Fold

Description

Run an algorithm over each item in a collection of data to create a new item, thus creating a whole new collection.

The etymology here is unclear to me. The terms 'fold' and 'folder' are used in the Rust compiler, although it appears to me to be more like a map than a fold in the usual sense. See the discussion below for more details.

Example

#![allow(unused)]
fn main() {
// The data we will fold, a simple AST.
mod ast {
    pub enum Stmt {
        Expr(Box<Expr>),
        Let(Box<Name>, Box<Expr>),
    }

    pub struct Name {
        value: String,
    }

    pub enum Expr {
        IntLit(i64),
        Add(Box<Expr>, Box<Expr>),
        Sub(Box<Expr>, Box<Expr>),
    }
}

// The abstract folder
mod fold {
    use ast::*;

    pub trait Folder {
        // A leaf node just returns the node itself. In some cases, we can do this
        // to inner nodes too.
        fn fold_name(&mut self, n: Box<Name>) -> Box<Name> { n }
        // Create a new inner node by folding its children.
        fn fold_stmt(&mut self, s: Box<Stmt>) -> Box<Stmt> {
            match *s {
                Stmt::Expr(e) => Box::new(Stmt::Expr(self.fold_expr(e))),
                Stmt::Let(n, e) => Box::new(Stmt::Let(self.fold_name(n), self.fold_expr(e))),
            }
        }
        fn fold_expr(&mut self, e: Box<Expr>) -> Box<Expr> { ... }
    }
}

use fold::*;
use ast::*;

// An example concrete implementation - renames every name to 'foo'.
struct Renamer;
impl Folder for Renamer {
    fn fold_name(&mut self, n: Box<Name>) -> Box<Name> {
        Box::new(Name { value: "foo".to_owned() })
    }
    // Use the default methods for the other nodes.
}
}

The result of running the Renamer on an AST is a new AST identical to the old one, but with every name changed to foo. A real life folder might have some state preserved between nodes in the struct itself.

A folder can also be defined to map one data structure to a different (but usually similar) data structure. For example, we could fold an AST into a HIR tree (HIR stands for high-level intermediate representation).

Motivation

It is common to want to map a data structure by performing some operation on each node in the structure. For simple operations on simple data structures, this can be done using Iterator::map. For more complex operations, perhaps where earlier nodes can affect the operation on later nodes, or where iteration over the data structure is non-trivial, using the fold pattern is more appropriate.

Like the visitor pattern, the fold pattern allows us to separate traversal of a data structure from the operations performed to each node.

Discussion

Mapping data structures in this fashion is common in functional languages. In OO languages, it would be more common to mutate the data structure in place. The 'functional' approach is common in Rust, mostly due to the preference for immutability. Using fresh data structures, rather than mutating old ones, makes reasoning about the code easier in most circumstances.

The trade-off between efficiency and reusability can be tweaked by changing how nodes are accepted by the fold_* methods.

In the above example we operate on Box pointers. Since these own their data exclusively, the original copy of the data structure cannot be re-used. On the other hand if a node is not changed, reusing it is very efficient.

If we were to operate on borrowed references, the original data structure can be reused; however, a node must be cloned even if unchanged, which can be expensive.

Using a reference counted pointer gives the best of both worlds - we can reuse the original data structure and we don't need to clone unchanged nodes. However, they are less ergonomic to use and mean that the data structures cannot be mutable.

See also

Iterators have a fold method, however this folds a data structure into a value, rather than into a new data structure. An iterator's map is more like this fold pattern.

In other languages, fold is usually used in the sense of Rust's iterators, rather than this pattern. Some functional languages have powerful constructs for performing flexible maps over data structures.

The visitor pattern is closely related to fold. They share the concept of walking a data structure performing an operation on each node. However, the visitor does not create a new data structure nor consume the old one.