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// Copyright Materialize, Inc. and contributors. All rights reserved.
//
// Use of this software is governed by the Business Source License
// included in the LICENSE file.
//
// As of the Change Date specified in that file, in accordance with
// the Business Source License, use of this software will be governed
// by the Apache License, Version 2.0.
//! Utilities for abstract interpretation of [crate::plan::Plan] structures.
//!
//! Those can be used to define analysis passes over [crate::plan::Plan]s in a
//! consistent and unified manner. The primary abstraction here is the
//! [Interpreter] trait.
use std::collections::BTreeMap;
use std::fmt::Debug;
use differential_dataflow::lattice::Lattice;
use itertools::zip_eq;
use mz_expr::{
EvalError, Id, LetRecLimit, LocalId, MapFilterProject, MirScalarExpr, TableFunc,
RECURSION_LIMIT,
};
use mz_ore::cast::CastFrom;
use mz_ore::stack::{CheckedRecursion, RecursionGuard, RecursionLimitError};
use mz_ore::{assert_none, soft_panic_or_log};
use mz_repr::{Diff, Row};
use crate::plan::join::JoinPlan;
use crate::plan::reduce::{KeyValPlan, ReducePlan};
use crate::plan::threshold::ThresholdPlan;
use crate::plan::top_k::TopKPlan;
use crate::plan::{AvailableCollections, GetPlan, Plan};
/// An [abstract interpreter] for [Plan] expressions.
///
/// This is an [object algebra] / [tagless final encoding] of the language
/// defined by [crate::plan::Plan], with the exception of the `Let*`
/// variants. The latter are modeled as part of the various recursion methods,
/// as they are constructs to introduce and reference context.
///
/// [abstract interpreter]:
/// <https://en.wikipedia.org/wiki/Abstract_interpretation>
/// [object algebra]:
/// <https://www.cs.utexas.edu/~wcook/Drafts/2012/ecoop2012.pdf>
/// [tagless final encoding]: <https://okmij.org/ftp/tagless-final/>
///
/// TODO(#24943): align this with the `Plan` structure
pub trait Interpreter<T = mz_repr::Timestamp> {
/// TODO(#25239): Add documentation.
type Domain: Debug + Sized;
/// TODO(#25239): Add documentation.
fn constant(
&self,
ctx: &Context<Self::Domain>,
rows: &Result<Vec<(Row, T, Diff)>, EvalError>,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn get(
&self,
ctx: &Context<Self::Domain>,
id: &Id,
keys: &AvailableCollections,
plan: &GetPlan,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn mfp(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
mfp: &MapFilterProject,
input_key_val: &Option<(Vec<MirScalarExpr>, Option<Row>)>,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn flat_map(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
func: &TableFunc,
exprs: &Vec<MirScalarExpr>,
mfp: &MapFilterProject,
input_key: &Option<Vec<MirScalarExpr>>,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn join(
&self,
ctx: &Context<Self::Domain>,
inputs: Vec<Self::Domain>,
plan: &JoinPlan,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn reduce(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
key_val_plan: &KeyValPlan,
plan: &ReducePlan,
input_key: &Option<Vec<MirScalarExpr>>,
mfp_after: &MapFilterProject,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn top_k(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
top_k_plan: &TopKPlan,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn negate(&self, ctx: &Context<Self::Domain>, input: Self::Domain) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn threshold(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
threshold_plan: &ThresholdPlan,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn union(
&self,
ctx: &Context<Self::Domain>,
inputs: Vec<Self::Domain>,
consolidate_output: bool,
) -> Self::Domain;
/// TODO(#25239): Add documentation.
fn arrange_by(
&self,
ctx: &Context<Self::Domain>,
input: Self::Domain,
forms: &AvailableCollections,
input_key: &Option<Vec<MirScalarExpr>>,
input_mfp: &MapFilterProject,
) -> Self::Domain;
}
/// An [Interpreter] context.
#[derive(Debug)]
pub struct InterpreterContext<Domain> {
/// The bindings currently in the context.
pub bindings: BTreeMap<LocalId, ContextEntry<Domain>>,
/// Is the context recursive (i.e., is one of our ancestors a `LetRec` binding) or not.
pub is_rec: bool,
}
/// TODO(#25239): Add documentation.
pub type Context<Domain> = InterpreterContext<Domain>;
impl<Domain> Default for InterpreterContext<Domain> {
fn default() -> Self {
InterpreterContext {
bindings: Default::default(),
is_rec: false,
}
}
}
/// An entry in an [Interpreter] context.
///
/// Each entry corresponds to a binding identified by a [LocalId] that is
/// visible in the current context.
#[derive(Debug)]
pub struct ContextEntry<Domain> {
/// Is this entry correspond to a recursive binding or not.
pub is_rec: bool,
/// The domain value associated with this binding.
pub value: Domain,
}
impl<Domain> ContextEntry<Domain> {
fn of_let(value: Domain) -> Self {
Self {
is_rec: false,
value,
}
}
fn of_let_rec(value: Domain) -> Self {
Self {
is_rec: true,
value,
}
}
}
/// A lattice with existing `top` and `bottom` elements.
pub trait BoundedLattice: Lattice {
/// The top element of this lattice (represents the most general
/// approximation).
fn top() -> Self;
/// The bottom element of this lattice (represents the most constrained
/// approximation).
fn bottom() -> Self;
}
/// The maximum of iterations of running lattice-based dataflow inference for
/// the LetRec nodes before falling back to a conservative estimate of all
/// bottom() elements for all recursive bindings.
const MAX_LET_REC_ITERATIONS: u64 = 100;
/// A wrapper for a recursive fold invocation over a [Plan] that cannot
/// mutate its input.
#[allow(missing_debug_implementations)]
pub struct Fold<I, T>
where
I: Interpreter<T>,
{
interpret: I,
ctx: Context<I::Domain>,
}
impl<I, T> Fold<I, T>
where
I: Interpreter<T>,
I::Domain: BoundedLattice + Clone,
{
/// TODO(#25239): Add documentation.
pub fn new(interpreter: I) -> Self {
Self {
interpret: interpreter,
ctx: Context::default(),
}
}
/// An immutable fold (structural recursion) over a [Plan] instance.
///
/// Runs an abstract interpreter over the given `expr` in a bottom-up
/// manner, keeping the `ctx` field of the enclosing field up to date, and
/// returns the final result for the entire `expr`.
pub fn apply(&mut self, expr: &Plan<T>) -> Result<I::Domain, RecursionLimitError> {
self.apply_rec(expr, &RecursionGuard::with_limit(RECURSION_LIMIT))
}
fn apply_rec(
&mut self,
expr: &Plan<T>,
rg: &RecursionGuard,
) -> Result<I::Domain, RecursionLimitError> {
use Plan::*;
rg.checked_recur(|_| {
match expr {
Constant { rows, lir_id: _ } => {
// Interpret the current node.
Ok(self.interpret.constant(&self.ctx, rows))
}
Get {
id,
keys,
plan,
lir_id: _,
} => {
// Interpret the current node.
Ok(self.interpret.get(&self.ctx, id, keys, plan))
}
Let {
id,
value,
body,
lir_id: _,
} => {
// Extend context with the `value` result.
let res_value = self.apply_rec(value, rg)?;
let old_entry = self
.ctx
.bindings
.insert(*id, ContextEntry::of_let(res_value));
assert_none!(old_entry, "No shadowing");
// Descend into `body` with the extended context.
let res_body = self.apply_rec(body, rg);
// Revert the context.
self.ctx.bindings.remove(id);
// Return result from `body`.
res_body
}
LetRec {
ids,
values,
limits,
body,
lir_id: _,
} => {
// Make context recursive and extend it with `bottom` for each recursive
// binding. This corresponds to starting with the most optimistic value.
let previous_is_rec = self.ctx.is_rec;
self.ctx.is_rec = true;
for id in ids.iter() {
let new_entry = ContextEntry::of_let_rec(I::Domain::bottom());
let old_entry = self.ctx.bindings.insert(*id, new_entry);
assert_none!(old_entry);
}
let min_max_iter = LetRecLimit::min_max_iter(limits);
let mut curr_iteration = 0;
loop {
// Check for conditions (2) and (3).
if curr_iteration >= MAX_LET_REC_ITERATIONS
|| min_max_iter
.map(|min_max_iter| curr_iteration >= min_max_iter)
.unwrap_or(false)
{
if curr_iteration > u64::cast_from(ids.len()) {
soft_panic_or_log!(
"LetRec loop in Plan fold has not converged in |{}|",
ids.len()
);
}
// Reset all ids to `top` (a conservative value).
for id in ids.iter() {
let new_entry = ContextEntry::of_let_rec(I::Domain::top());
self.ctx.bindings.insert(*id, new_entry);
}
break;
}
// Check for condition (1).
let mut change = false;
for (id, value) in zip_eq(ids.iter(), values.iter()) {
// Compute and join new with the current estimate.
let mut res_value_new = self.apply_rec(value, rg)?;
res_value_new.join_assign(&self.ctx.bindings.get(id).unwrap().value);
// If the estimate has changed
if res_value_new != self.ctx.bindings.get(id).unwrap().value {
// Set the change flag.
change = true;
// Update the context entry.
let new_entry = ContextEntry::of_let_rec(res_value_new);
self.ctx.bindings.insert(*id, new_entry);
}
}
if !change {
break;
}
curr_iteration += 1;
}
// Descend into `body` with the extended context.
// Note, however, that while the body uses bindings
// that are recursive, its recursiveness is given
// by the previous context.
self.ctx.is_rec = previous_is_rec;
let res_body = self.apply_rec(body, rg);
// Revert the context.
for id in ids.iter() {
self.ctx.bindings.remove(id);
}
// Return result from `body`.
res_body
}
Mfp {
input,
mfp,
input_key_val,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self.interpret.mfp(&self.ctx, input, mfp, input_key_val))
}
FlatMap {
input,
func,
exprs,
mfp_after: mfp,
input_key,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self
.interpret
.flat_map(&self.ctx, input, func, exprs, mfp, input_key))
}
Join {
inputs,
plan,
lir_id: _,
} => {
// Descend recursively into all children.
let inputs = inputs
.iter()
.map(|input| self.apply_rec(input, rg))
.collect::<Result<Vec<_>, _>>()?;
// Interpret the current node.
Ok(self.interpret.join(&self.ctx, inputs, plan))
}
Reduce {
input,
key_val_plan,
plan,
input_key,
mfp_after,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self.interpret.reduce(
&self.ctx,
input,
key_val_plan,
plan,
input_key,
mfp_after,
))
}
TopK {
input,
top_k_plan,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self.interpret.top_k(&self.ctx, input, top_k_plan))
}
Negate { input, lir_id: _ } => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self.interpret.negate(&self.ctx, input))
}
Threshold {
input,
threshold_plan,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self.interpret.threshold(&self.ctx, input, threshold_plan))
}
Union {
inputs,
consolidate_output,
lir_id: _,
} => {
// Descend recursively into all children.
let inputs = inputs
.iter()
.map(|input| self.apply_rec(input, rg))
.collect::<Result<Vec<_>, _>>()?;
// Interpret the current node.
Ok(self.interpret.union(&self.ctx, inputs, *consolidate_output))
}
ArrangeBy {
input,
forms,
input_key,
input_mfp,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
Ok(self
.interpret
.arrange_by(&self.ctx, input, forms, input_key, input_mfp))
}
}
})
}
}
/// A wrapper for a recursive fold invocation over a [Plan] that can
/// mutate its input.
#[allow(missing_debug_implementations)]
pub struct FoldMut<I, T, Action>
where
I: Interpreter<T>,
{
interpret: I,
action: Action,
ctx: Context<I::Domain>,
}
impl<I, T, A> FoldMut<I, T, A>
where
I: Interpreter<T>,
I::Domain: BoundedLattice + Clone,
A: FnMut(&mut Plan<T>, &I::Domain, &[I::Domain]),
{
/// TODO(#25239): Add documentation.
pub fn new(interpreter: I, action: A) -> Self {
Self {
interpret: interpreter,
action,
ctx: Context::default(),
}
}
/// An immutable fold (structural recursion) over a [Plan] instance.
///
/// Runs an abstract interpreter over the given `expr` in a bottom-up
/// manner, keeping the `ctx` field of the enclosing field up to date, and
/// returns the final result for the entire `expr`.
///
/// At each step, the current `expr` is passed along with the interpretation
/// result of itself and its children to an `action` callback that can
/// optionally mutate it.
pub fn apply(&mut self, expr: &mut Plan<T>) -> Result<I::Domain, RecursionLimitError> {
self.apply_rec(expr, &RecursionGuard::with_limit(RECURSION_LIMIT))
}
fn apply_rec(
&mut self,
expr: &mut Plan<T>,
rg: &RecursionGuard,
) -> Result<I::Domain, RecursionLimitError> {
use Plan::*;
rg.checked_recur(|_| {
match expr {
Constant { rows, lir_id: _ } => {
// Interpret the current node.
let result = self.interpret.constant(&self.ctx, rows);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[]);
// Pass the interpretation result up.
Ok(result)
}
Get {
id,
keys,
plan,
lir_id: _,
} => {
// Interpret the current node.
let result = self.interpret.get(&self.ctx, id, keys, plan);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[]);
// Pass the interpretation result up.
Ok(result)
}
Let {
id,
value,
body,
lir_id: _,
} => {
// Extend context with the `value` result.
let res_value = self.apply_rec(value, rg)?;
let old_entry = self
.ctx
.bindings
.insert(*id, ContextEntry::of_let(res_value));
assert_none!(old_entry, "No shadowing");
// Descend into `body` with the extended context.
let res_body = self.apply_rec(body, rg);
// Revert the context.
self.ctx.bindings.remove(id);
// Return result from `body`.
res_body
}
LetRec {
ids,
values,
limits,
body,
lir_id: _,
} => {
// Make context recursive and extend it with `bottom` for each recursive
// binding. This corresponds to starting with the most optimistic value.
let previous_is_rec = self.ctx.is_rec;
self.ctx.is_rec = true;
for id in ids.iter() {
let new_entry = ContextEntry::of_let_rec(I::Domain::bottom());
let old_entry = self.ctx.bindings.insert(*id, new_entry);
assert_none!(old_entry);
}
let min_max_iter = LetRecLimit::min_max_iter(limits);
let mut curr_iteration = 0;
loop {
// Check for conditions (2) and (3).
if curr_iteration >= MAX_LET_REC_ITERATIONS
|| min_max_iter
.map(|min_max_iter| curr_iteration >= min_max_iter)
.unwrap_or(false)
{
if curr_iteration > u64::cast_from(ids.len()) {
soft_panic_or_log!(
"LetRec loop in Plan fold has not converged in |{}|",
ids.len()
);
}
// Reset all ids to `top` (a conservative value).
for id in ids.iter() {
let new_entry = ContextEntry::of_let_rec(I::Domain::top());
self.ctx.bindings.insert(*id, new_entry);
}
break;
}
// Check for condition (1).
let mut change = false;
for (id, value) in zip_eq(ids.iter(), values.iter_mut()) {
// Compute and join new with the current estimate.
let mut res_value_new = self.apply_rec(value, rg)?;
res_value_new.join_assign(&self.ctx.bindings.get(id).unwrap().value);
// If the estimate has changed
if res_value_new != self.ctx.bindings.get(id).unwrap().value {
// Set the change flag.
change = true;
// Update the context entry.
let new_entry = ContextEntry::of_let_rec(res_value_new);
self.ctx.bindings.insert(*id, new_entry);
}
}
if !change {
break;
}
curr_iteration += 1;
}
// Descend into `body` with the extended context.
// Note, however, that while the body uses bindings
// that are recursive, its recursiveness is given
// by the previous context.
self.ctx.is_rec = previous_is_rec;
let res_body = self.apply_rec(body, rg);
// Revert the context.
for id in ids.iter() {
self.ctx.bindings.remove(id);
}
// Return result from `body`.
res_body
}
Mfp {
input,
mfp,
input_key_val,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self
.interpret
.mfp(&self.ctx, input.clone(), mfp, input_key_val);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
FlatMap {
input,
func,
exprs,
mfp_after: mfp,
input_key,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self.interpret.flat_map(
&self.ctx,
input.clone(),
func,
exprs,
mfp,
input_key,
);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
Join {
inputs,
plan,
lir_id: _,
} => {
// Descend recursively into all children.
let inputs: Vec<_> = inputs
.iter_mut()
.map(|input| self.apply_rec(input, rg))
.collect::<Result<Vec<_>, _>>()?;
// Interpret the current node.
let result = self.interpret.join(&self.ctx, inputs.clone(), plan);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &inputs);
// Pass the interpretation result up.
Ok(result)
}
Reduce {
input,
key_val_plan,
plan,
input_key,
mfp_after,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self.interpret.reduce(
&self.ctx,
input.clone(),
key_val_plan,
plan,
input_key,
mfp_after,
);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
TopK {
input,
top_k_plan,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self.interpret.top_k(&self.ctx, input.clone(), top_k_plan);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
Negate { input, lir_id: _ } => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self.interpret.negate(&self.ctx, input.clone());
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
Threshold {
input,
threshold_plan,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self
.interpret
.threshold(&self.ctx, input.clone(), threshold_plan);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
Union {
inputs,
consolidate_output,
lir_id: _,
} => {
// Descend recursively into all children.
let inputs: Vec<_> = inputs
.iter_mut()
.map(|input| self.apply_rec(input, rg))
.collect::<Result<Vec<_>, _>>()?;
// Interpret the current node.
let result =
self.interpret
.union(&self.ctx, inputs.clone(), *consolidate_output);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &inputs);
// Pass the interpretation result up.
Ok(result)
}
ArrangeBy {
input,
forms,
input_key,
input_mfp,
lir_id: _,
} => {
// Descend recursively into all children.
let input = self.apply_rec(input, rg)?;
// Interpret the current node.
let result = self.interpret.arrange_by(
&self.ctx,
input.clone(),
forms,
input_key,
input_mfp,
);
// Mutate the current node using the given `action`.
(self.action)(expr, &result, &[input]);
// Pass the interpretation result up.
Ok(result)
}
}
})
}
}