diff --git a/.github/workflows/check.yml b/.github/workflows/check.yml
index 33cf544..aced2f1 100644
--- a/.github/workflows/check.yml
+++ b/.github/workflows/check.yml
@@ -21,9 +21,6 @@ on:
 concurrency:
   group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }}
   cancel-in-progress: true
-defaults:
- run:
-  working-directory: ./optd-persistent
 name: check
 jobs:
   fmt:
@@ -61,22 +58,6 @@ jobs:
           components: clippy
       - name: cargo clippy
         run: cargo clippy --locked --all-targets --all-features -- -D warnings
-  doc:
-    # run docs generation on nightly rather than stable. This enables features like
-    # https://doc.rust-lang.org/beta/unstable-book/language-features/doc-cfg.html which allows an
-    # API be documented as only available in some specific platforms.
-    runs-on: ubuntu-latest
-    name: nightly / doc
-    steps:
-      - uses: actions/checkout@v4
-        with:
-          submodules: true
-      - name: Install nightly
-        uses: dtolnay/rust-toolchain@nightly
-      - name: Install cargo-docs-rs
-        uses: dtolnay/install@cargo-docs-rs
-      - name: cargo docs-rs
-        run: cargo docs-rs
   hack:
     # cargo-hack checks combinations of feature flags to ensure that features are all additive
     # which is required for feature unification
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index d6253a0..565c9eb 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -17,9 +17,6 @@ on:
 concurrency:
   group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }}
   cancel-in-progress: true
-defaults:
- run:
-  working-directory: ./optd-persistent
 name: test
 jobs:
   required:
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..86281ff
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,13 @@
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+debug/
+target/
+
+# These are backup files generated by rustfmt.
+**/*.rs.bk
+
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+**/*.db
+
+# We will check in all code-generated entity files, as newer versions of `sea-orm-cli` might
+# conflict with previous versions.
+# **/entities
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..8acb13b
--- /dev/null
+++ b/Cargo.lock
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diff --git a/optd-mvp/Cargo.toml b/optd-mvp/Cargo.toml
new file mode 100644
index 0000000..f4a3a62
--- /dev/null
+++ b/optd-mvp/Cargo.toml
@@ -0,0 +1,29 @@
+[package]
+name = "optd-mvp"
+version = "0.1.0"
+edition = "2021"
+authors = ["Connor Tsui"]
+
+[dependencies]
+
+# `VARIANTS` constant made public in "1.1.1".
+sea-orm = { version = "1.1.1", features = [
+    "sqlx-sqlite",
+    "runtime-tokio-rustls",
+    "macros",
+    "debug-print",
+    "with-json",
+] }
+sea-orm-migration = "1.0"
+serde = "1.0"
+serde_json = "1.0.118" # Support `Hash` on `serde_json::Value` in "1.0.118".
+tokio = { version = "1.0", features = ["macros", "rt-multi-thread"] }
+trait-variant = "0.1.2" # Support `make(Send)` syntax in "0.1.2".
+thiserror = "2.0"
+fxhash = "0.2"
+
+# Pin more recent versions for `-Zminimal-versions`.
+async-trait = "0.1.43" # Remove lifetime parameter from "0.1.42".
+async-stream = "0.3.1"  # Fix unsatisfied trait bound from "0.3.0".
+strum = "0.26.0" # Fix `std::marker::Sized` from "0.25.0".
+
diff --git a/optd-mvp/DESIGN.md b/optd-mvp/DESIGN.md
new file mode 100644
index 0000000..6d1863d
--- /dev/null
+++ b/optd-mvp/DESIGN.md
@@ -0,0 +1,214 @@
+# Duplicate Elimination Memo Table
+
+_Connor Tsui, December 2024_
+
+Note that most of the details are in `src/memo/persistent/implementation.rs`.
+
+For this document, we are assuming that the memo table is backed by a database / ORM. Both the
+problems and the features detailed in this document are unique to this design, and likely do not
+apply to an in-memory memo table.
+
+## Group Merging
+
+During logical exploration, there will be rules that create cycles between groups. The easy solution
+for this is to immediately merge two groups together when the engine determines that adding an
+expression would result in a duplicate expression from another group.
+
+However, if we want to support parallel exploration, this could be prone to high contention. By
+definition, merging group 1 into group 2 would mean that _every expression_ that has a child of
+group 1 with would need to be rewritten to point to group 2 instead.
+
+This is prohibitive in a parallel setting, as that would mean every single task that gets affected
+would need to either wait for the rewrites to happen before resuming work, or potentially need to
+abort their work because data has changed underneath them.
+
+So immediate / eager group merging is not a great idea for parallel exploration. However, if we
+don't merge two groups that are equivalent, we are subject to doing duplicate work for every
+duplicate expression in the memo table during physical optimization.
+
+Instead of merging groups together immediately, we can instead maintain an auxiliary data structure
+that records the groups that _eventually_ need to get merged, and "lazily" merge those groups
+together once every group has finished exploration. We will refer to merging groups as the act of
+recording that the groups should eventually be merged together after exploration is finished.
+
+## Union-Find Group Sets
+
+We use the well-known Union-Find algorithm and corresponding data structure as the auxiliary data
+structure that tracks the to-be-merged groups.
+
+Union-Find supports `Union` and `Find` operations, where `Union` merges sets and `Find` searches for
+a "canonical" or "root" element that is shared between all elements in a given set. Note that we
+will also support an iteration operation that iterates over all elements in a given set. We will
+need this for [duplicate detection](#fingerprinting--group-merge), which is explained below.
+
+For more information about Union-Find, see these
+[15-451 lecture notes](https://www.cs.cmu.edu/~15451-f24/lectures/lecture08-union-find.pdf). We will
+use the exact same data structure, but add an additional `next` pointer for each node that embeds
+a circular linked list for each set.
+
+Here, we make the elements the groups themselves (really the group IDs), which allows us to merge
+group sets together and also determine a "root group" that all groups in a set can agree on.
+
+When every group in a group set has finished exploration, we can safely begin to merge them
+together by moving all expressions from every group in the group set into a single large group.
+Other than making sure that any reference to an old group in the group set points to this new large
+group, exploration of all groups is done and physical optimization can start.
+
+Note that since we are now waiting for exploration of all groups to finish, this algorithm is much
+closer to the Volcano framework than the Cascades' incremental search. However, since we eventually
+will want to store trails / breadcrumbs of decisions made to skip work in the future, and since we
+essentially have unlimited space due to the memo table being backed by a DBMS, this is not as much
+of a problem.
+
+## Duplicate Detection
+
+Deciding that we will merge groups lazily does not solve all of our problems. We have to know _when_
+we want to merge these groups.
+
+A naive approach is to simply loop over every expression in the memo table and check if we are about
+to insert a duplicate. This, of course, is bad for performance.
+
+We will use a fingerprinting / hashing method to detect when a duplicate expression might be
+inserted into the memo table (returning an error instead of inserting), and we will use that to
+trigger group merges.
+
+For every logical expression we insert into the memo table, we will create a fingerprint that
+contains both the kind of expression / relation (Scan, Filter, Join) and a hash of all
+information that makes that expression unique. For example:
+
+-   The fingerprint of a Scan should probably contain a hash of the table name and the pushdown
+    predicate.
+-   The fingerprint of a Filter should probably contain a hash of its child group ID and predicate.
+-   The fingerprint of a Join should probably contain a hash of the left group ID and the right group
+    ID, as well as the join predicate.
+
+Note that the above descriptions are slightly inaccurate, and we'll explain why in a later
+[section](#fingerprinting--group-merge).
+
+Also, if we have duplicate detection for logical expression, and we do not start physical
+optimization until after full plan enumeration, then we do not actually need to do duplicate
+detection of physical expressions, since they are derivative of the deduplicated logical
+expressions.
+
+### Fingerprint Matching Algorithm
+
+When an expression is added to the memo table, it will first calculate the fingerprint of the
+expression. The memo table will compare this fingerprint with every fingerprint in the memo table to
+check if we have seen this expression before (in any group). While this is effectively a scan
+through every expression, supporting the fingerprint table with an B+tree index will speed up this
+operation dramatically (since these fingerprints can be sorted by expression / relation kind).
+
+If there are no identical fingerprints, then there is no duplicate expression, and we can safely
+add the expression into the memo table. However, if there are matching fingerprints, we need to
+further check for false positives due to hash collisions.
+
+We do full exact match equality checks with every expression that had a fingerprint match. If there
+are no exact matches, then we can safely add the expression into the memo table. However, if we find
+an exact match (note that there can be at most one exact match since we have an invariant that there
+cannot be duplicate expressions), then we know that the expression we are trying to add already
+exists in the memo table.
+
+### Fingerprinting + Group Merge
+
+There is a slight problem with the algorithm described above. It does not account for when a child
+group has merged into another group.
+
+For example, let's say we have groups 1, 2, and 3. We insert an expression Join(1, 2) into the
+memo table with its fingerprint calculated with groups 1 and 2. It is possible that we find out that
+groups 2 and 3 need to merged. This means that Join(1, 2) and Join (1, 3) are actually identical
+expressions, and the fingerprinting strategies for expressions described above do not handle this.
+
+We will solve this problem by adding allowing multiple fingerprints to reference the same logical
+expression, and we will generate a new fingerprint for every expression that is affected by a group
+merge / every expression who's parent group now has a new root group.
+
+In the above scenario, we will find every expression in the memo table that has group 2 as a child.
+For each expression, we will generate another fingerprint with group 2 "rewritten" as group 3 in the
+hash. Note that we _do not_ modify the original expression, we are simply adding another fingerprint
+into the memo table.
+
+Finally, we need to handle when multiple groups in a group set are merged into another group set.
+For example, if a left group set { 1, 2, 3, 4, 5 } with root 1 needs to be merged into a right group
+set { 6, 7, 8, 9, 10 } with root 6, then we need to generate a new fingerprint for every expression
+in groups 1, 2, 3, 4, and 5 with group 1 "rewritten" as group 6.
+
+More formally, we are maintaining this invariant:
+**For every expression, there exists a fingerprint that maps back to the expression that uses the**
+**root groups of their children to calculate the hash.**
+
+For example, if we have a group set { 1, 3, 5 } with root group 1 and group set { 2, 4, 6 } with
+root group 2, the fingerprint of Join(5, 4) should really be a fingerprint of Join(1, 2).
+
+This invariant means that when we are checking if some expression already exists, we should use the
+root groups of the child groups in our expression to calculate the fingerprint, and we can guarantee
+that no fingerprint matches implies no duplicates.
+
+A further implication of this invariant means that new fingerprints need to be generated every time
+we merge groups. If we have a left group set { 1, 3, 5 } with root group 1 and right group set
+{ 2, 4, 6 } with root group 2, and we merge the first group set into the second, then every
+expression that has a child group of 1, 3, or 5 now has a stale fingerprint that uses root group 1
+instead of root group 2.
+
+Thus, when we merge the left group into the right group, we need to do the following:
+
+1. Gather the group set, i.e. every single group that has root group 1 (iterate)
+2. Retrieve every single expression that has a child group in the group set (via junction table)
+3. Generate a new fingerprint for each expression and add it into the memo table
+
+The speed of steps 2 and 3 above are largely dependent on the backing DBMS. However, we can support
+step 1 directly in the union find data structure by maintain a circular linked list for every set.
+Each group now tracks both a `parent` pointer and a `next` pointer. When merging / unioning a set
+into another set, we swap the `next` pointers of the two roots to maintain the circular linked list.
+This allows us to do step 1 in linear time relative to the size of the group set.
+
+### Discovered Duplicates
+
+The above algorithm has one more problem: merging groups can cause the memo table to "discover" that
+there are duplicate expressions in the memo table.
+
+Here is an example: let's say we have the following groups, each with one expression (note that the
+example will work even with multiple expressions):
+
+1. `Scan(1)`
+2. `Scan(2)`
+3. `Filter(1)`
+4. `Filter(2)`
+5. `Filter(4)`
+6. `Join(3, 4)`
+7. `Join(3, 5)`
+8. `Sort(6)`
+9. `Sort(7)`
+
+Note how groups 5 is just a second filter on top of group 2. Suppose that we find out that
+`(Filter(4) = Filter(Filter(2))) == Filter(2)`. In that case, we need to merge groups 4 and 5. The
+problem here is that groups 6 and 7 are considered separate groups, but we have now discovered that
+they are actually the same. The same is true for groups 8 and 9. In this scenario, the merging of
+groups has "generated" a duplicate expression.
+
+However, this is not as big of a problem as it might seem. The issue we want to avoid is lots of
+duplicate work or even an infinite loop of rule application. Observe that if we apply a rule to both
+the expression in group 6 and group 7 that we will get the same exact expression.
+
+For example, if we apply join commutativity to the expression in group 6 (`Join(3, 4)`), we would
+add `Join(4, 3)` into group 6. When we apply join commutativity to the expression in group 7
+(`Join(3, 5)`), we would get back `Join(5, 3)`. However, the memo table will detect this as a
+duplicate because it will use the root group of 4 and 5 to generate the fingerprint and see that
+`Join(4, 3)` already exists. Again, similar logic applies for groups 8 and 9.
+
+At a high level, almost all of our operations are lazy. Work does not need to be done unless it is
+absolutely necessary for correctness. By allowing some amount of duplicates, we get some nice
+properties with respect to parallelizing memo table access.
+
+## Efficiency and Parallelism
+
+Fingerprinting by itself is very efficient, as creating a fingerprint and looking up a fingerprint
+can be made quite efficient with indexes. The real concern here is that merging two groups is very,
+very expensive. Depending on the workload, it is both possible that the amortized cost is low or
+that group merging takes a majority of the work.
+
+However, we must remember that we want to parallelize access to the memo table. The above algorithms
+are notably **read and append only**. There is never a point where we need to update an expression
+to maintain invariants. This is important, as it means that we can add and lookup expression and
+groups _without having to take any locks_. If we enforce a serializable isolation level, then every
+method on the memo table can be done in parallel with relatively low contention due to there being
+zero write-write conflicts.
diff --git a/optd-mvp/entities.md b/optd-mvp/entities.md
new file mode 100644
index 0000000..fc13a39
--- /dev/null
+++ b/optd-mvp/entities.md
@@ -0,0 +1,27 @@
+# Generate the `entities` module
+
+To make changes to the database tables and schema, you will have to modify files in the `migrator` module and then update the `entities` module using `sea-orm-cli`.
+
+This assumes that you already have the `sqlite3` binary installed. First, make sure you have installed `sea-orm-cli`:
+
+```sh
+$ cargo install sea-orm-cli
+```
+
+Make sure your working directory is in the crate root (not workspace):
+
+```sh
+$ cd optd-mvp
+```
+
+If you have not generate the `sqlite.db` file yet, you will need to run this command which will generate the `sqlite.db` file and run all of the migrations:
+
+```sh
+$ cargo run --bin migrate
+```
+
+Finally, run this command to generate / overwrite the `entities` module in the `src` directory.
+
+```sh
+$ sea-orm-cli generate entity -u sqlite:./sqlite.db -o src/entities
+```
diff --git a/optd-mvp/src/bin/migrate.rs b/optd-mvp/src/bin/migrate.rs
new file mode 100644
index 0000000..0634f23
--- /dev/null
+++ b/optd-mvp/src/bin/migrate.rs
@@ -0,0 +1,19 @@
+//! A simple script that generates the database file needed for `sea-orm-cli` to extract the schemas
+//! from and generate the `entities` module.
+
+use optd_mvp::{migrate, DATABASE_FILENAME, DATABASE_URL};
+use sea_orm::*;
+use sea_orm_migration::prelude::*;
+
+#[tokio::main]
+async fn main() {
+    let _ = std::fs::remove_file(DATABASE_FILENAME);
+
+    let db = Database::connect(DATABASE_URL)
+        .await
+        .expect("Unable to connect to the database");
+
+    migrate(&db)
+        .await
+        .expect("Something went wrong during migration");
+}
diff --git a/optd-mvp/src/entities/fingerprint.rs b/optd-mvp/src/entities/fingerprint.rs
new file mode 100644
index 0000000..608ca57
--- /dev/null
+++ b/optd-mvp/src/entities/fingerprint.rs
@@ -0,0 +1,33 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "fingerprint")]
+pub struct Model {
+    #[sea_orm(primary_key)]
+    pub id: i32,
+    pub logical_expression_id: i32,
+    pub kind: i16,
+    pub hash: i64,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(
+        belongs_to = "super::logical_expression::Entity",
+        from = "Column::LogicalExpressionId",
+        to = "super::logical_expression::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    LogicalExpression,
+}
+
+impl Related<super::logical_expression::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::LogicalExpression.def()
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/group.rs b/optd-mvp/src/entities/group.rs
new file mode 100644
index 0000000..b5b1686
--- /dev/null
+++ b/optd-mvp/src/entities/group.rs
@@ -0,0 +1,82 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "group")]
+pub struct Model {
+    #[sea_orm(primary_key)]
+    pub id: i32,
+    pub status: i8,
+    pub winner: Option<i32>,
+    pub cost: Option<i64>,
+    pub set_size: i32,
+    pub parent_id: Option<i32>,
+    pub next_id: Option<i32>,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(
+        belongs_to = "Entity",
+        from = "Column::NextId",
+        to = "Column::Id",
+        on_update = "Cascade",
+        on_delete = "SetNull"
+    )]
+    SelfRef2,
+    #[sea_orm(
+        belongs_to = "Entity",
+        from = "Column::ParentId",
+        to = "Column::Id",
+        on_update = "Cascade",
+        on_delete = "SetNull"
+    )]
+    SelfRef1,
+    #[sea_orm(has_many = "super::logical_children::Entity")]
+    LogicalChildren,
+    #[sea_orm(has_many = "super::logical_expression::Entity")]
+    LogicalExpression,
+    #[sea_orm(has_many = "super::physical_children::Entity")]
+    PhysicalChildren,
+    #[sea_orm(
+        belongs_to = "super::physical_expression::Entity",
+        from = "Column::Winner",
+        to = "super::physical_expression::Column::Id",
+        on_update = "Cascade",
+        on_delete = "SetNull"
+    )]
+    PhysicalExpression,
+}
+
+impl Related<super::logical_children::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::LogicalChildren.def()
+    }
+}
+
+impl Related<super::physical_children::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::PhysicalChildren.def()
+    }
+}
+
+impl Related<super::logical_expression::Entity> for Entity {
+    fn to() -> RelationDef {
+        super::logical_children::Relation::LogicalExpression.def()
+    }
+    fn via() -> Option<RelationDef> {
+        Some(super::logical_children::Relation::Group.def().rev())
+    }
+}
+
+impl Related<super::physical_expression::Entity> for Entity {
+    fn to() -> RelationDef {
+        super::physical_children::Relation::PhysicalExpression.def()
+    }
+    fn via() -> Option<RelationDef> {
+        Some(super::physical_children::Relation::Group.def().rev())
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/logical_children.rs b/optd-mvp/src/entities/logical_children.rs
new file mode 100644
index 0000000..31e86c9
--- /dev/null
+++ b/optd-mvp/src/entities/logical_children.rs
@@ -0,0 +1,46 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "logical_children")]
+pub struct Model {
+    #[sea_orm(primary_key, auto_increment = false)]
+    pub logical_expression_id: i32,
+    #[sea_orm(primary_key, auto_increment = false)]
+    pub group_id: i32,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(
+        belongs_to = "super::group::Entity",
+        from = "Column::GroupId",
+        to = "super::group::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    Group,
+    #[sea_orm(
+        belongs_to = "super::logical_expression::Entity",
+        from = "Column::LogicalExpressionId",
+        to = "super::logical_expression::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    LogicalExpression,
+}
+
+impl Related<super::group::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::Group.def()
+    }
+}
+
+impl Related<super::logical_expression::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::LogicalExpression.def()
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/logical_expression.rs b/optd-mvp/src/entities/logical_expression.rs
new file mode 100644
index 0000000..9311776
--- /dev/null
+++ b/optd-mvp/src/entities/logical_expression.rs
@@ -0,0 +1,56 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "logical_expression")]
+pub struct Model {
+    #[sea_orm(primary_key)]
+    pub id: i32,
+    pub group_id: i32,
+    pub kind: i16,
+    pub data: Json,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(has_many = "super::fingerprint::Entity")]
+    Fingerprint,
+    #[sea_orm(
+        belongs_to = "super::group::Entity",
+        from = "Column::GroupId",
+        to = "super::group::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    Group,
+    #[sea_orm(has_many = "super::logical_children::Entity")]
+    LogicalChildren,
+}
+
+impl Related<super::fingerprint::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::Fingerprint.def()
+    }
+}
+
+impl Related<super::logical_children::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::LogicalChildren.def()
+    }
+}
+
+impl Related<super::group::Entity> for Entity {
+    fn to() -> RelationDef {
+        super::logical_children::Relation::Group.def()
+    }
+    fn via() -> Option<RelationDef> {
+        Some(
+            super::logical_children::Relation::LogicalExpression
+                .def()
+                .rev(),
+        )
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/mod.rs b/optd-mvp/src/entities/mod.rs
new file mode 100644
index 0000000..8bdd8f7
--- /dev/null
+++ b/optd-mvp/src/entities/mod.rs
@@ -0,0 +1,10 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+pub mod prelude;
+
+pub mod fingerprint;
+pub mod group;
+pub mod logical_children;
+pub mod logical_expression;
+pub mod physical_children;
+pub mod physical_expression;
diff --git a/optd-mvp/src/entities/physical_children.rs b/optd-mvp/src/entities/physical_children.rs
new file mode 100644
index 0000000..94859a6
--- /dev/null
+++ b/optd-mvp/src/entities/physical_children.rs
@@ -0,0 +1,46 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "physical_children")]
+pub struct Model {
+    #[sea_orm(primary_key, auto_increment = false)]
+    pub physical_expression_id: i32,
+    #[sea_orm(primary_key, auto_increment = false)]
+    pub group_id: i32,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(
+        belongs_to = "super::group::Entity",
+        from = "Column::GroupId",
+        to = "super::group::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    Group,
+    #[sea_orm(
+        belongs_to = "super::physical_expression::Entity",
+        from = "Column::PhysicalExpressionId",
+        to = "super::physical_expression::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    PhysicalExpression,
+}
+
+impl Related<super::group::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::Group.def()
+    }
+}
+
+impl Related<super::physical_expression::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::PhysicalExpression.def()
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/physical_expression.rs b/optd-mvp/src/entities/physical_expression.rs
new file mode 100644
index 0000000..918ac03
--- /dev/null
+++ b/optd-mvp/src/entities/physical_expression.rs
@@ -0,0 +1,48 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+use sea_orm::entity::prelude::*;
+
+#[derive(Clone, Debug, PartialEq, DeriveEntityModel, Eq)]
+#[sea_orm(table_name = "physical_expression")]
+pub struct Model {
+    #[sea_orm(primary_key)]
+    pub id: i32,
+    pub group_id: i32,
+    pub kind: i16,
+    pub data: Json,
+}
+
+#[derive(Copy, Clone, Debug, EnumIter, DeriveRelation)]
+pub enum Relation {
+    #[sea_orm(
+        belongs_to = "super::group::Entity",
+        from = "Column::GroupId",
+        to = "super::group::Column::Id",
+        on_update = "Cascade",
+        on_delete = "Cascade"
+    )]
+    Group,
+    #[sea_orm(has_many = "super::physical_children::Entity")]
+    PhysicalChildren,
+}
+
+impl Related<super::physical_children::Entity> for Entity {
+    fn to() -> RelationDef {
+        Relation::PhysicalChildren.def()
+    }
+}
+
+impl Related<super::group::Entity> for Entity {
+    fn to() -> RelationDef {
+        super::physical_children::Relation::Group.def()
+    }
+    fn via() -> Option<RelationDef> {
+        Some(
+            super::physical_children::Relation::PhysicalExpression
+                .def()
+                .rev(),
+        )
+    }
+}
+
+impl ActiveModelBehavior for ActiveModel {}
diff --git a/optd-mvp/src/entities/prelude.rs b/optd-mvp/src/entities/prelude.rs
new file mode 100644
index 0000000..1e27a2c
--- /dev/null
+++ b/optd-mvp/src/entities/prelude.rs
@@ -0,0 +1,10 @@
+//! `SeaORM` Entity, @generated by sea-orm-codegen 1.1.2
+
+#![allow(unused_imports)]
+
+pub use super::fingerprint::Entity as Fingerprint;
+pub use super::group::Entity as Group;
+pub use super::logical_children::Entity as LogicalChildren;
+pub use super::logical_expression::Entity as LogicalExpression;
+pub use super::physical_children::Entity as PhysicalChildren;
+pub use super::physical_expression::Entity as PhysicalExpression;
diff --git a/optd-mvp/src/expression/logical_expression.rs b/optd-mvp/src/expression/logical_expression.rs
new file mode 100644
index 0000000..486f1cb
--- /dev/null
+++ b/optd-mvp/src/expression/logical_expression.rs
@@ -0,0 +1,223 @@
+//! Definition of logical expressions / relations in our query optimization framework.
+//!
+//! FIXME: All fields are placeholders.
+//!
+//! TODO Figure out if each relation should be in a different submodule.
+//! TODO This entire file is a WIP.
+
+use crate::{entities::logical_expression::Model, memo::GroupId};
+use fxhash::hash;
+use serde::{Deserialize, Serialize};
+use std::fmt::Debug;
+
+/// An interface defining what an in-memory logical expression representation should be able to do.
+pub trait LogicalExpression: From<Model> + Into<Model> + Clone + Debug {
+    /// Returns the kind of relation / operator node encoded as an integer.
+    fn kind(&self) -> i16;
+
+    /// Retrieves the child groups IDs of this logical expression.
+    fn children(&self) -> Vec<GroupId>;
+
+    /// Computes the fingerprint of this expression, which should generate an integer for equality
+    /// checks that has a low collision rate.
+    fn fingerprint(&self) -> i64;
+
+    /// Checks if the current expression is a duplicate of the other expression.
+    ///
+    /// Note that this is similar to `Eq` and `PartialEq`, but the implementor should be aware that
+    /// different expressions can be duplicates of each other without having the exact same data.
+    fn is_duplicate(&self, other: &Self) -> bool;
+
+    /// Rewrites the expression to use new child groups IDs, where `rewrites` is a slice of tuples
+    /// representing `(old_group_id, new_group_id)`.
+    ///
+    /// TODO: There's definitely a better way to represent this API
+    fn rewrite(&self, rewrites: &[(GroupId, GroupId)]) -> Self;
+}
+
+#[derive(Clone, Debug)]
+pub enum DefaultLogicalExpression {
+    Scan(Scan),
+    Filter(Filter),
+    Join(Join),
+}
+
+impl LogicalExpression for DefaultLogicalExpression {
+    fn kind(&self) -> i16 {
+        match self {
+            Self::Scan(_) => 0,
+            Self::Filter(_) => 1,
+            Self::Join(_) => 2,
+        }
+    }
+
+    fn children(&self) -> Vec<GroupId> {
+        match self {
+            Self::Scan(_) => vec![],
+            Self::Filter(filter) => vec![filter.child],
+            Self::Join(join) => vec![join.left, join.right],
+        }
+    }
+
+    fn fingerprint(&self) -> i64 {
+        let kind = self.kind() as u16 as usize;
+        let hash = match self {
+            Self::Scan(scan) => hash(scan.table.as_str()),
+            Self::Filter(filter) => hash(&filter.child.0) ^ hash(filter.expression.as_str()),
+            Self::Join(join) => {
+                // Make sure that there is a difference between `Join(A, B)` and `Join(B, A)`.
+                hash(&(join.left.0 + 1))
+                    ^ hash(&(join.right.0 + 2))
+                    ^ hash(join.expression.as_str())
+            }
+        };
+
+        // Mask out the bottom 16 bits of `hash` and replace them with `kind`.
+        ((hash & !0xFFFF) | kind) as i64
+    }
+
+    fn is_duplicate(&self, other: &Self) -> bool {
+        match (self, other) {
+            (Self::Scan(scan_left), Self::Scan(scan_right)) => scan_left.table == scan_right.table,
+            (Self::Filter(filter_left), Self::Filter(filter_right)) => {
+                filter_left.child == filter_right.child
+                    && filter_left.expression == filter_right.expression
+            }
+            (Self::Join(join_left), Self::Join(join_right)) => {
+                join_left.left == join_right.left
+                    && join_left.right == join_right.right
+                    && join_left.expression == join_right.expression
+            }
+            _ => false,
+        }
+    }
+
+    fn rewrite(&self, rewrites: &[(GroupId, GroupId)]) -> Self {
+        let rewrite = |x: GroupId| {
+            if rewrites.is_empty() {
+                return x;
+            }
+
+            if let Some(i) = rewrites.iter().position(|(curr, _new)| &x == curr) {
+                assert_eq!(rewrites[i].0, x);
+                rewrites[i].1
+            } else {
+                x
+            }
+        };
+
+        match self {
+            Self::Scan(_) => self.clone(),
+            Self::Filter(filter) => Self::Filter(Filter {
+                child: rewrite(filter.child),
+                expression: filter.expression.clone(),
+            }),
+            Self::Join(join) => Self::Join(Join {
+                left: rewrite(join.left),
+                right: rewrite(join.right),
+                expression: join.expression.clone(),
+            }),
+        }
+    }
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug)]
+pub struct Scan {
+    table: String,
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug)]
+pub struct Filter {
+    child: GroupId,
+    expression: String,
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug)]
+pub struct Join {
+    left: GroupId,
+    right: GroupId,
+    expression: String,
+}
+
+impl From<Model> for DefaultLogicalExpression {
+    fn from(value: Model) -> Self {
+        match value.kind {
+            0 => Self::Scan(
+                serde_json::from_value(value.data)
+                    .expect("unable to deserialize data into a logical `Scan`"),
+            ),
+            1 => Self::Filter(
+                serde_json::from_value(value.data)
+                    .expect("Unable to deserialize data into a logical `Filter`"),
+            ),
+            2 => Self::Join(
+                serde_json::from_value(value.data)
+                    .expect("Unable to deserialize data into a logical `Join`"),
+            ),
+            _ => panic!(),
+        }
+    }
+}
+
+impl From<DefaultLogicalExpression> for Model {
+    fn from(value: DefaultLogicalExpression) -> Model {
+        fn create_logical_expression(kind: i16, data: serde_json::Value) -> Model {
+            Model {
+                id: -1,
+                group_id: -1,
+                kind,
+                data,
+            }
+        }
+
+        let kind = value.kind();
+        match value {
+            DefaultLogicalExpression::Scan(scan) => create_logical_expression(
+                kind,
+                serde_json::to_value(scan).expect("unable to serialize logical `Scan`"),
+            ),
+            DefaultLogicalExpression::Filter(filter) => create_logical_expression(
+                kind,
+                serde_json::to_value(filter).expect("unable to serialize logical `Filter`"),
+            ),
+            DefaultLogicalExpression::Join(join) => create_logical_expression(
+                kind,
+                serde_json::to_value(join).expect("unable to serialize logical `Join`"),
+            ),
+        }
+    }
+}
+
+#[cfg(test)]
+pub use build::*;
+
+#[cfg(test)]
+mod build {
+    use super::*;
+    use crate::expression::DefaultLogicalExpression;
+
+    pub fn scan(table_schema: String) -> DefaultLogicalExpression {
+        DefaultLogicalExpression::Scan(Scan {
+            table: table_schema,
+        })
+    }
+
+    pub fn filter(child_group: GroupId, expression: String) -> DefaultLogicalExpression {
+        DefaultLogicalExpression::Filter(Filter {
+            child: child_group,
+            expression,
+        })
+    }
+
+    pub fn join(
+        left_group: GroupId,
+        right_group: GroupId,
+        expression: String,
+    ) -> DefaultLogicalExpression {
+        DefaultLogicalExpression::Join(Join {
+            left: left_group,
+            right: right_group,
+            expression,
+        })
+    }
+}
diff --git a/optd-mvp/src/expression/mod.rs b/optd-mvp/src/expression/mod.rs
new file mode 100644
index 0000000..0efbb44
--- /dev/null
+++ b/optd-mvp/src/expression/mod.rs
@@ -0,0 +1,9 @@
+//! In-memory representation of logical and physical expression / operators / relations.
+//!
+//! TODO more docs.
+
+mod logical_expression;
+pub use logical_expression::*;
+
+mod physical_expression;
+pub use physical_expression::*;
diff --git a/optd-mvp/src/expression/physical_expression.rs b/optd-mvp/src/expression/physical_expression.rs
new file mode 100644
index 0000000..d7f71de
--- /dev/null
+++ b/optd-mvp/src/expression/physical_expression.rs
@@ -0,0 +1,126 @@
+//! Definition of physical expressions / operators in our query optimization framework.
+//!
+//! FIXME: All fields are placeholders.
+//!
+//! TODO Remove dead code.
+//! TODO Figure out if each operator should be in a different submodule.
+//! TODO This entire file is a WIP.
+
+#![allow(dead_code)]
+
+use crate::{entities::physical_expression::Model, memo::GroupId};
+use serde::{Deserialize, Serialize};
+use std::fmt::Debug;
+
+/// An interface defining what an in-memory physical expression representation should be able to do.
+pub trait PhysicalExpression: From<Model> + Into<Model> + Clone + Debug {
+    /// Returns the kind of relation / operator node encoded as an integer.
+    fn kind(&self) -> i16;
+
+    /// Retrieves the child groups IDs of this logical expression.
+    fn children(&self) -> Vec<GroupId>;
+}
+
+impl PhysicalExpression for DefaultPhysicalExpression {
+    fn kind(&self) -> i16 {
+        match self {
+            Self::TableScan(_) => 0,
+            Self::Filter(_) => 1,
+            Self::HashJoin(_) => 2,
+        }
+    }
+
+    fn children(&self) -> Vec<GroupId> {
+        match self {
+            Self::TableScan(_) => vec![],
+            Self::Filter(filter) => vec![filter.child],
+            Self::HashJoin(hash_join) => vec![hash_join.left, hash_join.right],
+        }
+    }
+}
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum DefaultPhysicalExpression {
+    TableScan(TableScan),
+    Filter(PhysicalFilter),
+    HashJoin(HashJoin),
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug, PartialEq, Eq)]
+pub struct TableScan {
+    table_schema: String,
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug, PartialEq, Eq)]
+pub struct PhysicalFilter {
+    child: GroupId,
+    expression: String,
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug, PartialEq, Eq)]
+pub struct HashJoin {
+    left: GroupId,
+    right: GroupId,
+    expression: String,
+}
+
+impl From<Model> for DefaultPhysicalExpression {
+    fn from(value: Model) -> Self {
+        match value.kind {
+            0 => Self::TableScan(
+                serde_json::from_value(value.data)
+                    .expect("unable to deserialize data into a physical `TableScan`"),
+            ),
+            1 => Self::Filter(
+                serde_json::from_value(value.data)
+                    .expect("Unable to deserialize data into a physical `Filter`"),
+            ),
+            2 => Self::HashJoin(
+                serde_json::from_value(value.data)
+                    .expect("Unable to deserialize data into a physical `HashJoin`"),
+            ),
+            _ => panic!(),
+        }
+    }
+}
+
+impl From<DefaultPhysicalExpression> for Model {
+    fn from(value: DefaultPhysicalExpression) -> Model {
+        fn create_physical_expression(kind: i16, data: serde_json::Value) -> Model {
+            Model {
+                id: -1,
+                group_id: -1,
+                kind,
+                data,
+            }
+        }
+
+        match value {
+            DefaultPhysicalExpression::TableScan(scan) => create_physical_expression(
+                0,
+                serde_json::to_value(scan).expect("unable to serialize physical `TableScan`"),
+            ),
+            DefaultPhysicalExpression::Filter(filter) => create_physical_expression(
+                1,
+                serde_json::to_value(filter).expect("unable to serialize physical `Filter`"),
+            ),
+            DefaultPhysicalExpression::HashJoin(join) => create_physical_expression(
+                2,
+                serde_json::to_value(join).expect("unable to serialize physical `HashJoin`"),
+            ),
+        }
+    }
+}
+
+#[cfg(test)]
+pub use build::*;
+
+#[cfg(test)]
+mod build {
+    use super::*;
+    use crate::expression::DefaultPhysicalExpression;
+
+    pub fn table_scan(table_schema: String) -> DefaultPhysicalExpression {
+        DefaultPhysicalExpression::TableScan(TableScan { table_schema })
+    }
+}
diff --git a/optd-mvp/src/lib.rs b/optd-mvp/src/lib.rs
new file mode 100644
index 0000000..2e238e0
--- /dev/null
+++ b/optd-mvp/src/lib.rs
@@ -0,0 +1,45 @@
+//! This crate is an attempt to make an MVP of a duplicate-detecting memo table for query
+//! optimization.
+//!
+//! TODO write more docs.
+
+use sea_orm::*;
+use sea_orm_migration::prelude::*;
+use thiserror::Error;
+
+mod migrator;
+use migrator::Migrator;
+
+mod entities;
+
+pub mod expression;
+pub mod memo;
+
+/// The filename of the SQLite database for migration.
+pub const DATABASE_FILENAME: &str = "sqlite.db";
+/// The URL of the SQLite database for migration.
+pub const DATABASE_URL: &str = "sqlite:./sqlite.db?mode=rwc";
+
+/// An error type wrapping all the different kinds of error the optimizer might raise.
+#[allow(missing_docs)]
+#[derive(Error, Debug)]
+pub enum OptimizerError {
+    #[error("SeaORM error")]
+    Database(#[from] sea_orm::error::DbErr),
+    #[error("Memo table logical error")]
+    Memo(#[from] memo::MemoError),
+    #[error("unknown error")]
+    Unknown,
+}
+
+/// Shorthand for a [`Result`] with an error type [`OptimizerError`].
+pub type OptimizerResult<T> = Result<T, OptimizerError>;
+
+/// Applies all migrations.
+///
+/// # Errors
+///
+/// Returns a [`DbErr`] if unable to apply any migrations.
+pub async fn migrate(db: &DatabaseConnection) -> Result<(), DbErr> {
+    Migrator::refresh(db).await
+}
diff --git a/optd-mvp/src/main.rs b/optd-mvp/src/main.rs
new file mode 100644
index 0000000..e7a11a9
--- /dev/null
+++ b/optd-mvp/src/main.rs
@@ -0,0 +1,3 @@
+fn main() {
+    println!("Hello, world!");
+}
diff --git a/optd-mvp/src/memo/mod.rs b/optd-mvp/src/memo/mod.rs
new file mode 100644
index 0000000..690bdee
--- /dev/null
+++ b/optd-mvp/src/memo/mod.rs
@@ -0,0 +1,52 @@
+//! This module contains items related to the memo table.
+//!
+//! TODO more docs.
+
+#![warn(missing_docs)]
+#![warn(clippy::missing_docs_in_private_items)]
+#![warn(clippy::missing_errors_doc)]
+#![warn(clippy::missing_panics_doc)]
+#![warn(clippy::missing_safety_doc)]
+
+use serde::{Deserialize, Serialize};
+use thiserror::Error;
+
+/// A new type of an integer identifying a unique group.
+#[derive(Serialize, Deserialize, Clone, Copy, Debug, PartialEq, Eq)]
+#[serde(transparent)]
+pub struct GroupId(pub i32);
+
+/// A new type of an integer identifying a unique logical expression.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct LogicalExpressionId(pub i32);
+
+/// A new type of an integer identifying a unique physical expression.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct PhysicalExpressionId(pub i32);
+
+/// A status enum representing the different states a group can be during query optimization.
+#[repr(u8)]
+pub enum GroupStatus {
+    /// Represents a group that is currently being logically explored.
+    InProgress = 0,
+    /// Represents a logically explored group that is currently being physically optimized.
+    Explored = 1,
+    /// Represents a fully optimized group.
+    Optimized = 2,
+}
+
+/// The different kinds of errors that might occur while running operations on a memo table.
+#[allow(missing_docs)]
+#[derive(Error, Debug)]
+pub enum MemoError {
+    #[error("unknown group ID {0:?}")]
+    UnknownGroup(GroupId),
+    #[error("unknown logical expression ID {0:?}")]
+    UnknownLogicalExpression(LogicalExpressionId),
+    #[error("unknown physical expression ID {0:?}")]
+    UnknownPhysicalExpression(PhysicalExpressionId),
+    #[error("invalid expression encountered")]
+    InvalidExpression,
+}
+
+pub mod persistent;
diff --git a/optd-mvp/src/memo/persistent/implementation.rs b/optd-mvp/src/memo/persistent/implementation.rs
new file mode 100644
index 0000000..9ce30ce
--- /dev/null
+++ b/optd-mvp/src/memo/persistent/implementation.rs
@@ -0,0 +1,764 @@
+//! This module contains the implementation of [`PersistentMemo`].
+//!
+//! TODO For parallelism, almost all of these methods need to be under transactions.
+//! TODO Write more docs.
+//! TODO Remove dead code.
+
+#![allow(dead_code)]
+
+use super::{PersistentMemo, PersistentMemoTransaction};
+use crate::{
+    entities::*,
+    expression::{LogicalExpression, PhysicalExpression},
+    memo::{GroupId, GroupStatus, LogicalExpressionId, MemoError, PhysicalExpressionId},
+    OptimizerResult, DATABASE_URL,
+};
+use sea_orm::{
+    entity::{prelude::*, IntoActiveModel, NotSet, Set},
+    Database, DatabaseTransaction, TransactionTrait,
+};
+use std::{collections::HashSet, marker::PhantomData};
+
+impl<L, P> PersistentMemo<L, P>
+where
+    L: LogicalExpression,
+    P: PhysicalExpression,
+{
+    /// Creates a new `PersistentMemo` struct by connecting to a database defined at
+    /// [`DATABASE_URL`].
+    ///
+    /// # Panics
+    ///
+    /// Panics if unable to create a databse connection to [`DATABASE_URL`].
+    pub async fn new() -> Self {
+        Self {
+            db: Database::connect(DATABASE_URL).await.unwrap(),
+            _phantom_logical: PhantomData,
+            _phantom_physical: PhantomData,
+        }
+    }
+
+    /// Starts a new database transaction.
+    ///
+    /// # Errors
+    ///
+    /// Returns a [`DbErr`] if unable to create a new transaction.
+    pub async fn begin(&self) -> OptimizerResult<PersistentMemoTransaction<L, P>> {
+        Ok(PersistentMemoTransaction::new(self.db.begin().await?).await)
+    }
+
+    /// Deletes all objects in the backing database.
+    ///
+    /// Since there is no asynchronous drop yet in Rust, in order to drop all objects in the
+    /// database, the user must call this manually.
+    ///
+    /// # Panics
+    ///
+    /// May panic if unable to delete entities from any table.
+    pub async fn cleanup(&self) {
+        /// Simple private macro to teardown all tables in the database.
+        /// Note that these have to be specified manually, so when adding a new table to the
+        /// database, we must make sure to add that table here.
+        macro_rules! delete_all {
+            ($($module: ident),+ $(,)?) => {
+                $(
+                    $module::Entity::delete_many()
+                        .exec(&self.db)
+                        .await
+                        .unwrap();
+                )+
+            };
+        }
+
+        delete_all! {
+            group,
+            fingerprint,
+            logical_expression,
+            logical_children,
+            physical_expression,
+            physical_children
+        };
+    }
+}
+
+impl<L, P> PersistentMemoTransaction<L, P>
+where
+    L: LogicalExpression,
+    P: PhysicalExpression,
+{
+    /// Creates a new transaction object.
+    pub async fn new(txn: DatabaseTransaction) -> Self {
+        Self {
+            txn,
+            _phantom_logical: PhantomData,
+            _phantom_physical: PhantomData,
+        }
+    }
+
+    /// Commits the transaction.
+    ///
+    /// # Errors
+    ///
+    /// Returns a [`DbErr`] if unable to commit the transaction.
+    pub async fn commit(self) -> OptimizerResult<()> {
+        Ok(self.txn.commit().await?)
+    }
+
+    /// Rolls back the transaction.
+    ///
+    /// # Errors
+    ///
+    /// Returns a [`DbErr`] if unable to roll back the transaction.
+    pub async fn rollback(self) -> OptimizerResult<()> {
+        Ok(self.txn.rollback().await?)
+    }
+
+    /// Retrieves a [`group::Model`] given its ID.
+    ///
+    /// FIXME: use an in-memory representation of a group instead.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error.
+    pub async fn get_group(&self, group_id: GroupId) -> OptimizerResult<group::Model> {
+        Ok(group::Entity::find_by_id(group_id.0)
+            .one(&self.txn)
+            .await?
+            .ok_or(MemoError::UnknownGroup(group_id))?)
+    }
+
+    /// Retrieves the root / canonical group ID of the given group ID.
+    ///
+    /// The groups form a union find / disjoint set parent pointer forest, where group merging
+    /// causes two trees to merge.
+    ///
+    /// This function uses the path compression optimization, which amortizes the cost to a single
+    /// lookup (theoretically in constant time, but we must be wary of the I/O roundtrip).
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. This function
+    /// also performs path compression pointer updates, so any of those updates can fail with a
+    /// [`DbErr`].
+    pub async fn get_root_group(&self, group_id: GroupId) -> OptimizerResult<GroupId> {
+        let curr_group = self.get_group(group_id).await?;
+
+        // If we have no parent, then we are at the root.
+        let Some(parent_id) = curr_group.parent_id else {
+            return Ok(GroupId(curr_group.id));
+        };
+
+        // Recursively find the root group ID.
+        let root_id = Box::pin(self.get_root_group(GroupId(parent_id))).await?;
+
+        // Path Compression Optimization:
+        // For every group along the path that we walked, set their parent id pointer to the root.
+        // This allows for an amortized O(1) cost for `get_root_group`.
+        let mut active_group = curr_group.into_active_model();
+
+        // Update the group to point to the new parent.
+        active_group.parent_id = Set(Some(root_id.0));
+        active_group.update(&self.txn).await?;
+
+        Ok(GroupId(root_id.0))
+    }
+
+    /// Retrieves every group ID of groups that share the same root group with the input group.
+    ///
+    /// The group records form a union-find data structure that also maintains a circular linked
+    /// list in every set that allows us to iterate over all elements in a set in linear time.
+    ///
+    /// # Errors
+    ///
+    /// If the input group does not exist, or if any pointer along the path is invalid, returns a
+    /// [`MemoError::UnknownGroup`] error.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the embedded union-find data structure is malformed.
+    pub async fn get_group_set(&self, group_id: GroupId) -> OptimizerResult<Vec<GroupId>> {
+        // Iterate over the circular linked list until we reach ourselves again.
+        let base_group = self.get_group(group_id).await?;
+
+        // The only case when `next_id` is set to `None` is if the current group is a root, which
+        // means that this group is the only group in the set.
+        if base_group.next_id.is_none() {
+            assert!(base_group.parent_id.is_none());
+            return Ok(vec![group_id]);
+        }
+
+        // Iterate over the circular linked list until we see ourselves again, collecting nodes
+        // along the way.
+        let mut set = vec![group_id];
+        let mut next_id = base_group
+            .next_id
+            .expect("next pointer cannot be null if it is in a cycle");
+        loop {
+            let curr_group = self.get_group(GroupId(next_id)).await?;
+
+            if curr_group.id == group_id.0 {
+                break;
+            }
+
+            set.push(GroupId(curr_group.id));
+            next_id = curr_group
+                .next_id
+                .expect("next pointer cannot be null if it is in a cycle");
+        }
+
+        Ok(set)
+    }
+
+    /// Retrieves a [`physical_expression::Model`] given a [`PhysicalExpressionId`].
+    ///
+    /// # Errors
+    ///
+    /// If the physical expression does not exist, returns a
+    /// [`MemoError::UnknownPhysicalExpression`] error.
+    pub async fn get_physical_expression(
+        &self,
+        physical_expression_id: PhysicalExpressionId,
+    ) -> OptimizerResult<(GroupId, P)> {
+        // Lookup the entity in the database via the unique expression ID.
+        let model = physical_expression::Entity::find_by_id(physical_expression_id.0)
+            .one(&self.txn)
+            .await?
+            .ok_or(MemoError::UnknownPhysicalExpression(physical_expression_id))?;
+
+        let group_id = GroupId(model.group_id);
+        let expr = model.into();
+
+        Ok((group_id, expr))
+    }
+
+    /// Retrieves a [`logical_expression::Model`] given its [`LogicalExpressionId`].
+    ///
+    /// # Errors
+    ///
+    /// If the logical expression does not exist, returns a [`MemoError::UnknownLogicalExpression`]
+    /// error.
+    pub async fn get_logical_expression(
+        &self,
+        logical_expression_id: LogicalExpressionId,
+    ) -> OptimizerResult<(GroupId, L)> {
+        // Lookup the entity in the database via the unique expression ID.
+        let model = logical_expression::Entity::find_by_id(logical_expression_id.0)
+            .one(&self.txn)
+            .await?
+            .ok_or(MemoError::UnknownLogicalExpression(logical_expression_id))?;
+
+        let group_id = GroupId(model.group_id);
+        let expr = model.into();
+
+        Ok((group_id, expr))
+    }
+
+    /// Retrieves all of the logical expression "children" IDs of a group.
+    ///
+    /// FIXME: `find_related` does not work for some reason, have to use manual `filter`.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. Can also return
+    /// a [`DbErr`] if the something goes wrong with the filter scan.
+    pub async fn get_logical_children(
+        &self,
+        group_id: GroupId,
+    ) -> OptimizerResult<Vec<LogicalExpressionId>> {
+        // First ensure that the group exists.
+        let _ = self.get_group(group_id).await?;
+
+        // Search for expressions that have the given parent group ID.
+        let children = logical_expression::Entity::find()
+            .filter(logical_expression::Column::GroupId.eq(group_id.0))
+            .all(&self.txn)
+            .await?
+            .into_iter()
+            .map(|m| LogicalExpressionId(m.id))
+            .collect();
+
+        Ok(children)
+    }
+
+    /// Retrieves all of the physical expression "children" IDs of a group.
+    ///
+    /// FIXME: `find_related` does not work for some reason, have to use manual `filter`.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. Can also return
+    /// a [`DbErr`] if the something goes wrong with the filter scan.
+    pub async fn get_physical_children(
+        &self,
+        group_id: GroupId,
+    ) -> OptimizerResult<Vec<PhysicalExpressionId>> {
+        // First ensure that the group exists.
+        let _ = self.get_group(group_id).await?;
+
+        // Search for expressions that have the given parent group ID.
+        let children = physical_expression::Entity::find()
+            .filter(physical_expression::Column::GroupId.eq(group_id.0))
+            .all(&self.txn)
+            .await?
+            .into_iter()
+            .map(|m| PhysicalExpressionId(m.id))
+            .collect();
+
+        Ok(children)
+    }
+
+    /// Updates / replaces a group's status. Returns the previous group status.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. Can also return a
+    /// [`DbErr`] if the update fails.
+    pub async fn update_group_status(
+        &mut self,
+        group_id: GroupId,
+        status: GroupStatus,
+    ) -> OptimizerResult<GroupStatus> {
+        // First retrieve the group record.
+        let mut group = self.get_group(group_id).await?.into_active_model();
+
+        // Update the group's status.
+        let old_status = group.status;
+        group.status = Set(status as u8 as i8);
+        group.update(&self.txn).await?;
+
+        let old_status = match old_status.unwrap() {
+            0 => GroupStatus::InProgress,
+            1 => GroupStatus::Explored,
+            2 => GroupStatus::Optimized,
+            _ => unreachable!("encountered an invalid group status"),
+        };
+
+        Ok(old_status)
+    }
+
+    /// Updates / replaces a group's best physical plan (winner). Optionally returns the previous
+    /// winner's physical expression ID.
+    ///
+    /// FIXME: In the future, this should first check that we aren't overwriting a winner that was
+    /// updated from another thread by comparing against the cost of the plan.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. Can also return a
+    /// [`DbErr`] if the update fails.
+    pub async fn update_group_winner(
+        &mut self,
+        group_id: GroupId,
+        physical_expression_id: PhysicalExpressionId,
+    ) -> OptimizerResult<Option<PhysicalExpressionId>> {
+        // First retrieve the group record.
+        let mut group = self.get_group(group_id).await?.into_active_model();
+
+        // Update the group to point to the new winner.
+        let old_id = group.winner;
+        group.winner = Set(Some(physical_expression_id.0));
+        group.update(&self.txn).await?;
+
+        // Note that the `unwrap` here is unwrapping the `ActiveValue`, not the `Option`.
+        let old_id = old_id.unwrap().map(PhysicalExpressionId);
+        Ok(old_id)
+    }
+
+    /// Adds a logical expression to an existing group via its ID.
+    ///
+    /// The caller is required to pass in a slice of [`GroupId`] that represent the child groups of
+    /// the input expression.
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error.
+    ///
+    /// If the memo table detects that the input logical expression is a duplicate expression, this
+    /// function will **not** insert the expression into the memo table. Instead, it will return an
+    /// `Ok(Err(expression_id))`, which is a unique identifier of the expression that the input is a
+    /// duplicate of. The caller can use this ID to retrieve the group the original belongs to.
+    ///
+    /// If the memo table detects that the input is unique, it will insert the expression into the
+    /// input group and return an `Ok(Ok(expression_id))`.
+    ///
+    /// # Errors
+    ///
+    /// Note that the return value is a [`Result`] wrapped in an [`OptimizerResult`]. The outer
+    /// result is used for raising [`DbErr`] or other database/IO-related errors. The inner result
+    /// is used for notifying the caller if the expression that they attempted to insert was a
+    /// duplicate expression or not.
+    pub async fn add_logical_expression_to_group(
+        &mut self,
+        group_id: GroupId,
+        logical_expression: L,
+        children: &[GroupId],
+    ) -> OptimizerResult<Result<LogicalExpressionId, (GroupId, LogicalExpressionId)>> {
+        // Check if the expression already exists anywhere in the memo table.
+        if let Some(existing_id) = self
+            .is_duplicate_logical_expression(&logical_expression, children)
+            .await?
+        {
+            return Ok(Err(existing_id));
+        }
+
+        // Check if the group actually exists.
+        let _ = self.get_group(group_id).await?;
+
+        // Insert the expression.
+        let model: logical_expression::Model = logical_expression.into();
+        let mut active_model = model.into_active_model();
+        active_model.group_id = Set(group_id.0);
+        active_model.id = NotSet;
+        let new_model = active_model.insert(&self.txn).await?;
+
+        let expr_id = new_model.id;
+
+        // Insert the child groups of the expression into the junction / children table.
+        logical_children::Entity::insert_many(children.iter().copied().map(|child_id| {
+            logical_children::ActiveModel {
+                logical_expression_id: Set(expr_id),
+                group_id: Set(child_id.0),
+            }
+        }))
+        .on_empty_do_nothing()
+        .exec(&self.txn)
+        .await?;
+
+        // Finally, insert the fingerprint of the logical expression as well.
+        let new_expr: L = new_model.into();
+        let kind = new_expr.kind();
+
+        // In order to calculate a correct fingerprint, we will want to use the IDs of the root
+        // groups of the children instead of the child ID themselves.
+        let mut rewrites = vec![];
+        for &child_id in children {
+            let root_id = self.get_root_group(child_id).await?;
+            rewrites.push((child_id, root_id));
+        }
+        let hash = new_expr.rewrite(&rewrites).fingerprint();
+
+        let fingerprint = fingerprint::ActiveModel {
+            id: NotSet,
+            logical_expression_id: Set(expr_id),
+            kind: Set(kind),
+            hash: Set(hash),
+        };
+        fingerprint::Entity::insert(fingerprint)
+            .exec(&self.txn)
+            .await?;
+
+        Ok(Ok(LogicalExpressionId(expr_id)))
+    }
+
+    /// Adds a physical expression to an existing group via its ID.
+    ///
+    /// The caller is required to pass in a slice of [`GroupId`] that represent the child groups of
+    /// the input expression.
+    ///
+    /// On successful insertion, returns the ID of the physical expression.
+    ///
+    /// # Errors
+    ///
+    /// If the group does not exist, returns a [`MemoError::UnknownGroup`] error. Can also fail if
+    /// insertion of the new physical expression or any of its child junction entries are not able
+    /// to be inserted.
+    pub async fn add_physical_expression_to_group(
+        &mut self,
+        group_id: GroupId,
+        physical_expression: P,
+        children: &[GroupId],
+    ) -> OptimizerResult<PhysicalExpressionId> {
+        // Check if the group actually exists.
+        let _ = self.get_group(group_id).await?;
+
+        // Insert the expression.
+        let model: physical_expression::Model = physical_expression.into();
+        let mut active_model = model.into_active_model();
+        active_model.group_id = Set(group_id.0);
+        active_model.id = NotSet;
+        let new_model = active_model.insert(&self.txn).await?;
+
+        // Insert the child groups of the expression into the junction / children table.
+        physical_children::Entity::insert_many(children.iter().copied().map(|child_id| {
+            physical_children::ActiveModel {
+                physical_expression_id: Set(new_model.id),
+                group_id: Set(child_id.0),
+            }
+        }))
+        .on_empty_do_nothing()
+        .exec(&self.txn)
+        .await?;
+
+        Ok(PhysicalExpressionId(new_model.id))
+    }
+
+    /// Checks if the given logical expression is a duplicate / already exists in the memo table.
+    ///
+    /// In order to prevent a large amount of duplicate work, the memo table must support duplicate
+    /// expression detection.
+    ///
+    /// Returns `Some((group_id, expression_id))` if the memo table detects that the expression
+    /// already exists, and `None` otherwise.
+    ///
+    /// This function assumes that the child groups of the expression are currently roots of their
+    /// group sets. For example, if G1 and G2 should be merged, and G1 is the root, then the input
+    /// expression should _not_ have G2 as a child, and should be replaced with G1.
+    ///
+    /// # Errors
+    ///
+    /// Returns a [`DbErr`] when a database operation fails.
+    pub async fn is_duplicate_logical_expression(
+        &self,
+        logical_expression: &L,
+        children: &[GroupId],
+    ) -> OptimizerResult<Option<(GroupId, LogicalExpressionId)>> {
+        let model: logical_expression::Model = logical_expression.clone().into();
+
+        // Lookup all expressions that have the same fingerprint and kind. There may be false
+        // positives, but we will check for those next.
+        let kind = model.kind;
+
+        // In order to calculate a correct fingerprint, we will want to use the IDs of the root
+        // groups of the children instead of the child ID themselves.
+        let mut rewrites = vec![];
+        for &child_id in children {
+            let root_id = self.get_root_group(child_id).await?;
+            rewrites.push((child_id, root_id));
+        }
+        let fingerprint = logical_expression.rewrite(&rewrites).fingerprint();
+
+        // Filter first by the fingerprint, and then the kind.
+        // FIXME: The kind is already embedded into the fingerprint, so we may not actually need the
+        // second filter?
+        let potential_matches = fingerprint::Entity::find()
+            .filter(fingerprint::Column::Hash.eq(fingerprint))
+            .filter(fingerprint::Column::Kind.eq(kind))
+            .all(&self.txn)
+            .await?;
+
+        if potential_matches.is_empty() {
+            return Ok(None);
+        }
+
+        // Now that we have all of the expressions that match the given fingerprint, we need to
+        // filter out all of the expressions that might have had the same fingerprint but are not
+        // actually equivalent (hash collisions).
+        let mut match_id = None;
+        for potential_match in potential_matches {
+            let expr_id = LogicalExpressionId(potential_match.logical_expression_id);
+            let (group_id, expr) = self.get_logical_expression(expr_id).await?;
+
+            // We need to add the root groups of the new expression to the rewrites vector.
+            // TODO make this much more efficient by making rewrites a hash map, potentially im::HashMap.
+            let mut rewrites = rewrites.clone();
+            for child_id in expr.children() {
+                let root_id = self.get_root_group(child_id).await?;
+                rewrites.push((child_id, root_id));
+            }
+
+            // Check for an exact match after rewrites.
+            if logical_expression
+                .rewrite(&rewrites)
+                .is_duplicate(&expr.rewrite(&rewrites))
+            {
+                match_id = Some((group_id, expr_id));
+
+                // There should be at most one duplicate expression, so we can break here.
+                break;
+            }
+        }
+
+        Ok(match_id)
+    }
+
+    /// Adds a new group into the memo table via a logical expression, creating a new group if the
+    /// logical expression does not already exist.
+    ///
+    /// The caller is required to pass in a slice of [`GroupId`] that represent the child groups of
+    /// the input expression.
+    ///
+    /// If the expression already exists, then this function will return the [`GroupId`] of the
+    /// parent group and the corresponding (already existing) [`LogicalExpressionId`]. It will also
+    /// completely ignore the group ID field of the input expression as well as ignore the input
+    /// slice of child groups.
+    ///
+    /// If the expression does not exist, this function will create a new group and a new
+    /// expression, returning brand new IDs for both.
+    ///
+    /// # Errors
+    ///
+    /// Note that the return value is a [`Result`] wrapped in an [`OptimizerResult`]. The outer
+    /// result is used for raising [`DbErr`] or other database/IO-related errors. The inner result
+    /// is used for notifying the caller if the expression/group that they attempted to insert was a
+    /// duplicate expression or not.
+    pub async fn add_group(
+        &mut self,
+        logical_expression: L,
+        children: &[GroupId],
+    ) -> OptimizerResult<Result<(GroupId, LogicalExpressionId), (GroupId, LogicalExpressionId)>>
+    {
+        // Check if the expression already exists in the memo table.
+        if let Some((group_id, existing_id)) = self
+            .is_duplicate_logical_expression(&logical_expression, children)
+            .await?
+        {
+            return Ok(Err((group_id, existing_id)));
+        }
+
+        // The expression does not exist yet, so we need to create a new group and new expression.
+        let group = group::ActiveModel {
+            status: Set(0), // `GroupStatus::InProgress` status.
+            set_size: Set(1),
+            ..Default::default()
+        };
+
+        // Create the new group.
+        let group_res = group::Entity::insert(group).exec(&self.txn).await?;
+        let group_id = group_res.last_insert_id;
+
+        // Insert the input expression into the newly created group.
+        let expression: logical_expression::Model = logical_expression.clone().into();
+        let mut active_expression = expression.into_active_model();
+        active_expression.group_id = Set(group_id);
+        active_expression.id = NotSet;
+        let new_expression = active_expression.insert(&self.txn).await?;
+
+        let group_id = new_expression.group_id;
+        let expr_id = new_expression.id;
+
+        // Insert the child groups of the expression into the junction / children table.
+        logical_children::Entity::insert_many(children.iter().copied().map(|child_id| {
+            logical_children::ActiveModel {
+                logical_expression_id: Set(new_expression.id),
+                group_id: Set(child_id.0),
+            }
+        }))
+        .on_empty_do_nothing()
+        .exec(&self.txn)
+        .await?;
+
+        // Finally, insert the fingerprint of the logical expression as well.
+        let new_logical_expression: L = new_expression.into();
+        let kind = new_logical_expression.kind();
+
+        // In order to calculate a correct fingerprint, we will want to use the IDs of the root
+        // groups of the children instead of the child ID themselves.
+        let mut rewrites = vec![];
+        for &child_id in children {
+            let root_id = self.get_root_group(child_id).await?;
+            rewrites.push((child_id, root_id));
+        }
+        let hash = new_logical_expression.rewrite(&rewrites).fingerprint();
+
+        let fingerprint = fingerprint::ActiveModel {
+            id: NotSet,
+            logical_expression_id: Set(expr_id),
+            kind: Set(kind),
+            hash: Set(hash),
+        };
+        fingerprint::Entity::insert(fingerprint)
+            .exec(&self.txn)
+            .await?;
+
+        Ok(Ok((GroupId(group_id), LogicalExpressionId(expr_id))))
+    }
+
+    /// Merges two groups sets together.
+    ///
+    /// If either of the input groups do not exist, returns a [`MemoError::UnknownGroup`] error.
+    ///
+    /// TODO write docs.
+    /// TODO highly inefficient, need to understand metrics and performance testing.
+    /// TODO Optimization: add rank / size into data structure
+    ///
+    /// # Errors
+    ///
+    /// TODO
+    pub async fn merge_groups(
+        &mut self,
+        left_group_id: GroupId,
+        right_group_id: GroupId,
+    ) -> OptimizerResult<GroupId> {
+        let mut left_root_id = self.get_root_group(left_group_id).await?;
+        let mut left_root = self.get_group(left_root_id).await?;
+        let mut left_size = left_root.set_size;
+
+        let mut right_root_id = self.get_root_group(right_group_id).await?;
+        let mut right_root = self.get_group(right_root_id).await?;
+        let mut right_size = left_root.set_size;
+
+        // Rank/size optimization: merge the smaller set into the larger set.
+        if left_size > right_size {
+            std::mem::swap(&mut left_root_id, &mut right_root_id);
+            std::mem::swap(&mut left_root, &mut right_root);
+            std::mem::swap(&mut left_size, &mut right_size);
+        }
+
+        // A `None` next pointer means it should technically be pointing to itself.
+        let left_next = left_root.next_id.unwrap_or(left_root_id.0);
+        let mut active_left_root = left_root.into_active_model();
+        // A `None` next pointer means it should technically be pointing to itself.
+        let right_next = right_root.next_id.unwrap_or(right_root_id.0);
+        let mut active_right_root = right_root.into_active_model();
+
+        // Before we actually update the group records, We first need to generate new fingerprints
+        // for every single expression that has a child group in the left set.
+        // TODO make this more efficient, this code is doing double work from `get_group_set`.
+        let group_set_ids = self.get_group_set(left_group_id).await?;
+        let mut left_group_models = Vec::with_capacity(group_set_ids.len());
+        for &group_id in &group_set_ids {
+            left_group_models.push(self.get_group(group_id).await?);
+        }
+
+        // Retrieve every single expression that has a child group in the left set.
+        let left_group_expressions: Vec<Vec<logical_expression::Model>> = left_group_models
+            .load_many_to_many(
+                logical_expression::Entity,
+                logical_children::Entity,
+                &self.txn,
+            )
+            .await?;
+
+        // Need to replace every single occurrence of groups in the set with the new root.
+        let rewrites: Vec<(GroupId, GroupId)> = group_set_ids
+            .iter()
+            .map(|&group_id| (group_id, right_root_id))
+            .collect();
+
+        // For each expression, generate a new fingerprint.
+        let mut seen = HashSet::new();
+        for model in left_group_expressions.into_iter().flatten() {
+            let expr_id = model.id;
+
+            // There may be duplicates in the expressions list.
+            if seen.contains(&expr_id) {
+                continue;
+            } else {
+                seen.insert(expr_id);
+            }
+
+            let logical_expression: L = model.into();
+            let hash = logical_expression.rewrite(&rewrites).fingerprint();
+
+            let fingerprint = fingerprint::ActiveModel {
+                id: NotSet,
+                logical_expression_id: Set(expr_id),
+                kind: Set(logical_expression.kind()),
+                hash: Set(hash),
+            };
+            fingerprint::Entity::insert(fingerprint)
+                .exec(&self.txn)
+                .await?;
+        }
+
+        // Update the left group root to point to the right group root.
+        active_left_root.parent_id = Set(Some(right_root_id.0));
+
+        // Swap the next pointers of each root to maintain the circular linked list.
+        active_left_root.next_id = Set(Some(right_next));
+        active_right_root.next_id = Set(Some(left_next));
+
+        active_left_root.update(&self.txn).await?;
+        active_right_root.update(&self.txn).await?;
+
+        Ok(right_root_id)
+    }
+}
diff --git a/optd-mvp/src/memo/persistent/mod.rs b/optd-mvp/src/memo/persistent/mod.rs
new file mode 100644
index 0000000..dfddffa
--- /dev/null
+++ b/optd-mvp/src/memo/persistent/mod.rs
@@ -0,0 +1,37 @@
+//! This module contains the definition and implementation of the [`PersistentMemo`] type, which
+//! implements the `Memo` trait and supports memo table operations necessary for query optimization.
+
+use sea_orm::{DatabaseConnection, DatabaseTransaction};
+use std::marker::PhantomData;
+
+#[cfg(test)]
+mod tests;
+
+/// A persistent memo table, backed by a database on disk.
+///
+/// TODO more docs.
+pub struct PersistentMemo<L, P> {
+    /// This `PersistentMemo` is reliant on the SeaORM [`DatabaseConnection`] that stores all of the
+    /// objects needed for query optimization.
+    db: DatabaseConnection,
+
+    /// Generic marker for a generic logical expression.
+    _phantom_logical: PhantomData<L>,
+
+    /// Generic marker for a generic physical expression.
+    _phantom_physical: PhantomData<P>,
+}
+
+/// TODO docs.
+pub struct PersistentMemoTransaction<L, P> {
+    /// A database transaction over the [`PersistentMemo`] table.
+    txn: DatabaseTransaction,
+
+    /// Generic marker for a generic logical expression.
+    _phantom_logical: PhantomData<L>,
+
+    /// Generic marker for a generic physical expression.
+    _phantom_physical: PhantomData<P>,
+}
+
+pub mod implementation;
diff --git a/optd-mvp/src/memo/persistent/tests.rs b/optd-mvp/src/memo/persistent/tests.rs
new file mode 100644
index 0000000..8fe1aeb
--- /dev/null
+++ b/optd-mvp/src/memo/persistent/tests.rs
@@ -0,0 +1,483 @@
+use crate::{expression::*, memo::persistent::PersistentMemo};
+
+/// Tests that exact expression matches are detected and handled by the txn table.
+#[ignore]
+#[tokio::test]
+async fn test_simple_logical_duplicates() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    let scan = scan("t1".to_string());
+    let scan1a = scan.clone();
+    let scan1b = scan.clone();
+    let scan2a = scan.clone();
+    let scan2b = scan.clone();
+
+    // Insert a new group and its corresponding expression.
+    let (group_id, logical_expression_id) = txn.add_group(scan, &[]).await.unwrap().ok().unwrap();
+
+    // Test `add_logical_expression`.
+    {
+        // Attempting to create a new group with a duplicate expression should fail every time.
+        let (group_id_1a, logical_expression_id_1a) =
+            txn.add_group(scan1a, &[]).await.unwrap().err().unwrap();
+        assert_eq!(group_id, group_id_1a);
+        assert_eq!(logical_expression_id, logical_expression_id_1a);
+
+        // Try again just in case...
+        let (group_id_1b, logical_expression_id_1b) =
+            txn.add_group(scan1b, &[]).await.unwrap().err().unwrap();
+        assert_eq!(group_id, group_id_1b);
+        assert_eq!(logical_expression_id, logical_expression_id_1b);
+    }
+
+    // Test `add_logical_expression_to_group`.
+    {
+        // Attempting to add a duplicate expression into the same group should also fail every time.
+        let (group_id_2a, logical_expression_id_2a) = txn
+            .add_logical_expression_to_group(group_id, scan2a, &[])
+            .await
+            .unwrap()
+            .err()
+            .unwrap();
+        assert_eq!(group_id, group_id_2a);
+        assert_eq!(logical_expression_id, logical_expression_id_2a);
+
+        let (group_id_2b, logical_expression_id_2b) = txn
+            .add_logical_expression_to_group(group_id, scan2b, &[])
+            .await
+            .unwrap()
+            .err()
+            .unwrap();
+        assert_eq!(group_id, group_id_2b);
+        assert_eq!(logical_expression_id, logical_expression_id_2b);
+    }
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests that physical expression are _not_ subject to duplicate detection and elimination.
+///
+/// !!! Important !!! Note that this behavior should not actually be seen during query optimization,
+/// since if logical expression have been deduplicated, there should not be any duplicate physical
+/// expressions as they are derivative of the deduplicated logical expressions.
+#[ignore]
+#[tokio::test]
+async fn test_simple_add_physical_expression() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Insert a new group and its corresponding expression.
+    let scan = scan("t1".to_string());
+    let (group_id, _) = txn.add_group(scan, &[]).await.unwrap().ok().unwrap();
+
+    // Insert two identical physical expressions into the _same_ group.
+    let table_scan_1 = table_scan("t1".to_string());
+    let table_scan_2 = table_scan_1.clone();
+
+    let physical_expression_id_1 = txn
+        .add_physical_expression_to_group(group_id, table_scan_1, &[])
+        .await
+        .unwrap();
+
+    let physical_expression_id_2 = txn
+        .add_physical_expression_to_group(group_id, table_scan_2, &[])
+        .await
+        .unwrap();
+
+    // Since physical expressions do not need duplicate detection,
+    assert_ne!(physical_expression_id_1, physical_expression_id_2);
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests if the txn tables able to correctly retrieve a group's expressions.
+#[ignore]
+#[tokio::test]
+async fn test_simple_tree() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Create two scan groups.
+    let scan1: DefaultLogicalExpression = scan("t1".to_string());
+    let scan2 = scan("t2".to_string());
+    let (scan_id_1, scan_expr_id_1) = txn.add_group(scan1, &[]).await.unwrap().ok().unwrap();
+    let (scan_id_2, scan_expr_id_2) = txn.add_group(scan2, &[]).await.unwrap().ok().unwrap();
+
+    assert_eq!(
+        txn.get_logical_children(scan_id_1).await.unwrap(),
+        &[scan_expr_id_1]
+    );
+    assert_eq!(
+        txn.get_logical_children(scan_id_2).await.unwrap(),
+        &[scan_expr_id_2]
+    );
+
+    // Create two join expression that should be in the same group.
+    let join1 = join(scan_id_1, scan_id_2, "t1.a = t2.b".to_string());
+    let join2 = join(scan_id_2, scan_id_1, "t1.a = t2.b".to_string());
+
+    // Create the group, adding the first expression.
+    let (join_id, join_expr_id_1) = txn
+        .add_group(join1, &[scan_id_1, scan_id_2])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    // Add the second expression.
+    let join_expr_id_2 = txn
+        .add_logical_expression_to_group(join_id, join2, &[scan_id_2, scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    assert_ne!(join_expr_id_1, join_expr_id_2);
+    assert_eq!(
+        txn.get_logical_children(join_id).await.unwrap(),
+        &[join_expr_id_1, join_expr_id_2]
+    );
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests a single group merge. See comments in the test itself for more information.
+#[ignore]
+#[tokio::test]
+async fn test_simple_group_link() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Create two scan groups.
+    let scan1 = scan("t1".to_string());
+    let scan2 = scan("t2".to_string());
+    let (scan_id_1, _) = txn.add_group(scan1, &[]).await.unwrap().ok().unwrap();
+    let (scan_id_2, _) = txn.add_group(scan2, &[]).await.unwrap().ok().unwrap();
+
+    // Create two join expression that should be in the same group.
+    // Even though these are obviously the same expression (to humans), the fingerprints will be
+    // different, and so they will be put into different groups.
+    let join1 = join(scan_id_1, scan_id_2, "t1.a = t2.b".to_string());
+    let join2 = join(scan_id_2, scan_id_1, "t2.b = t1.a".to_string());
+    let join_unknown = join2.clone();
+
+    let (join_group_1, _) = txn
+        .add_group(join1, &[scan_id_1, scan_id_2])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (join_group_2, join_expr_2) = txn
+        .add_group(join2, &[scan_id_2, scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    assert_ne!(join_group_1, join_group_2);
+
+    // Assume that some rule was applied to `join1`, and it outputs something like `join_unknown`.
+    // The txn table will tell us that `join_unknown == join2`.
+    // Take note here that `join_unknown` is a clone of `join2`, not `join1`.
+    let (existing_group, not_actually_new_expr_id) = txn
+        .add_logical_expression_to_group(join_group_1, join_unknown, &[scan_id_2, scan_id_1])
+        .await
+        .unwrap()
+        .err()
+        .unwrap();
+    assert_eq!(existing_group, join_group_2);
+    assert_eq!(not_actually_new_expr_id, join_expr_2);
+
+    // The above tells the application that the expression already exists in the txn, specifically
+    // under `existing_group`. Thus, we should link these two groups together.
+    txn.merge_groups(join_group_1, join_group_2).await.unwrap();
+
+    let test_root_1 = txn.get_root_group(join_group_1).await.unwrap();
+    let test_root_2 = txn.get_root_group(join_group_2).await.unwrap();
+    assert_eq!(test_root_1, test_root_2);
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests merging groups up a chain.
+#[ignore]
+#[tokio::test]
+async fn test_group_merge_ladder() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Build up a tree of true filters that should be collapsed into a single table scan.
+    let scan_base = scan("t1".to_string());
+    let (scan_id, _) = txn.add_group(scan_base, &[]).await.unwrap().ok().unwrap();
+
+    let filter0 = filter(scan_id, "true".to_string());
+    let (filter_id_0, _) = txn
+        .add_group(filter0, &[scan_id])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    let filter1 = filter(filter_id_0, "true".to_string());
+    let (filter_id_1, _) = txn
+        .add_group(filter1, &[scan_id])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    let filter2 = filter(filter_id_1, "true".to_string());
+    let (filter_id_2, _) = txn
+        .add_group(filter2, &[scan_id])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    let filter3 = filter(filter_id_2, "true".to_string());
+    let (filter_id_3, _) = txn
+        .add_group(filter3, &[scan_id])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    let mut groups = vec![scan_id, filter_id_0, filter_id_1, filter_id_2, filter_id_3];
+
+    let m0 = txn.merge_groups(filter_id_3, filter_id_2).await.unwrap();
+    let m1 = txn.merge_groups(filter_id_2, filter_id_1).await.unwrap();
+    let m2 = txn.merge_groups(filter_id_1, filter_id_0).await.unwrap();
+    let root = txn.merge_groups(filter_id_0, scan_id).await.unwrap();
+    groups.extend_from_slice(&[m0, m1, m2, root]);
+
+    for group_id in groups {
+        assert_eq!(root, txn.get_root_group(group_id).await.unwrap());
+    }
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests merging a bunch of groups together in order to prevent duplicates from being added.
+#[ignore]
+#[tokio::test]
+async fn test_group_merge() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Create a base group.
+    let scan1 = scan("t1".to_string());
+    let (scan_id_1, _) = txn.add_group(scan1, &[]).await.unwrap().ok().unwrap();
+
+    // Create a bunch of equivalent groups.
+    let filter0 = filter(scan_id_1, "true".to_string());
+    let filter1 = filter(scan_id_1, "1 < 2".to_string());
+    let filter2 = filter(scan_id_1, "2 > 1".to_string());
+    let filter3 = filter(scan_id_1, "42 != 100".to_string());
+    let filter4 = filter(scan_id_1, "10000 > 0".to_string());
+    let filter5 = filter(scan_id_1, "1 + 2 = 3".to_string());
+    let filter6 = filter(scan_id_1, "true OR false".to_string());
+    let filter7 = filter(scan_id_1, "(1 + 1 > -1 AND true) OR false".to_string());
+    let (filter_id_0, _) = txn
+        .add_group(filter0, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_1, _) = txn
+        .add_group(filter1, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_2, _) = txn
+        .add_group(filter2, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_3, _) = txn
+        .add_group(filter3, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_4, _) = txn
+        .add_group(filter4, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_5, _) = txn
+        .add_group(filter5, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_6, _) = txn
+        .add_group(filter6, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let (filter_id_7, _) = txn
+        .add_group(filter7, &[scan_id_1])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+    let filters = vec![
+        filter_id_0,
+        filter_id_1,
+        filter_id_2,
+        filter_id_3,
+        filter_id_4,
+        filter_id_5,
+        filter_id_6,
+        filter_id_7,
+    ];
+
+    // Merge them all together.
+    let quarter_0 = txn.merge_groups(filters[0], filters[1]).await.unwrap();
+    let quarter_1 = txn.merge_groups(filters[2], filters[3]).await.unwrap();
+    let quarter_2 = txn.merge_groups(filters[4], filters[5]).await.unwrap();
+    let quarter_3 = txn.merge_groups(filters[6], filters[7]).await.unwrap();
+    let semi_0 = txn.merge_groups(quarter_0, quarter_1).await.unwrap();
+    let semi_1 = txn.merge_groups(quarter_2, quarter_3).await.unwrap();
+    let final_id = txn.merge_groups(semi_0, semi_1).await.unwrap();
+
+    // Check that the group set is properly representative.
+    {
+        let set = txn.get_group_set(final_id).await.unwrap();
+        assert_eq!(set.len(), 8);
+        for id in set {
+            assert!(filters.contains(&id));
+        }
+    }
+
+    // Create another base group.
+    let scan2 = scan("t2".to_string());
+    let (scan_id_2, _) = txn.add_group(scan2, &[]).await.unwrap().ok().unwrap();
+
+    // Add a join group.
+    let join0 = join(filter_id_0, scan_id_2, "t1.a = t2.a".to_string());
+    let (join_group_id, join_expr_id) = txn
+        .add_group(join0, &[filter_id_0, scan_id_2])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    // Adding the duplicate join expressions should return a duplication error containing the IDs of
+    // the already existing group and expression.
+    for filter_id in filters {
+        let join_test = join(filter_id, scan_id_2, "t1.a = t2.a".to_string());
+        let (join_group_id_test, join_expr_id_test) = txn
+            .add_group(join_test, &[filter_id, scan_id_2])
+            .await
+            .unwrap()
+            .err()
+            .unwrap();
+        assert_eq!(join_group_id, join_group_id_test);
+        assert_eq!(join_expr_id, join_expr_id_test);
+    }
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
+
+/// Tests the exact same scenario as in the "Discovered Duplicates" section in `DESIGN.md`.
+#[ignore]
+#[tokio::test]
+async fn test_cascading_merge() {
+    let memo = PersistentMemo::<DefaultLogicalExpression, DefaultPhysicalExpression>::new().await;
+    memo.cleanup().await;
+
+    let mut txn = memo.begin().await.unwrap();
+
+    // Create the base groups.
+    let scan1 = scan("t1".to_string());
+    let (g1, _) = txn.add_group(scan1, &[]).await.unwrap().ok().unwrap();
+    let scan2 = scan("t2".to_string());
+    let (g2, _) = txn.add_group(scan2, &[]).await.unwrap().ok().unwrap();
+
+    let filter1 = filter(g1, "x > 1000".to_string());
+    let (g3, _) = txn.add_group(filter1, &[g1]).await.unwrap().ok().unwrap();
+
+    // Create two groups that will need to be merged.
+    let filter2a = filter(g2, "a < 42".to_string());
+    let (g4, _) = txn.add_group(filter2a, &[g2]).await.unwrap().ok().unwrap();
+    let filter2b = filter(g4, "a < 42 AND 1 = 1".to_string());
+    let (g5, _) = txn.add_group(filter2b, &[g4]).await.unwrap().ok().unwrap();
+
+    // Create groups that are dependent on the to-be-merged groups.
+    let join1 = join(g3, g4, "t1.x = t2.a".to_string());
+    let (g6, _) = txn.add_group(join1, &[g3, g4]).await.unwrap().ok().unwrap();
+    let join2 = join(g3, g5, "t1.x = t2.a".to_string());
+    let (g7, _) = txn.add_group(join2, &[g3, g5]).await.unwrap().ok().unwrap();
+
+    // Create more groups that are dependent on the to-be-merged groups.
+    // TODO actually use a sort expression instead of a `filter` placeholder.
+    let sort1 = filter(g6, "ORDER BY a".to_string());
+    let (g8, _) = txn.add_group(sort1, &[g6]).await.unwrap().ok().unwrap();
+
+    let sort2 = filter(g7, "ORDER BY a".to_string());
+    let (g9, _) = txn.add_group(sort2, &[g7]).await.unwrap().ok().unwrap();
+
+    // Now that everything is set up, we can merge groups 4 and 5 to begin the cascading process.
+    let filter_root = txn.merge_groups(g4, g5).await.unwrap();
+    assert_eq!(txn.get_root_group(g4).await.unwrap(), filter_root);
+    assert_eq!(txn.get_root_group(g5).await.unwrap(), filter_root);
+
+    // After merging, the join groups (6 and 7) are technically identical, but we have not merged
+    // them together yet. However, applying rules will reveal that they are identical, and we will
+    // know that they need to get merged.
+    let join1_commute = join(g4, g3, "t1.x = t2.a".to_string());
+    let join1_commute_id = txn
+        .add_logical_expression_to_group(g6, join1_commute, &[g4, g3])
+        .await
+        .unwrap()
+        .ok()
+        .unwrap();
+
+    // Adding this expression should now result in a duplication error and return the above ID.
+    let join2_commute = join(g5, g3, "t1.x = t2.a".to_string());
+    let (existing_g6, existing_id) = txn
+        .add_logical_expression_to_group(g7, join2_commute, &[g5, g3])
+        .await
+        .unwrap()
+        .err()
+        .unwrap();
+    assert_eq!(existing_g6, g6);
+    assert_eq!(existing_id, join1_commute_id);
+
+    // Since the txn table has told us these are duplicates, we can now merge groups 6 and 7.
+    let join_root = txn.merge_groups(g6, g7).await.unwrap();
+    assert_eq!(txn.get_root_group(g6).await.unwrap(), join_root);
+    assert_eq!(txn.get_root_group(g7).await.unwrap(), join_root);
+
+    // Do a similar thing for the sort groups. We'll skip the expression adding for now and just
+    // merge them immediately, but remember that the application should observe a duplicate
+    // somewhere in the txn table before deciding to merge groups.
+    let sort_root = txn.merge_groups(g8, g9).await.unwrap();
+    assert_eq!(txn.get_root_group(g8).await.unwrap(), sort_root);
+    assert_eq!(txn.get_root_group(g9).await.unwrap(), sort_root);
+
+    txn.commit().await.unwrap();
+    memo.cleanup().await;
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_fingerprint.rs b/optd-mvp/src/migrator/memo/m20241127_000001_fingerprint.rs
new file mode 100644
index 0000000..e153b9e
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_fingerprint.rs
@@ -0,0 +1,49 @@
+//! An entity representing a logical expression fingerprint.
+//!
+//! TODO write docs.
+
+use crate::migrator::memo::logical_expression::LogicalExpression;
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum Fingerprint {
+    Table,
+    Id,
+    LogicalExpressionId,
+    Kind,
+    Hash,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(Fingerprint::Table)
+                    .if_not_exists()
+                    .col(pk_auto(Fingerprint::Id))
+                    .col(integer(Fingerprint::LogicalExpressionId))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(Fingerprint::Table, Fingerprint::LogicalExpressionId)
+                            .to(LogicalExpression::Table, LogicalExpression::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .col(small_integer(Fingerprint::Kind))
+                    .col(big_integer(Fingerprint::Hash))
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(Fingerprint::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_group.rs b/optd-mvp/src/migrator/memo/m20241127_000001_group.rs
new file mode 100644
index 0000000..6251b6a
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_group.rs
@@ -0,0 +1,140 @@
+//! FIXME We aren't really following the cascades framework anymore...
+//!
+//! An entity representing a group / equivalence class in the Cascades framework.
+//!
+//! Quoted from the Microsoft article _Extensible query optimizers in practice_:
+//!
+//! > In the memo, each class of equivalent expressions is called an equivalent class or a group,
+//! > and all equivalent expressions within the class are called group expressions or simply
+//! > expressions.
+//!
+//! A Cascades group is defined as a class of equivalent logical or physical expressions. The
+//! Cascades framework uses these groups as a way of storing the best query sub-plans for use in the
+//! dynamic programming search algorithm.
+//!
+//! For example, a Cascades group could be the set of expressions containing the logical expressions
+//! `Join(A, B)` and `Join(B, A)`, as well as the physical expressions `HashJoin(A, B)` and
+//! `NestedLoopJoin(B, A)`.
+//!
+//! # Columns
+//!
+//! Each group is assigned a monotonically-increasing (unique) ID. This ID will be important since
+//! there are many foreign key references from other tables to `group`.
+//!
+//! We store an `status` enumeration encoded as an 8-bit integer that is used for quickly
+//! determining the state of optimization for this group during the dynamic programming search.
+//!
+//! We additionally store a `winner` foreign key reference to a physical expression paired with a
+//! `cost` foreign key reference to a cost record (FIXME). See the
+//! [section](#best-physical-plan-winner) below for more details.
+//!
+//! Finally, we maintain a union-find graph structure embedded in the group records. See the
+//! `DESIGN.md` document for more information.
+//!
+//! # Entity Relationships
+//!
+//! ### Child Expressions (Logical and Physical)
+//!
+//! To retrieve all of a `group`'s equivalent expressions, you must query the
+//! [`logical_expression`] or the [`physical_expression`] entities via their foreign keys to
+//! `group`. The relationship between [`logical_expression`] and `group` is
+//! many-to-one, and the exact same many-to-one relationship is held for [`physical_expression`] to
+//! `group`.
+//!
+//! ### Parent Expressions (Logical and Physical)
+//!
+//! Additionally, each logical or physical expression can have any number of `group`s as
+//! children, and a group can be a child of any expression. Thus, `group` additionally has
+//! a many-to-many relationship with [`logical_expression`] and [`physical_expression`] via the
+//! [`logical_children`] and [`physical_children`] entities.
+//!
+//! To reiterate, `group` has **both** a one-to-many **and** a many-to-many relationship
+//! with both [`logical_expression`] and [`physical_expression`]. This is due to groups being both
+//! parents and children of expressions.
+//!
+//! ### Best Physical Plan (Winner)
+//!
+//! The `group` entity also stores a `winner` _nullable_ foreign key reference to
+//! a physical expression. This represents the most recent best query plan we have computed. The
+//! reason it is nullable is because we may not have come up with any best query plan yet.
+//!
+//! ### Logical Properties
+//!
+//! FIXME: Add a logical properties table.
+//!
+//! Lastly, each `group` record will have a set of logical properties store in the
+//! `logical_property` entity, where there is an many-to-one relationship from
+//! `logical_property` to `group`. Note that we do not store physical properties directly
+//! on the `group`, but rather we store them for each [`physical_expression`] record.
+//!
+//! [`logical_expression`]: super::logical_expression
+//! [`physical_expression`]: super::physical_expression
+//! [`logical_children`]: super::logical_children
+//! [`physical_children`]: super::physical_children
+//! `logical_property`: super::logical_property
+
+use crate::migrator::memo::physical_expression::PhysicalExpression;
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum Group {
+    Table,
+    Id,
+    Status,
+    Winner,
+    Cost,
+    SetSize,
+    ParentId,
+    NextId,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(Group::Table)
+                    .if_not_exists()
+                    .col(pk_auto(Group::Id))
+                    .col(tiny_integer(Group::Status))
+                    .col(integer_null(Group::Winner))
+                    .col(big_integer_null(Group::Cost))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(Group::Table, Group::Winner)
+                            .to(PhysicalExpression::Table, PhysicalExpression::Id)
+                            .on_delete(ForeignKeyAction::SetNull)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .col(integer(Group::SetSize))
+                    .col(integer_null(Group::ParentId))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(Group::Table, Group::ParentId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::SetNull)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .col(integer_null(Group::NextId))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(Group::Table, Group::NextId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::SetNull)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(Group::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_logical_children.rs b/optd-mvp/src/migrator/memo/m20241127_000001_logical_children.rs
new file mode 100644
index 0000000..12b5aa6
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_logical_children.rs
@@ -0,0 +1,65 @@
+//! An entity representing the [`group`] children of every [`logical_expression`].
+//!
+//! Formally, this entity is a junction which allows us to represent a many-to-many relationship
+//! between [`logical_expression`] and [`group`]. Expressions can have any number of child
+//! groups, and every group can be a child of many different expressions, hence the many-to-many
+//! relationship.
+//!
+//! See [`group`] for more details.
+//!
+//! [`group`]: super::group
+//! [`logical_expression`]: super::logical_expression
+
+use crate::migrator::memo::{group::Group, logical_expression::LogicalExpression};
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum LogicalChildren {
+    Table,
+    LogicalExpressionId,
+    GroupId,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(LogicalChildren::Table)
+                    .if_not_exists()
+                    .col(integer(LogicalChildren::LogicalExpressionId))
+                    .col(integer(LogicalChildren::GroupId))
+                    .primary_key(
+                        Index::create()
+                            .col(LogicalChildren::LogicalExpressionId)
+                            .col(LogicalChildren::GroupId),
+                    )
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(LogicalChildren::Table, LogicalChildren::LogicalExpressionId)
+                            .to(LogicalExpression::Table, LogicalExpression::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(LogicalChildren::Table, LogicalChildren::GroupId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(LogicalChildren::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_logical_expression.rs b/optd-mvp/src/migrator/memo/m20241127_000001_logical_expression.rs
new file mode 100644
index 0000000..9b5eefc
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_logical_expression.rs
@@ -0,0 +1,84 @@
+//! An entity representing a logical relational expression.
+//!
+//! Quoted from the Microsoft article _Extensible query optimizers in practice_:
+//!
+//! > A logical expression is defined as a tree of logical operators, and corresponds to a
+//! > relational algebraic expression.
+//!
+//! In the Cascades query optimization framework, the memo table stores equivalence classes of
+//! expressions (see [`group`]). These equivalence classes, or "groups", store both
+//! `logical_expression`s and [`physical_expression`]s.
+//!
+//! Optimization starts by "exploring" equivalent logical expressions within a group. For example,
+//! the logical expressions `Join(A, B)` and `Join(B, A)` are contained in the same group. The
+//! logical expressions are defined as a `Join` operator with the groups representing a scan of
+//! table `A` and a scan of table `B` as its children.
+//!
+//! # Columns
+//!
+//! Each `logical_expression` has a unique primary key ID, but it holds little importance other than
+//! helping distinguish between two different expressions.
+//!
+//! Finally, since there are many different types of operators, we store a variant tag and a data
+//! column as JSON to represent the semi-structured data fields of logical operators.
+//!
+//! # Entity Relationships
+//!
+//! The main relationship that `logical_expression` has is to [`group`]. It has **both** a
+//! one-to-many **and** a many-to-many relationship with [`group`], and you can see more
+//! details about this in the module-level documentation for [`group`].
+//!
+//! The other relationship that `logical_expression` has is to [`fingerprint`]. This table stores
+//! 1 or more fingerprints for every (unique) logical expression. The reason we have multiple
+//! fingerprints is that an expression can belong to multiple groups during the exploration phase
+//! before the merging of groups.
+//!
+//! [`group`]: super::group
+//! [`physical_expression`]: super::physical_expression
+//! [`fingerprint`]: super::fingerprint
+
+use crate::migrator::memo::group::Group;
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum LogicalExpression {
+    Table,
+    Id,
+    GroupId,
+    Kind,
+    Data,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(LogicalExpression::Table)
+                    .if_not_exists()
+                    .col(pk_auto(LogicalExpression::Id))
+                    .col(integer(LogicalExpression::GroupId))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(LogicalExpression::Table, LogicalExpression::GroupId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .col(small_integer(LogicalExpression::Kind))
+                    .col(json(LogicalExpression::Data))
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(LogicalExpression::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_physical_children.rs b/optd-mvp/src/migrator/memo/m20241127_000001_physical_children.rs
new file mode 100644
index 0000000..06ce259
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_physical_children.rs
@@ -0,0 +1,68 @@
+//! An entity representing the [`group`] children of every [`physical_expression`].
+//!
+//! Formally, this entity is a junction which allows us to represent a many-to-many relationship
+//! between [`physical_expression`] and [`group`]. Expressions can have any number of child
+//! groups, and every group can be a child of many different expressions, hence the many-to-many
+//! relationship.
+//!
+//! See [`group`] for more details.
+//!
+//! [`group`]: super::group
+//! [`physical_expression`]: super::physical_expression
+
+use crate::migrator::memo::{group::Group, physical_expression::PhysicalExpression};
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum PhysicalChildren {
+    Table,
+    PhysicalExpressionId,
+    GroupId,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(PhysicalChildren::Table)
+                    .if_not_exists()
+                    .col(integer(PhysicalChildren::PhysicalExpressionId))
+                    .col(integer(PhysicalChildren::GroupId))
+                    .primary_key(
+                        Index::create()
+                            .col(PhysicalChildren::PhysicalExpressionId)
+                            .col(PhysicalChildren::GroupId),
+                    )
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(
+                                PhysicalChildren::Table,
+                                PhysicalChildren::PhysicalExpressionId,
+                            )
+                            .to(PhysicalExpression::Table, PhysicalExpression::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(PhysicalChildren::Table, PhysicalChildren::GroupId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(PhysicalChildren::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/m20241127_000001_physical_expression.rs b/optd-mvp/src/migrator/memo/m20241127_000001_physical_expression.rs
new file mode 100644
index 0000000..88cd63b
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/m20241127_000001_physical_expression.rs
@@ -0,0 +1,84 @@
+//! An entity representing a physical plan expression.
+//!
+//! Quoted from the Microsoft article _Extensible query optimizers in practice_:
+//!
+//! > A physical expression is a tree of physical operators, which is also referred to as the
+//! > _physical plan_ or simply _plan_.
+//!
+//! In the Cascades query optimization framework, the memo table stores equivalence classes of
+//! expressions (see [`group`]). These equivalence classes, or "groups", store both
+//! [`logical_expression`]s and `physical_expression`s.
+//!
+//! Optimization starts by exploring equivalent logical expressions within a group, and then it
+//! proceeds to implement / optimize those logical operators into physical operators. For example,
+//! the logical expression `Join(A, B)` could be implemented into a `HashJoin(A, B)` or a
+//! `NestedLoopJoin(A, B)`, and both of these new physical expressions would be contained in the
+//! same group.
+//!
+//! # Columns
+//!
+//! Each `physical_expression` has a unique primary key ID, and other tables will store a foreign
+//! key reference to a specific `physical_expression`s.
+//!
+//! Note that `physical_expression` does **not** store a fingerprint. Remember that we want to
+//! detect duplicates in the logical exploration phase. If there are no duplicate logical
+//! expressions in the memo table, then there cannot be any duplicate physical expressions, which
+//! are derived from said deduplicated logical expressions.
+//!
+//! Finally, since there are many different types of operators, we store a variant tag and a data
+//! column as JSON to represent the semi-structured data fields of logical operators.
+//!
+//! # Entity Relationships
+//!
+//! The only relationship that `physical_expression` has is to [`group`]. It has **both** a
+//! one-to-many **and** a many-to-many relationship with [`group`], and you can see more
+//! details about this in the module-level documentation for [`group`].
+//!
+//! [`group`]: super::group
+//! [`logical_expression`]: super::logical_expression
+
+use crate::migrator::memo::group::Group;
+use sea_orm_migration::{prelude::*, schema::*};
+
+#[derive(DeriveIden)]
+pub enum PhysicalExpression {
+    Table,
+    Id,
+    GroupId,
+    Kind,
+    Data,
+}
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .create_table(
+                Table::create()
+                    .table(PhysicalExpression::Table)
+                    .if_not_exists()
+                    .col(pk_auto(PhysicalExpression::Id))
+                    .col(integer(PhysicalExpression::GroupId))
+                    .foreign_key(
+                        ForeignKey::create()
+                            .from(PhysicalExpression::Table, PhysicalExpression::GroupId)
+                            .to(Group::Table, Group::Id)
+                            .on_delete(ForeignKeyAction::Cascade)
+                            .on_update(ForeignKeyAction::Cascade),
+                    )
+                    .col(small_integer(PhysicalExpression::Kind))
+                    .col(json(PhysicalExpression::Data))
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .drop_table(Table::drop().table(PhysicalExpression::Table).to_owned())
+            .await
+    }
+}
diff --git a/optd-mvp/src/migrator/memo/mod.rs b/optd-mvp/src/migrator/memo/mod.rs
new file mode 100644
index 0000000..a419189
--- /dev/null
+++ b/optd-mvp/src/migrator/memo/mod.rs
@@ -0,0 +1,16 @@
+//! Entities related to the memo table used for dynamic programming in the our query optimization
+//! framework.
+
+pub(crate) mod m20241127_000001_fingerprint;
+pub(crate) mod m20241127_000001_group;
+pub(crate) mod m20241127_000001_logical_children;
+pub(crate) mod m20241127_000001_logical_expression;
+pub(crate) mod m20241127_000001_physical_children;
+pub(crate) mod m20241127_000001_physical_expression;
+
+pub(crate) use m20241127_000001_fingerprint as fingerprint;
+pub(crate) use m20241127_000001_group as group;
+pub(crate) use m20241127_000001_logical_children as logical_children;
+pub(crate) use m20241127_000001_logical_expression as logical_expression;
+pub(crate) use m20241127_000001_physical_children as physical_children;
+pub(crate) use m20241127_000001_physical_expression as physical_expression;
diff --git a/optd-mvp/src/migrator/mod.rs b/optd-mvp/src/migrator/mod.rs
new file mode 100644
index 0000000..92f100a
--- /dev/null
+++ b/optd-mvp/src/migrator/mod.rs
@@ -0,0 +1,32 @@
+//! This module defines the tables and their schemas for representing a persistent memo table.
+//!
+//! The most important tables represented here are the [`group`], [`logical_expression`], and
+//! [`physical_expression`] tables. See the corresponding modules for more information on their
+//! relations and fields.
+//!
+//! See the SeaORM docs for more information specific to migrations.
+//!
+//! [`group`]: memo::group
+//! [`logical_expression`]: memo::logical_expression
+//! [`physical_expression`]: memo::physical_expression
+
+use sea_orm_migration::prelude::*;
+
+mod memo;
+
+/// A unit struct that implements the [`MigratorTrait`] for running custom migrations.
+pub struct Migrator;
+
+#[async_trait::async_trait]
+impl MigratorTrait for Migrator {
+    fn migrations() -> Vec<Box<dyn MigrationTrait>> {
+        vec![
+            Box::new(memo::group::Migration),
+            Box::new(memo::fingerprint::Migration),
+            Box::new(memo::logical_expression::Migration),
+            Box::new(memo::logical_children::Migration),
+            Box::new(memo::physical_expression::Migration),
+            Box::new(memo::physical_children::Migration),
+        ]
+    }
+}