Type Exercise in Rust

(In Chinese) 数据库表达式执行的黑魔法：用 Rust 做类型体操

This is a short lecture on how to use the Rust type system to build necessary components in a database system.

Deep Dive Type Exercise Series (in Chinese)

On My Blog:

Part 0 - Part 1

On Zhihu:

Day 1: `Array` and `ArrayBuilder`

ArrayBuilder and Array are reciprocal traits. ArrayBuilder creates an Array, while we can create a new array using ArrayBuilder with existing Array. In day 1, we implement arrays for primitive types (like i32, f32) and for variable-length types (like String). We use associated types in traits to deduce the right type in generic functions and use GAT to unify the Array interfaces for both fixed-length and variable-length types. This framework is also very similar to libraries like Apache Arrow, but with much stronger type constraints and much lower runtime overhead.

The special thing is that, we use blanket implementation for i32 and f32 arrays -- PrimitiveArray<T>. This would make our journey much more challenging, as we need to carefully evaluate the trait bounds needed for them in the following days.

Goals

Developers can create generic functions over all types of arrays -- no matter fixed-length primitive array like I32Array, or variable-length array like StringArray.

Without our Array trait, developers might to implement...

fn build_i32_array_from_vec(items: &[Option<i32>]) -> Vec<i32> { /* .. */ }
fn build_str_array_from_vec(items: &[Option<&str>]) -> Vec<String> { /* .. */ }

Note that the function takes different parameter -- one i32 without lifetime, one &str. Our Array trait can unify their behavior:

fn build_array_from_vec<A: Array>(items: &[Option<A::RefItem<'_>>]) -> A {
    let mut builder = A::Builder::with_capacity(items.len());
    for item in items {
        builder.push(*item);
    }
    builder.finish()
}

#[test]
fn test_build_int32_array() {
    let data = vec![Some(1), Some(2), Some(3), None, Some(5)];
    let array = build_array_from_vec::<I32Array>(&data[..]);
}

#[test]
fn test_build_string_array() {
    let data = vec![Some("1"), Some("2"), Some("3"), None, Some("5"), Some("")];
    let array = build_array_from_vec::<StringArray>(&data[..]);
}

Day 2: `Scalar` and `ScalarRef`

Scalar and ScalarRef are reciprocal types. We can get a reference ScalarRef of a Scalar, and convert ScalarRef back to Scalar. By adding these two traits, we can write more generic functions with zero runtime overhead on type matching and conversion. Meanwhile, we associate Scalar with Array, so as to write functions more easily.

Goals

Without our Scalar implement, there could be problems:

fn build_array_repeated_owned<A: Array>(item: A::OwnedItem, len: usize) -> A {
    let mut builder = A::Builder::with_capacity(len);
    for _ in 0..len {
        builder.push(Some(item /* How to convert `item` to `RefItem`? */));
    }
    builder.finish()
}

With Scalar trait and corresponding implements,

fn build_array_repeated_owned<A: Array>(item: A::OwnedItem, len: usize) -> A {
    let mut builder = A::Builder::with_capacity(len);
    for _ in 0..len {
        builder.push(Some(item.as_scalar_ref())); // Now we have `as_scalar_ref` on `Scalar`!
    }
    builder.finish()
}

Day 3: `ArrayImpl`, `ArrayBuilderImpl`, `ScalarImpl` and `ScalarRefImpl`

It could be possible that some information is not available until runtime. Therefore, we use XXXImpl enums to cover all variants of a single type. At the same time, we also add TryFrom<ArrayImpl> and Into<ArrayImpl> bound for Array.

Goals

This is hard -- imagine we simply require TryFrom<ArrayImpl> and Into<ArrayImpl> bound on Array:

pub trait Array:
    Send + Sync + Sized + 'static + TryFrom<ArrayImpl> + Into<ArrayImpl>

Compiler will complain:

43 | impl<T> Array for PrimitiveArray<T>
   |         ^^^^^ the trait `From<PrimitiveArray<T>>` is not implemented for `array::ArrayImpl`
   |
   = note: required because of the requirements on the impl of `Into<array::ArrayImpl>` for `PrimitiveArray<T>`

This is because we use blanket implementation for PrimitiveArray to cover all primitive types. In day 3, we learn how to correctly add bounds to PrimitiveArray.

Day 4: More Types and Methods with Macro

ArrayImpl should supports common functions in traits, but Array trait doesn't have a unified interface for all types -- I32Array accepts get(&self, idx: usize) -> Option<i32> while StringArray accepts get(&self, idx: usize) -> &str. We need a get(&self, idx:usize) -> ScalarRefImpl<'_> on ArrayImpl. Therefore, we have to write the match arms to dispatch the methods.

Also, we have written so many boilerplate code for From and TryFrom. We need to eliminate such duplicated code.

As we are having more and more data types, we need to write the same code multiple times within a match arm. In day 4, we use declarative macros (instead of procedural macros or other kinds of code generator) to generate such code and avoid writing boilerplate code.

Goals

Before that, we need to implement every TryFrom or Scalar by ourselves:

impl<'a> ScalarRef<'a> for i32 {
    type ArrayType = I32Array;
    type ScalarType = i32;

    fn to_owned_scalar(&self) -> i32 {
        *self
    }
}

// repeat the same code fore i64, f64, ...

impl ArrayImpl {
    /// Get the value at the given index.
    pub fn get(&self, idx: usize) -> Option<ScalarRefImpl<'_>> {
        match self {
            Self::Int32(array) => array.get(idx).map(ScalarRefImpl::Int32),
            Self::Float64(array) => array.get(idx).map(ScalarRefImpl::Float64),
            // ...
            // repeat the types for every functions we added on `Array`
        }
    }

With macros, we can easily add more and more types. In day 4, we will support:

pub enum ArrayImpl {
    Int16(I16Array),
    Int32(I32Array),
    Int64(I64Array),
    Float32(F32Array),
    Float64(F64Array),
    Bool(BoolArray),
    String(StringArray),
}

With little code changed and eliminating boilerplate code.

Day 5: Binary Expressions

Now that we have Array, ArrayBuilder, Scalar and ScalarRef, we can convert every function we wrote to a vectorized one using generics.

Goals

Developers will only need to implement:

pub fn str_contains(i1: &str, i2: &str) -> bool {
    i1.contains(i2)
}

And they can create BinaryExpression around this function with any type:

// Vectorize `str_contains` to accept an array instead of a single value.
let expr = BinaryExpression::<StringArray, StringArray, BoolArray, _>::new(str_contains);
// We only need to pass `ArrayImpl` to the expression, and it will do everything for us,
// including type checks, loopping, etc.
let result = expr
    .eval(
        &StringArray::from_slice(&[Some("000"), Some("111"), None]).into(),
        &StringArray::from_slice(&[Some("0"), Some("0"), None]).into(),
    )
    .unwrap();

Developers can even create BinaryExpression around generic functions:

pub fn cmp_le<'a, I1: Array, I2: Array, C: Array + 'static>(
    i1: I1::RefItem<'a>,
    i2: I2::RefItem<'a>,
) -> bool
where
    I1::RefItem<'a>: Into<C::RefItem<'a>>,
    I2::RefItem<'a>: Into<C::RefItem<'a>>,
    C::RefItem<'a>: PartialOrd,
{
    i1.into().partial_cmp(&i2.into()).unwrap() == Ordering::Less
}

// Vectorize `cmp_le` to accept an array instead of a single value.
let expr = BinaryExpression::<I32Array, I32Array, BoolArray, _>::new(
        cmp_le::<I32Array, I32Array, I64Array>,
    );
let result: ArrayImpl = expr.eval(ArrayImpl, ArrayImpl).unwrap();

// `cmp_le` can also be used on `&str`.
let expr = BinaryExpression::<StringArray, StringArray, BoolArray, _>::new(
        cmp_le::<StringArray, StringArray, StringArray>,
    );
let result: ArrayImpl = expr.eval(ArrayImpl, ArrayImpl).unwrap();

Day 6: Erase Expression Lifetime

Vectorization looks fancy in the implementation in day 5, but there is a critical flaw -- BinaryExpression can only process &'a ArrayImpl instead of for any lifetime.

impl<'a, I1: Array, I2: Array, O: Array, F> BinaryExpression<I1, I2, O, F> {
    pub fn eval(&self, i1: &'a ArrayImpl, i2: &'a ArrayImpl) -> Result<ArrayImpl> {
        // ...
    }
}

In day 6, we erase the expression lifetime by defining a BinaryExprFunc trait and implements it for all expression functions.

impl<'a, I1: Array, I2: Array, O: Array, F> BinaryExpression<I1, I2, O, F> {
    pub fn eval(&self, i1: &ArrayImpl, i2: &ArrayImpl) -> Result<ArrayImpl> {
        // ...
    }
}

In this day, we have two solutions -- the hard way and the easy way.

Goals -- The Easy Way

If we make each scalar function into a struct, things will be a lot easier.

Developers will now implement scalar function as follows:

pub struct ExprStrContains;

impl BinaryExprFunc<StringArray, StringArray, BoolArray> for ExprStrContains {
    fn eval(&self, i1: &str, i2: &str) -> bool {
        i1.contains(i2)
    }
}

And now we can have an expression trait over all expression, with all type and lifetime erased:

pub trait Expression {
    /// Evaluate an expression with run-time number of [`ArrayImpl`]s.
    fn eval_expr(&self, data: &[&ArrayImpl]) -> Result<ArrayImpl>;
}

Expression can be made into a Box<dyn Expression>, therefore being used in building expressions at runtime.

Goals -- The Hard Way

In the hard way chapter, we will dive into the black magics and fight against (probably) compiler bugs, so as to make function vectorization look very approachable to SQL function developers.

To begin with, we will change the signature of BinaryExpression to take Scalar as parameter:

pub struct BinaryExpression<I1: Scalar, I2: Scalar, O: Scalar, F> {
    func: F,
    _phantom: PhantomData<(I1, I2, O)>,
}

Then we will do a lot of black magics on Scalar type, so as to do the conversion freely between Array::RefItem and Scalar::RefType. This will help us bypass most of the issues in GAT, and yields the following vectorization code:

builder.push(Some(O::cast_s_to_a(
    self.func
        .eval(I1::cast_a_to_s(i1), I2::cast_a_to_s(i2))
        .as_scalar_ref(),
)))

We will construct a bridge trait BinaryExprFunc between plain functions and the one that can be used by BinaryExpression.

And finally developers can simply write a function and supply it to BinaryExpression.

let expr = BinaryExpression::<String, String, bool, _>::new(str_contains);

Day 7: Physical Data Type and Logical Data Type

i32, i64 is simply physical types -- how types are stored in memory (or on disk). But in a database system, we also have logical types (like Char, and Varchar). In day 7, we learn how to associate logical types with physical types using macros.

Goals

Going back to our build_binary_expression function,

/// Build expression with runtime information.
pub fn build_binary_expression(
    f: ExpressionFunc,
) -> Box<dyn Expression> {
    match f {
        CmpLe => Box::new(BinaryExpression::<I32Array, I32Array, BoolArray, _>::new(
            ExprCmpLe::<_, _, I32Array>(PhantomData),
        )),
    /* ... */

Currently, we only support i32 < i32 for CmpLe expression. We should be able to support cross-type comparison here.

/// Build expression with runtime information.
pub fn build_binary_expression(
    f: ExpressionFunc,
    i1: DataType,
    i2: DataType
) -> Box<dyn Expression> {
    match f {
        CmpLe => match (i1, i2) {
            (SmallInt, SmallInt) => /* I16Array, I16Array */,
            (SmallInt, Real) => /* I16Array, Float32, cast to Float64 before comparison */,
            /* ... */
        }
    /* ... */

We have so many combinations of cross-type comparison, and we couldn't write them all by-hand. In day 7, we use macros to associate logical data type with Array traits, and reduce the complexity of writing such functions.

/// Build expression with runtime information.
pub fn build_binary_expression(
    f: ExpressionFunc,
    i1: DataType,
    i2: DataType,
) -> Box<dyn Expression> {
    use ExpressionFunc::*;

    use crate::array::*;
    use crate::expr::cmp::*;
    use crate::expr::string::*;

    match f {
        CmpLe => for_all_cmp_combinations! { impl_cmp_expression_of, i1, i2, ExprCmpLe },
        CmpGe => for_all_cmp_combinations! { impl_cmp_expression_of, i1, i2, ExprCmpGe },
        CmpEq => for_all_cmp_combinations! { impl_cmp_expression_of, i1, i2, ExprCmpEq },
        CmpNe => for_all_cmp_combinations! { impl_cmp_expression_of, i1, i2, ExprCmpNe },
        StrContains => Box::new(
            BinaryExpression::<StringArray, StringArray, BoolArray, _>::new(ExprStrContains),
        ),
    }
}

The goal is to write as less code as possible to generate all combinations of comparison.

TBD Lectures

Day 8: Aggregators

Aggregators are another kind of expressions. We learn how to implement them easily with our type system in day 8.

Day 9: Expression Framework

Now we are having more and more expression kinds, and we need an expression framework to unify them -- including unary, binary and expressions of more inputs.

At the same time, we will also experiment with return value optimizations in variable-size types.

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