    }
+
+    // remove key 2
+    {
+        let old_leaf = smt.get_leaf(&key_2);
+        let old_value_2 = smt.insert(key_2, EMPTY_WORD);
+        assert_eq!(old_value_2, value_2);
+        let prospective_leaf =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_2), &key_2, &old_value_2);
+
+        assert_eq!(
+            old_leaf.hash(),
+            prospective_leaf.hash(),
+            "removing and prospectively re-adding a leaf didn't yield the original leaf:\
+            \n  original leaf:    {old_leaf:?}\
+            \n  prospective leaf: {prospective_leaf:?}",
+        );
+    }
+
+    // remove key 1
+    {
+        let old_leaf = smt.get_leaf(&key_1);
+        let old_value_1 = smt.insert(key_1, EMPTY_WORD);
+        assert_eq!(old_value_1, value_1);
+        let prospective_leaf =
+            smt.construct_prospective_leaf(smt.get_leaf(&key_1), &key_1, &old_value_1);
+        assert_eq!(
+            old_leaf.hash(),
+            prospective_leaf.hash(),
+            "removing and prospectively re-adding a leaf didn't yield the original leaf:\
+            \n  original leaf:    {old_leaf:?}\
+            \n  prospective leaf: {prospective_leaf:?}",
+        );
+    }
+}
+
 /// Tests that 2 key-value pairs stored in the same leaf have the same path
 #[test]
 fn test_smt_path_to_keys_in_same_leaf_are_equal() {

src/merkle/smt/mod.rs

@@ -167,6 +167,20 @@ pub(crate) trait SparseMerkleTree<const DEPTH: u8> {
     /// Returns the hash of a leaf
     fn hash_leaf(leaf: &Self::Leaf) -> RpoDigest;
 
+    /// Returns what `existing_leaf` would look like if `key` and `value` WERE inserted into the
+    /// tree, without mutating the tree itself.
+    ///
+    /// `existing_leaf` must have the same index as the key, or the result will be meaningless. To
+    /// get a prospective leaf based on the current state of the tree, use `self.get_leaf(key)` as
+    /// the argument for `existing_leaf`. The return value from this function can be chained back
+    /// into this function as the first argument to continue making prospective changes.
+    fn construct_prospective_leaf(
+        &self,
+        existing_leaf: Self::Leaf,
+        key: &Self::Key,
+        value: &Self::Value,
+    ) -> Self::Leaf;
+
     /// Maps a key to a leaf index
     fn key_to_leaf_index(key: &Self::Key) -> LeafIndex<DEPTH>;
 

src/merkle/smt/simple/mod.rs

@@ -302,6 +302,15 @@ impl<const DEPTH: u8> SparseMerkleTree<DEPTH> for SimpleSmt<DEPTH> {
         leaf.into()
     }
 
+    fn construct_prospective_leaf(
+        &self,
+        _existing_leaf: Word,
+        _key: &LeafIndex<DEPTH>,
+        value: &Word,
+    ) -> Word {
+        *value
+    }
+
     fn key_to_leaf_index(key: &LeafIndex<DEPTH>) -> LeafIndex<DEPTH> {
         *key
     }