You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: analysis.rs
    path of file: ./repos/materialize/src/transform/src
    
    the code of the file until where you have to start completion: // 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.

//! Traits and types for reusable expression analysis

pub mod equivalences;

use mz_expr::MirRelationExpr;

pub use common::{Derived, DerivedBuilder, DerivedView};

pub use arity::Arity;
pub use non_negative::NonNegative;
pub use subtree::SubtreeSize;
pub use types::RelationType;
pub use unique_keys::UniqueKeys;

/// An analysis that can be applied bottom-up to a `MirRelationExpr`.
pub trait Analysis: 'static {
    /// The type of value this analysis associates with an expression.
    type Value;
    /// Announce any depencies this analysis has on other analyses.
    ///
    /// The method should invoke `builder.require::<Foo>()` for each other
    /// analysis `Foo` this analysis depends upon.
    fn announce_dependencies(_builder: &mut DerivedBuilder) {}
    /// The analysis value derived for an expression, given other analysis results.
    ///
    /// The other analysis results include the results of this analysis for all children,
    /// in `results`, and the results of other analyses this analysis has expressed a
    /// depen
    
        pub fn visit(self, expr: &MirRelationExpr) -> Derived {
            let mut result = self.result;

            // A stack of expressions to process (`Ok`) and let bindings to fill (`Err`).
            let mut todo = vec![Ok(expr)];
            // Expressions in reverse post-order: each expression, followed by its children in reverse order.
            // We will reverse this to get the post order, but must form it in reverse.
            let mut rev_post_order = Vec::new();
            while let Some(command) = todo.pop() {
                match command {
                    // An expression to visit.
                    Ok(expr) => {
                        match expr {
                            MirRelationExpr::Let { id, value, body } => {
                                todo.push(Ok(value));
                                todo.push(Err(*id));
                                todo.push(Ok(body));
                            }
                            MirRelationExpr::LetRec {
                                ids, values, body, ..
                            } => {
                                for (id, value) in ids.iter().zip(values) {
                                    todo.push(Ok(value));
                                    todo.push(Err(*id));
                                }
                                todo.push(Ok(body));
                            }
                            _ => {
                                todo.extend(expr.children().map(Ok));
                            }
                        }
                        rev_post_order.push(expr);
                    }
                    // A local id to install
                    Err(local_id) => {
                        // Capture the *remaining* work, which we'll need to flip around.
                        let prior = result.bindings.insert(local_id, rev_post_order.len());
                        assert!(prior.is_none(), "Shadowing not allowed");
                    }
                }
            }
            // Flip the offsets now that we know a length.
            for value in result.bindings.values_mut() {
                *value = rev_post_order.len() - *value - 1;
            }
            // Visit the pre-order in reverse order: post-order.
            while let Some(expr) = rev_post_order.pop() {
                // Apply each analysis to `expr` in order.
                for id in result.order.iter() {
                    if let Some(mut bundle) = result.analyses.remove(id) {
                        bundle.analyse(expr, &result);
                        result.analyses.insert(*id, bundle);
                    }
                }
            }

            result
        }