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09/05 — 2020
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# Auto-currying Rust Functions

This post contains a gentle introduction to procedural macros in Rust and a guide to writing a procedural macro to curry Rust functions. The source code for the entire library can be found here. It is also available on crates.io.

The following links might prove to be useful before getting started:

Or you can pretend you read them, because I have included a primer here :)

### Contents

1. Currying
2. Procedural Macros
3. Definitions
4. Refinement
5. The In-betweens
5.1 Dependencies
5.2 The attribute macro
5.3 Function Body
5.4 Function Signature
5.5 Getting it together
6. Debugging and Testing
7. Notes
8. Conclusion

### Currying

Currying is the process of transformation of a function call like `f(a, b, c)` to `f(a)(b)(c)`. A curried function returns a concrete value only when it receives all its arguments! If it does recieve an insufficient amount of arguments, say 1 of 3, it returns a curried function, that returns after receiving 2 arguments.

``````curry(f(a, b, c)) = h(a)(b)(c)

h(x) = g   <- curried function that takes upto 2 args (g)
g(y) = k   <- curried function that takes upto 1 arg (k)
k(z) = v   <- a value (v)

Keen readers will conclude the following,
h(x)(y)(z) = g(y)(z) = k(z) = v``````

Mathematically, if `f` is a function that takes two arguments `x` and `y`, such that `x ϵ X`, and `y ϵ Y` , we write it as:

``f: (X × Y) -> Z``

where `×` denotes the Cartesian product of set `X` and `Y`, and curried `f` (denoted by `h` here) is written as:

``h: X -> (Y -> Z)``

### Procedural Macros

These are functions that take code as input and spit out modified code as output. Powerful stuff. Rust has three kinds of proc-macros:

• Function like macros
• Derive macros: `#[derive(...)]`, used to automatically implement traits for structs/enums
• and Attribute macros: `#[test]`, usually slapped onto functions

We will be using Attribute macros to convert a Rust function into a curried Rust function, which we should be able to call via: `function(arg1)(arg2)`.

### Definitions

Being respectable programmers, we define the input to and the output from our proc-macro. Here’s a good non-trivial function to start out with:

``````fn add(x: u32, y: u32, z: u32) -> u32 {
return x + y + z;
}``````

Hmm, what would our output look like? What should our proc-macro generate ideally? Well, if we understood currying correctly, we should accept an argument and return a function that accepts an argument and returns … you get the point. Something like this should do:

``````fn add_curried1(x: u32) -> ? {
return fn add_curried2 (y: u32) -> ? {
return fn add_curried3 (z: u32) -> u32 {
return x + y + z;
}
}
}``````

A couple of things to note:

Return types
We have placed `?`s in place of return types. Let’s try to fix that. `add_curried3` returns the ‘value’, so `u32` is accurate. `add_curried2` returns `add_curried3`. What is the type of `add_curried3`? It is a function that takes in a `u32` and returns a `u32`. So a `fn(u32) -> u32` will do right? No, I’ll explain why in the next point, but for now, we will make use of the `Fn` trait, our return type is `impl Fn(u32) -> u32`. This basically tells the compiler that we will be returning something function-like, a.k.a, behaves like a `Fn`. Cool!

If you have been following along, you should be able to tell that the return type of `add_curried1` is:

``impl Fn(u32) -> (impl Fn(u32) -> u32)``

We can drop the parentheses because `->` is right associative:

``````impl Fn(u32) -> impl Fn(u32) -> u32
``````

Accessing environment
A function cannot access it’s environment. Our solution will not work. `add_curried3` attempts to access `x`, which is not allowed! A closure1 however, can. If we are returning a closure, our return type must be `impl Fn`, and not `fn`. The difference between the `Fn` trait and function pointers is beyond the scope of this post.

### Refinement

Armed with knowledge, we refine our expected output, this time, employing closures:

``````fn add(x: u32) -> impl Fn(u32) -> impl Fn(u32) -> u32 {
return move |y| move |z| x + y + z;
}``````

Alas, that does not compile either! It errors out with the following message:

``````error[E0562]: `impl Trait` not allowed outside of function
and inherent method return types
--> src/main.rs:17:37
|
| fn add(x: u32) -> impl Fn(u32) -> impl Fn(u32) -> u32
|                                   ^^^^^^^^^^^^^^^^^^^
``````

You are allowed to return an `impl Fn` only inside a function. We are currently returning it from another return! Or at least, that was the most I could make out of the error message.

We are going to have to cheat a bit to fix this issue; with type aliases and a convenient nightly feature 2:

``````#![feature(type_alias_impl_trait)]  // allows us to use `impl Fn` in type aliases!

type T0 = u32;                 // the return value when zero args are to be applied
type T1 = impl Fn(u32) -> T0;  // the return value when one arg is to be applied
type T2 = impl Fn(u32) -> T1;  // the return value when two args are to be applied

fn add(x: u32) -> T2 {
return move |y| move |z| x + y + z;
}``````

Drop that into a cargo project, call `add(4)(5)(6)`, cross your fingers, and run `cargo +nightly run`. You should see a 15 unless you forgot to print it!

### The In-Betweens

Let us write the magical bits that take us from function to curried function.

Initialize your workspace with `cargo new --lib currying`. Proc-macro crates are libraries with exactly one export, the macro itself. Add a `tests` directory to your crate root. Your directory should look something like this:

``````.
├── Cargo.toml
├── src
│   └── lib.rs
└── tests
└── smoke.rs``````

#### Dependencies

We will be using a total of 3 external crates:

Here’s a sample `Cargo.toml`:

``````# Cargo.toml

[dependencies]
proc-macro2 = "1.0.9"
quote = "1.0"

[dependencies.syn]
version = "1.0"
features = ["full"]

[lib]
proc-macro = true  # this is important!``````

We will be using an external `proc-macro2` crate as well as an internal `proc-macro` crate. Not confusing at all!

#### The attribute macro

Drop this into `src/lib.rs`, to get the ball rolling.

``````// src/lib.rs

use proc_macro::TokenStream;  // 1
use quote::quote;
use syn::{parse_macro_input, ItemFn};

#[proc_macro_attribute]   // 2
pub fn curry(_attr: TokenStream, item: TokenStream) -> TokenStream {
let parsed = parse_macro_input!(item as ItemFn);  // 3
generate_curry(parsed).into()  // 4
}

fn generate_curry(parsed: ItemFn) -> proc_macro2::TokenStream {}``````

1. Imports

A `Tokenstream` holds (hopefully valid) Rust code, this is the type of our input and output. Note that we are importing this type from `proc_macro` and not `proc_macro2`.

`quote!` from the `quote` crate is a macro that allows us to quickly produce `TokenStream`s. Much like the LISP `quote` procedure, you can use the `quote!` macro for symbolic transformations.

`ItemFn` from the `syn` crate holds the parsed `TokenStream` of a Rust function. `parse_macro_input!` is a helper macro provided by `syn`.

2. The lone export

Annotate the only `pub` of our crate with `#[proc_macro_attribute]`. This tells rustc that `curry` is a procedural macro, and allows us to use it as `#[crate_name::curry]` in other crates. Note the signature of the `curry` function. `_attr` is the `TokenStream` representing the attribute itself, `item` refers to the thing we slapped our macro into, in this case a function (like `add`). The return value is a modified `TokenStream`, this will contain our curried version of `add`.

3. The helper macro

A `TokenStream` is a little hard to work with, which is why we have the `syn` crate, which provides types to represent Rust tokens. An `RArrow` struct to represent the return arrow on a function and so on. One of those types is `ItemFn`, that represents an entire Rust function. The `parse_macro_input!` automatically puts the input to our macro into an `ItemFn`. What a gentleman!

4. Returning `TokenStream`s

We haven’t filled in `generate_curry` yet, but we can see that it returns a `proc_macro2::TokenStream` and not a `proc_macro::TokenStream`, so drop a `.into()` to convert it.

Lets move on, and fill in `generate_curry`, I would suggest keeping the documentation for `syn::ItemFn` and `syn::Signature` open.

``````// src/lib.rs

fn generate_curry(parsed: ItemFn) -> proc_macro2::TokenStream {
let fn_body = parsed.block;      // function body
let sig = parsed.sig;            // function signature
let vis = parsed.vis;            // visibility, pub or not
let fn_name = sig.ident;         // function name/identifier
let fn_args = sig.inputs;        // comma separated args
let fn_return_type = sig.output; // return type
}``````

We are simply extracting the bits of the function, we will be reusing the original function’s visibility and name. Take a look at what `syn::Signature` can tell us about a function:

``````                       .-- syn::Ident (ident)
/
fn add(x: u32, y: u32) -> u32
(fn_token)      /     ~~~~~~~,~~~~~~  ~~~~~~
syn::token::Fn --'            /               \       (output)
'                 `- syn::ReturnType
Punctuated<FnArg, Comma> (inputs)``````

Enough analysis, lets produce our first bit of Rust code.

#### Function Body

Recall that the body of a curried `add` should look like this:

``return move |y| move |z| x + y + z;``

And in general:

``return move |arg2| move |arg3| ... |argN| <function body here>``

We already have the function’s body, provided by `fn_body`, in our `generate_curry` function. All that’s left to add is the `move |arg2| move |arg3| ...` stuff, for which we need to extract the argument identifiers (doc: Punctuated, FnArg, PatType):

``````// src/lib.rs
use syn::punctuated::Punctuated;
use syn::{parse_macro_input, FnArg, Pat, ItemFn, Block};

fn extract_arg_idents(fn_args: Punctuated<FnArg, syn::token::Comma>) -> Vec<Box<Pat>> {
return fn_args.into_iter().map(extract_arg_pat).collect::<Vec<_>>();
}``````

Alright, so we are iterating over function args (`Punctuated` is a collection that you can iterate over) and mapping an `extract_arg_pat` to every item. What’s `extract_arg_pat`?

``````// src/lib.rs

fn extract_arg_pat(a: FnArg) -> Box<Pat> {
match a {
FnArg::Typed(p) => p.pat,
_ => panic!("Not supported on types with `self`!"),
}
}``````

`FnArg` is an enum type as you might have guessed. The `Typed` variant encompasses args that are written as `name: type` and the other variant, `Reciever` refers to `self` types. Ignore those for now, keep it simple.

Every `FnArg::Typed` value contains a `pat`, which is in essence, the name of the argument. The type of the arg is accessible via `p.ty` (we will be using this later).

With that done, we should be able to write the codegen for the function body:

``````// src/lib.rs

fn generate_body(fn_args: &[Box<Pat>], body: Box<Block>) -> proc_macro2::TokenStream {
quote! {
return #( move |#fn_args|  )* #body
}
}``````

That is some scary looking syntax! Allow me to explain. The `quote!{ ... }` returns a `proc_macro2::TokenStream`, if we wrote `quote!{ let x = 1 + 2; }`, it wouldn’t create a new variable `x` with value 3, it would literally produce a stream of tokens with that expression.

The `#` enables variable interpolation. `#body` will look for `body` in the current scope, take its value, and insert it in the returned `TokenStream`. Kinda like quasi quoting in LISPs, you have written one.

What about `#( move |#fn_args| )*`? That is repetition. `quote` iterates through `fn_args`, and drops a `move` behind each one, it then places pipes (`|`), around it.

Let us test our first bit of codegen! Modify `generate_curry` like so:

``````// src/lib.rs

fn generate_curry(parsed: ItemFn) -> TokenStream {
let fn_body = parsed.block;
let sig = parsed.sig;
let vis = parsed.vis;
let fn_name = sig.ident;
let fn_args = sig.inputs;
let fn_return_type = sig.output;

+  let arg_idents = extract_arg_idents(fn_args.clone());
+  let first_ident = &arg_idents.first().unwrap();

+  // remember, our curried body starts with the second argument!
+  let curried_body = generate_body(&arg_idents[1..], fn_body.clone());
+  println!("{}", curried_body);

}``````

Add a little test to `tests/`:

``````// tests/smoke.rs

#[currying::curry]
fn add(x: u32, y: u32, z: u32) -> u32 {
x + y + z
}

#[test]
fn works() {
assert!(true);
}``````

You should find something like this in the output of `cargo test`:

``return move | y | move | z | { x + y + z }``

Glorious `println!` debugging!

#### Function signature

This section gets into the more complicated bits of the macro, generating type aliases and the function signature. By the end of this section, we should have a full working auto-currying macro!

Recall what our generated type aliases should look like, for our `add` function:

``````type T0 = u32;
type T1 = impl Fn(u32) -> T0;
type T2 = impl Fn(u32) -> T1;``````

In general:

``````type T0 = <return type>;
type T1 = impl Fn(<type of arg N>) -> T0;
type T2 = impl Fn(<type of arg N - 1>) -> T1;
.
.
.
type T(N-1) = impl Fn(<type of arg 2>) -> T(N-2);``````

To codegen that, we need the types of:

• all our inputs (arguments)
• the output (the return type)

To fetch the types of all our inputs, we can simply reuse the bits we wrote to fetch the names of all our inputs! (doc: Type)

``````// src/lib.rs

use syn::{parse_macro_input, Block, FnArg, ItemFn, Pat, ReturnType, Type};

fn extract_type(a: FnArg) -> Box<Type> {
match a {
FnArg::Typed(p) => p.ty,  // notice `ty` instead of `pat`
_ => panic!("Not supported on types with `self`!"),
}
}

fn extract_arg_types(fn_args: Punctuated<FnArg, syn::token::Comma>) -> Vec<Box<Type>> {
return fn_args.into_iter().map(extract_type).collect::<Vec<_>>();

}``````

A good reader would have looked at the docs for output member of the `syn::Signature` struct. It has the type `syn::ReturnType`. So there is no extraction to do here right? There are actually a couple of things we have to ensure here:

1. We need to ensure that the function returns! A function that does not return is pointless in this case, and I will tell you why, in the Notes section.

2. A `ReturnType` encloses the arrow of the return as well, we need to get rid of that. Recall:

``````type T0 = u32
// and not
type T0 = -> u32``````

Here is the snippet that handles extraction of the return type (doc: syn::ReturnType):

``````// src/lib.rs

fn extract_return_type(a: ReturnType) -> Box<Type> {
match a {
ReturnType::Type(_, p) => p,
_ => panic!("Not supported on functions without return types!"),
}
}``````

You might notice that we are making extensive use of the `panic!` macro. Well, that is because it is a good idea to quit on receiving an unsatisfactory `TokenStream`.

With all our types ready, we can get on with generating type aliases:

``````// src/lib.rs

use quote::{quote, format_ident};

fn generate_type_aliases(
fn_arg_types: &[Box<Type>],
fn_return_type: Box<Type>,
fn_name: &syn::Ident,
) -> Vec<proc_macro2::TokenStream> {    // 1

let type_t0 = format_ident!("_{}_T0", fn_name);    // 2
let mut type_aliases = vec![quote! { type #type_t0 = #fn_return_type  }];

// 3
for (i, t) in (1..).zip(fn_arg_types.into_iter().rev()) {
let p = format_ident!("_{}_{}", fn_name, format!("T{}", i - 1));
let n = format_ident!("_{}_{}", fn_name, format!("T{}", i));

type_aliases.push(quote! {
type #n = impl Fn(#t) -> #p
});
}

return type_aliases;
}``````

1. The return value
We are returning a `Vec<proc_macro2::TokenStream>`, i. e., a list of `TokenStream`s, where each item is a type alias.

2. Format identifier?
I’ve got some explanation to do on this line. Clearly, we are trying to write the first type alias, and initialize our `TokenStream` vector with `T0`, because it is different from the others:

``````type T0 = something
// the others are of the form
type Tr = impl Fn(something) -> something``````

`format_ident!` is similar to `format!`. Instead of returning a formatted string, it returns a `syn::Ident`. Therefore, `type_t0` is actually an identifier for, in the case of our `add` function, `_add_T0`. Why is this formatting important? Namespacing.

Picture this, we have two functions, `add` and `subtract`, that we wish to curry with our macro:

``````#[curry]
fn add(...) -> u32 { ... }

#[curry]
fn sub(...) -> u32 { ... }``````

Here is the same but with macros expanded:

``````type T0 = u32;
type T1 = impl Fn(u32) -> T0;
fn add( ... ) -> T1 { ... }

type T0 = u32;
type T1 = impl Fn(u32) -> T0;
fn sub( ... ) -> T1 { ... }``````

We end up with two definitions of `T0`! Now, if we do the little `format_ident!` dance we did up there:

``````type _add_T0 = u32;

type _sub_T0 = u32;
type _sub_T1 = impl Fn(u32) -> _sub_T0;
fn sub( ... ) -> _sub_T1 { ... }``````

Voilà! The type aliases don’t tread on each other. Remember to import `format_ident` from the `quote` crate.

3. The TokenStream Vector

We iterate over our types in reverse order (`T0` is the last return, `T1` is the second last, so on), assign a number to each iteration with `zip`, generate type names with `format_ident`, push a `TokenStream` with the help of `quote` and variable interpolation.

If you are wondering why we used `(1..).zip()` instead of `.enumerate()`, it’s because we wanted to start counting from 1 instead of 0 (we are already done with `T0`!).

#### Getting it together

I promised we’d have a fully working macro by the end of last section. I lied, we have to tie everything together in our `generate_curry` function:

``````// src/lib.rs

fn generate_curry(parsed: ItemFn) -> proc_macro2::TokenStream {
let fn_body = parsed.block;
let sig = parsed.sig;
let vis = parsed.vis;
let fn_name = sig.ident;
let fn_args = sig.inputs;
let fn_return_type = sig.output;

let arg_idents = extract_arg_idents(fn_args.clone());
let first_ident = &arg_idents.first().unwrap();
let curried_body = generate_body(&arg_idents[1..], fn_body.clone());

+  let arg_types = extract_arg_types(fn_args.clone());
+  let first_type = &arg_types.first().unwrap();
+  let type_aliases = generate_type_aliases(
+      &arg_types[1..],
+      extract_return_type(fn_return_type),
+      &fn_name,
+  );

+  let return_type = format_ident!("_{}_{}", &fn_name, format!("T{}", type_aliases.len() - 1));

+  return quote! {
+      #(#type_aliases);* ;
+      #vis fn #fn_name (#first_ident: #first_type) -> #return_type {
+          #curried_body ;
+      }
+  };
}``````

Most of the additions are self explanatory, I’ll go through the return statement with you. We are returning a `quote!{ ... }`, so a `proc_macro2::TokenStream`. We are iterating through the `type_aliases` variable, which you might recall, is a `Vec<TokenStream>`. You might notice the sneaky semicolon before the `*`. This basically tells `quote`, to insert an item, then a semicolon, and then the next one, another semicolon, and so on. The semicolon is a separator. We need to manually insert another semicolon at the end of it all, `quote` doesn’t insert a separator at the end of the iteration.

We retain the visibility and name of our original function. Our curried function takes as args, just the first argument of our original function. The return type of our curried function is actually, the last type alias we create. If you think back to our manually curried `add` function, we returned `T2`, which was in fact, the last type alias we created.

I am sure, at this point, you are itching to test this out, but before that, let me introduce you to some good methods of debugging proc-macro code.

### Debugging and Testing

Install `cargo-expand` via:

``cargo install cargo-expand``

`cargo-expand` is a neat little tool that expands your macro in places where it is used, and lets you view the generated code! For example:

``````# create a bin package hello
\$ cargo new hello

# view the expansion of the println! macro
\$ cargo expand

#![feature(prelude_import)]
#[prelude_import]
use std::prelude::v1::*;
#[macro_use]
extern crate std;
fn main() {
{
::std::io::_print(::core::fmt::Arguments::new_v1(
&["Hello, world!\n"],
&match () {
() => [],
},
));
};
}``````

Writing proc-macros without `cargo-expand` is tantamount to driving a vehicle without rear view mirrors! Keep an eye on what is going on behind your back.

Now, your macro won’t always compile, you might just recieve the bee movie script as an error. `cargo-expand` will not work in such cases. I would suggest printing out your variables to inspect them. `TokenStream` implements `Display` as well as `Debug`. We don’t always have to be respectable programmers. Just print it.

Enough of that, lets get testing:

``````// tests/smoke.rs

#![feature(type_alias_impl_trait)]

#[crate_name::curry]
fn add(x: u32, y: u32, z: u32) -> u32 {
x + y + z
}

#[test]
fn works() {
}``````

Run `cargo +nightly test`. You should see a pleasing message:

``````running 1 test
test tests::works ... ok``````

Take a look at the expansion for our curry macro, via `cargo +nightly expand --tests smoke`:

``````type _add_T0 = u32;
return (move |y| {
move |z| {
return x + y + z;
}
});
}

// a bunch of other stuff generated by #[test] and assert_eq!``````

A sight for sore eyes.

Here is a more complex example that generates ten multiples of the first ten natural numbers:

``````#[curry]
fn product(x: u32, y: u32) -> u32 {
x * y
}

fn multiples() -> Vec<Vec<u32>>{
let v = (1..=10).map(product);
return (1..=10)
.map(|x| v.clone().map(|f| f(x)).collect())
.collect();
}``````

### Notes

I didn’t quite explain why we use `move |arg|` in our closure. This is because we want to take ownership of the variable supplied to us. Take a look at this example:

``````let v = add(5);
let g;
{
let x = 5;
g = v(x);
}
println!("{}", g(2));``````

Variable `x` goes out of scope before `g` can return a concrete value. If we take ownership of `x` by `move`ing it into our closure, we can expect this to work reliably. In fact, rustc understands this, and forces you to use `move`.

This usage of `move` is exactly why a curried function without a return is useless. Every variable we pass to our curried function gets moved into its local scope. Playing with these variables cannot cause a change outside this scope. Returning is our only method of interaction with anything beyond this function.

### Conclusion

Currying may not seem to be all that useful. Curried functions are unwieldy in Rust because the standard library is not built around currying. If you enjoy the possibilities posed by currying, consider taking a look at Haskell or Scheme.

My original intention with peppe.rs was to post condensed articles, a micro blog, but this one turned out extra long.

Perhaps I should call it a ‘macro’ blog :)

1. caniuse.rs contains an indexed list of features and their status.↩︎

Hi.

I'm Akshay, programmer and pixel-artist.

I write open-source stuff to pass time. I also design fonts: scientifica, curie.

Send me a mail at [email protected] or a message at [email protected]

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