Macros, A Practical Introduction

This chapter will introduce Rust's declarative Macro-By-Example system using a relatively simple, practical example. It does not attempt to explain all of the intricacies of the system; its goal is to get you comfortable with how and why macros are written.

There is also the Macros chapter of the Rust Book which is another high-level explanation, and the methodical introduction chapter of this book, which explains the macro system in detail.

A Little Context

Note: don't panic! What follows is the only math that will be talked about. You can quite safely skip this section if you just want to get to the meat of the article.

If you aren't familiar, a recurrence relation is a sequence where each value is defined in terms of one or more previous values, with one or more initial values to get the whole thing started. For example, the Fibonacci sequence can be defined by the relation:

\[F_{n} = 0, 1, ..., F_{n-1} + F_{n-2}\]

Thus, the first two numbers in the sequence are 0 and 1, with the third being \( F_{0} + F_{1} = 0 + 1 = 1\), the fourth \( F_{1} + F_{2} = 1 + 1 = 2\), and so on forever.

Now, because such a sequence can go on forever, that makes defining a fibonacci function a little tricky, since you obviously don't want to try returning a complete vector. What you want is to return something which will lazily compute elements of the sequence as needed.

In Rust, that means producing an Iterator. This is not especially hard, but there is a fair amount of boilerplate involved: you need to define a custom type, work out what state needs to be stored in it, then implement the Iterator trait for it.

However, recurrence relations are simple enough that almost all of these details can be abstracted out with a little macro_rules! macro-based code generation.

So, with all that having been said, let's get started.

Construction

Usually, when working on a new macro_rules! macro, the first thing I do is decide what the invocation should look like. In this specific case, my first attempt looked like this:

let fib = recurrence![a[n] = 0, 1, ..., a[n-1] + a[n-2]];

for e in fib.take(10) { println!("{}", e) }

From that, we can take a stab at how the macro_rules! macro should be defined, even if we aren't sure of the actual expansion. This is useful because if you can't figure out how to parse the input syntax, then maybe you need to change it.

macro_rules! recurrence {
    ( a[n] = $($inits:expr),+ , ... , $recur:expr ) => { /* ... */ };
}
fn main() {}

Assuming you aren't familiar with the syntax, allow me to elucidate. This is defining a syntax extension, using the macro_rules! system, called recurrence!. This macro_rules! macro has a single parsing rule. That rule says the input to the invocation must match:

  • the literal token sequence a [ n ] =,
  • a repeating (the $( ... )) sequence, using , as a separator, and one or more (+) repeats of:
    • a valid expression captured into the metavariable inits ($inits:expr)
  • the literal token sequence , ... ,,
  • a valid expression captured into the metavariable recur ($recur:expr).

Finally, the rule says that if the input matches this rule, then the invocation should be replaced by the token sequence /* ... */.

It's worth noting that inits, as implied by the name, actually contains all the expressions that match in this position, not just the first or last. What's more, it captures them as a sequence as opposed to, say, irreversibly pasting them all together. Also note that you can do "zero or more" with a repetition by using * instead of + and even optional, "zero or one" with ?. There is no support for "zero or one" or more specific numbers of repetitions.

As an exercise, let's take the proposed input and feed it through the rule, to see how it is processed. The "Position" column will show which part of the syntax pattern needs to be matched against next, denoted by a "⌂". Note that in some cases, there might be more than one possible "next" element to match against. "Input" will contain all of the tokens that have not been consumed yet. inits and recur will contain the contents of those bindings.

Position Input inits recur
a[n] = $($inits:expr),+ , ... , $recur:expr a[n] = 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr [n] = 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr n] = 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr ] = 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr = 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr 0, 1, ..., a[n-1] + a[n-2]
a[n] = $($inits:expr),+ , ... , $recur:expr ⌂ ⌂ , 1, ..., a[n-1] + a[n-2] 0
Note: there are two ⌂ here, because the next input token might match either the comma separator betweenem> elements in the repetition, or the comma after the repetition. The macro system will keep track of both possibilities, until it is able to decide which one to follow.
a[n] = $($inits:expr),+ , ... , $recur:expr ⌂ ⌂ 1, ..., a[n-1] + a[n-2] 0
a[n] = $($inits:expr),+ , ... , $recur:expr ⌂ ⌂ , ..., a[n-1] + a[n-2] 0, 1
Note: the third, crossed-out marker indicates that the macro system has, as a consequence of the last token consumed, eliminated one of the previous possible branches.
a[n] = $($inits:expr),+ , ... , $recur:expr ⌂ ⌂ ..., a[n-1] + a[n-2] 0, 1
a[n] = $($inits:expr),+ , ... , $recur:expr , a[n-1] + a[n-2] 0, 1
a[n] = $($inits:expr),+ , ... , $recur:expr a[n-1] + a[n-2] 0, 1
a[n] = $($inits:expr),+ , ... , $recur:expr 0, 1 a[n-1] + a[n-2]
Note: this particular step should make it clear that a binding like $recur:expr will consume an entire expression, using the compiler's knowledge of what constitutes a valid expression. As will be noted later, you can do this for other language constructs, too.

The key take-away from this is that the macro system will try to incrementally match the tokens provided as input to the macro against the provided rules. We'll come back to the "try" part.

Now, let's begin writing the final, fully expanded form. For this expansion, I was looking for something like:

let fib = {
    struct Recurrence {
        mem: [u64; 2],
        pos: usize,
    }

This will be the actual iterator type. mem will be the memo buffer to hold the last few values so the recurrence can be computed. pos is to keep track of the value of n.

Aside: I've chosen u64 as a "sufficiently large" type for the elements of this sequence. Don't worry about how this will work out for other sequences; we'll come to it.

    impl Iterator for Recurrence {
        type Item = u64;

        fn next(&mut self) -> Option<Self::Item> {
            if self.pos < 2 {
                let next_val = self.mem[self.pos];
                self.pos += 1;
                Some(next_val)

We need a branch to yield the initial values of the sequence; nothing tricky.

            } else {
                let a = /* something */;
                let n = self.pos;
                let next_val = a[n-1] + a[n-2];

                self.mem.TODO_shuffle_down_and_append(next_val);

                self.pos += 1;
                Some(next_val)
            }
        }
    }

This is a bit harder; we'll come back and look at how exactly to define a. Also, TODO_shuffle_down_and_append is another placeholder; I want something that places next_val on the end of the array, shuffling the rest down by one space, dropping the 0th element.


    Recurrence { mem: [0, 1], pos: 0 }
};

for e in fib.take(10) { println!("{}", e) }

Lastly, return an instance of our new structure, which can then be iterated over. To summarize, the complete expansion is:

let fib = {
    struct Recurrence {
        mem: [u64; 2],
        pos: usize,
    }

    impl Iterator for Recurrence {
        type Item = u64;

        fn next(&mut self) -> Option<u64> {
            if self.pos < 2 {
                let next_val = self.mem[self.pos];
                self.pos += 1;
                Some(next_val)
            } else {
                let a = /* something */;
                let n = self.pos;
                let next_val = (a[n-1] + a[n-2]);

                self.mem.TODO_shuffle_down_and_append(next_val.clone());

                self.pos += 1;
                Some(next_val)
            }
        }
    }

    Recurrence { mem: [0, 1], pos: 0 }
};

for e in fib.take(10) { println!("{}", e) }

Aside: Yes, this does mean we're defining a different Recurrence struct and its implementation for each invocation. Most of this will optimise away in the final binary.

It's also useful to check your expansion as you're writing it. If you see anything in the expansion that needs to vary with the invocation, but isn't in the actual accepted syntax of our macro, you should work out where to introduce it. In this case, we've added u64, but that's not necessarily what the user wants, nor is it in the macro syntax. So let's fix that.

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ , ... , $recur:expr ) => { /* ... */ };
}

/*
let fib = recurrence![a[n]: u64 = 0, 1, ..., a[n-1] + a[n-2]];

for e in fib.take(10) { println!("{}", e) }
*/
fn main() {}

Here, I've added a new metavariable: sty which should be a type.

Aside: if you're wondering, the bit after the colon in a metavariable can be one of several kinds of syntax matchers. The most common ones are item, expr, and ty. A complete explanation can be found in Macros, A Methodical Introduction; macro_rules! (Matchers).

There's one other thing to be aware of: in the interests of future-proofing the language, the compiler restricts what tokens you're allowed to put after a matcher, depending on what kind it is. Typically, this comes up when trying to match expressions or statements; those can only be followed by one of =>, ,, and ;.

A complete list can be found in Macros, A Methodical Introduction; Minutiae; Metavariables and Expansion Redux.

Indexing and Shuffling

I will skim a bit over this part, since it's effectively tangential to the macro-related stuff. We want to make it so that the user can access previous values in the sequence by indexing a; we want it to act as a sliding window keeping the last few (in this case, 2) elements of the sequence.

We can do this pretty easily with a wrapper type:

struct IndexOffset<'a> {
    slice: &'a [u64; 2],
    offset: usize,
}

impl<'a> Index<usize> for IndexOffset<'a> {
    type Output = u64;

    fn index<'b>(&'b self, index: usize) -> &'b u64 {
        use std::num::Wrapping;

        let index = Wrapping(index);
        let offset = Wrapping(self.offset);
        let window = Wrapping(2);

        let real_index = index - offset + window;
        &self.slice[real_index.0]
    }
}

Aside: since lifetimes come up a lot with people new to Rust, a quick explanation: 'a and 'b are lifetime parameters that are used to track where a reference (i.e. a borrowed pointer to some data) is valid. In this case, IndexOffset borrows a reference to our iterator's data, so it needs to keep track of how long it's allowed to hold that reference for, using 'a.

'b is used because the Index::index function (which is how subscript syntax is actually implemented) is also parameterized on a lifetime, on account of returning a borrowed reference. 'a and 'b are not necessarily the same thing in all cases. The borrow checker will make sure that even though we don't explicitly relate 'a and 'b to one another, we don't accidentally violate memory safety.

This changes the definition of a to:

let a = IndexOffset { slice: &self.mem, offset: n };

The only remaining question is what to do about TODO_shuffle_down_and_append. I wasn't able to find a method in the standard library with exactly the semantics I wanted, but it isn't hard to do by hand.

{
    use std::mem::swap;

    let mut swap_tmp = next_val;
    for i in (0..2).rev() {
        swap(&mut swap_tmp, &mut self.mem[i]);
    }
}

This swaps the new value into the end of the array, swapping the other elements down one space.

Aside: doing it this way means that this code will work for non-copyable types, as well.

The working code thus far now looks like this:

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ , ... , $recur:expr ) => { /* ... */ };
}

fn main() {
    /*
    let fib = recurrence![a[n]: u64 = 0, 1, ..., a[n-1] + a[n-2]];

    for e in fib.take(10) { println!("{}", e) }
    */
    let fib = {
        use std::ops::Index;

        struct Recurrence {
            mem: [u64; 2],
            pos: usize,
        }

        struct IndexOffset<'a> {
            slice: &'a [u64; 2],
            offset: usize,
        }

        impl<'a> Index<usize> for IndexOffset<'a> {
            type Output = u64;

            #[inline(always)]
            fn index<'b>(&'b self, index: usize) -> &'b u64 {
                use std::num::Wrapping;

                let index = Wrapping(index);
                let offset = Wrapping(self.offset);
                let window = Wrapping(2);

                let real_index = index - offset + window;
                &self.slice[real_index.0]
            }
        }

        impl Iterator for Recurrence {
            type Item = u64;

            #[inline]
            fn next(&mut self) -> Option<u64> {
                if self.pos < 2 {
                    let next_val = self.mem[self.pos];
                    self.pos += 1;
                    Some(next_val)
                } else {
                    let next_val = {
                        let n = self.pos;
                        let a = IndexOffset { slice: &self.mem, offset: n };
                        (a[n-1] + a[n-2])
                    };

                    {
                        use std::mem::swap;

                        let mut swap_tmp = next_val;
                        for i in (0..2).rev() {
                            swap(&mut swap_tmp, &mut self.mem[i]);
                        }
                    }

                    self.pos += 1;
                    Some(next_val)
                }
            }
        }

        Recurrence { mem: [0, 1], pos: 0 }
    };

    for e in fib.take(10) { println!("{}", e) }
}

Note that I've changed the order of the declarations of n and a, as well as wrapped them(along with the recurrence expression) in a block. The reason for the first should be obvious(n needs to be defined first so I can use it for a). The reason for the second is that the borrowed reference &self.mem will prevent the swaps later on from happening (you cannot mutate something that is aliased elsewhere). The block ensures that the &self.mem borrow expires before then.

Incidentally, the only reason the code that does the mem swaps is in a block is to narrow the scope in which std::mem::swap is available, for the sake of being tidy.

If we take this code and run it, we get:

0
1
1
2
3
5
8
13
21
34

Success! Now, let's copy & paste this into the macro expansion, and replace the expanded code with an invocation. This gives us:

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ , ... , $recur:expr ) => {
        {
            /*
                What follows here is *literally* the code from before,
                cut and pasted into a new position. No other changes
                have been made.
            */

            use std::ops::Index;

            struct Recurrence {
                mem: [u64; 2],
                pos: usize,
            }

            struct IndexOffset<'a> {
                slice: &'a [u64; 2],
                offset: usize,
            }

            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = u64;

                fn index<'b>(&'b self, index: usize) -> &'b u64 {
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(2);

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }

            impl Iterator for Recurrence {
                type Item = u64;

                fn next(&mut self) -> Option<u64> {
                    if self.pos < 2 {
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let n = self.pos;
                            let a = IndexOffset { slice: &self.mem, offset: n };
                            (a[n-1] + a[n-2])
                        };

                        {
                            use std::mem::swap;

                            let mut swap_tmp = next_val;
                            for i in (0..2).rev() {
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }

                        self.pos += 1;
                        Some(next_val)
                    }
                }
            }

            Recurrence { mem: [0, 1], pos: 0 }
        }
    };
}

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1, ..., a[n-1] + a[n-2]];

    for e in fib.take(10) { println!("{}", e) }
}

Obviously, we aren't using the metavariables yet, but we can change that fairly easily. However, if we try to compile this, rustc aborts, telling us:

error: local ambiguity: multiple parsing options: built-in NTs expr ('inits') or 1 other option.
  --> src/main.rs:75:45
   |
75 |     let fib = recurrence![a[n]: u64 = 0, 1, ..., a[n-1] + a[n-2]];
   |

Here, we've run into a limitation of the macro_rules system. The problem is that second comma. When it sees it during expansion, macro_rules can't decide if it's supposed to parse another expression for inits, or .... Sadly, it isn't quite clever enough to realise that ... isn't a valid expression, so it gives up. Theoretically, this should work as desired, but currently doesn't.

Aside: I did fib a little about how our rule would be interpreted by the macro system. In general, it should work as described, but doesn't in this case. The macro_rules machinery, as it stands, has its foibles, and its worthwhile remembering that on occasion, you'll need to contort a little to get it to work.

In this particular case, there are two issues. First, the macro system doesn't know what does and does not constitute the various grammar elements (e.g. an expression); that's the parser's job. As such, it doesn't know that ... isn't an expression. Secondly, it has no way of trying to capture a compound grammar element (like an expression) without 100% committing to that capture.

In other words, it can ask the parser to try and parse some input as an expression, but the parser will respond to any problems by aborting. The only way the macro system can currently deal with this is to just try to forbid situations where this could be a problem.

On the bright side, this is a state of affairs that exactly no one is enthusiastic about. The macro keyword has already been reserved for a more rigorously-defined future macro system. Until then, needs must.

Thankfully, the fix is relatively simple: we remove the comma from the syntax. To keep things balanced, we'll remove both commas around ...:

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ ... $recur:expr ) => {
//                                     ^~~ changed
        /* ... */
        // Cheat :D
        (vec![0u64, 1, 2, 3, 5, 8, 13, 21, 34]).into_iter()
    };
}

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1 ... a[n-1] + a[n-2]];
//                                         ^~~ changed

    for e in fib.take(10) { println!("{}", e) }
}

Success! ... or so we thought. Turns out this is being rejected by the compiler nowadays, while it was fine back when this was written. The reason for this is that the compiler now recognizes the ... as a token, and as we know we may only use =>, , or ; after an expression fragment. So unfortunately we are now out of luck as our dreamed up syntax will not work out this way, so let us just choose one that looks the most befitting that we are allowed to use instead, I'd say replacing , with ; works.

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
//                                     ^~~~~~^ changed
        /* ... */
        // Cheat :D
        (vec![0u64, 1, 2, 3, 5, 8, 13, 21, 34]).into_iter()
    };
}

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1; ...; a[n-1] + a[n-2]];
//                                        ^~~~~^ changed

    for e in fib.take(10) { println!("{}", e) }
}

Success! But for real this time.

Substitution

Substituting something you've captured in a macro is quite simple; you can insert the contents of a metavariable $sty:ty by using $sty. So, let's go through and fix the u64s:

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
        {
            use std::ops::Index;

            struct Recurrence {
                mem: [$sty; 2],
//                    ^~~~ changed
                pos: usize,
            }

            struct IndexOffset<'a> {
                slice: &'a [$sty; 2],
//                          ^~~~ changed
                offset: usize,
            }

            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = $sty;
//                            ^~~~ changed

                #[inline(always)]
                fn index<'b>(&'b self, index: usize) -> &'b $sty {
//                                                          ^~~~ changed
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(2);

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }

            impl Iterator for Recurrence {
                type Item = $sty;
//                          ^~~~ changed

                #[inline]
                fn next(&mut self) -> Option<$sty> {
//                                           ^~~~ changed
                    /* ... */
                    if self.pos < 2 {
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let n = self.pos;
                            let a = IndexOffset { slice: &self.mem, offset: n };
                            (a[n-1] + a[n-2])
                        };

                        {
                            use std::mem::swap;

                            let mut swap_tmp = next_val;
                            for i in (0..2).rev() {
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }

                        self.pos += 1;
                        Some(next_val)
                    }
                }
            }

            Recurrence { mem: [0, 1], pos: 0 }
        }
    };
}

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1; ...; a[n-1] + a[n-2]];

    for e in fib.take(10) { println!("{}", e) }
}

Let's tackle a harder one: how to turn inits into both the array literal [0, 1] and the array type, [$sty; 2]. The first one we can do like so:

            Recurrence { mem: [$($inits),+], pos: 0 }
//                             ^~~~~~~~~~~ changed

This effectively does the opposite of the capture: repeat inits one or more times, separating each with a comma. This expands to the expected sequence of tokens: 0, 1.

Somehow turning inits into a literal 2 is a little trickier. It turns out that there's no direct way to do this, but we can do it by using a second macro_rules! macro. Let's take this one step at a time.

macro_rules! count_exprs {
    /* ??? */
    () => {}
}
fn main() {}

The obvious case is: given zero expressions, you would expect count_exprs to expand to a literal 0.

macro_rules! count_exprs {
    () => (0);
//  ^~~~~~~~~~ added
}
fn main() {
    const _0: usize = count_exprs!();
    assert_eq!(_0, 0);
}

Aside: You may have noticed I used parentheses here instead of curly braces for the expansion. macro_rules really doesn't care what you use, so long as it's one of the "matcher" pairs: ( ), { } or [ ]. In fact, you can switch out the matchers on the macro itself(i.e. the matchers right after the macro name), the matchers around the syntax rule, and the matchers around the corresponding expansion.

You can also switch out the matchers used when you invoke a macro, but in a more limited fashion: a macro invoked as { ... } or ( ... ); will always be parsed as an item (i.e. like a struct or fn declaration). This is important when using macros in a function body; it helps disambiguate between "parse like an expression" and "parse like a statement".

What if you have one expression? That should be a literal 1.

macro_rules! count_exprs {
    () => (0);
    ($e:expr) => (1);
//  ^~~~~~~~~~~~~~~~~ added
}
fn main() {
    const _0: usize = count_exprs!();
    const _1: usize = count_exprs!(x);
    assert_eq!(_0, 0);
    assert_eq!(_1, 1);
}

Two?

macro_rules! count_exprs {
    () => (0);
    ($e:expr) => (1);
    ($e0:expr, $e1:expr) => (2);
//  ^~~~~~~~~~~~~~~~~~~~~~~~~~~~ added
}
fn main() {
    const _0: usize = count_exprs!();
    const _1: usize = count_exprs!(x);
    const _2: usize = count_exprs!(x, y);
    assert_eq!(_0, 0);
    assert_eq!(_1, 1);
    assert_eq!(_2, 2);
}

We can "simplify" this a little by re-expressing the case of two expressions recursively.

macro_rules! count_exprs {
    () => (0);
    ($e:expr) => (1);
    ($e0:expr, $e1:expr) => (1 + count_exprs!($e1));
//                           ^~~~~~~~~~~~~~~~~~~~~ changed
}
fn main() {
    const _0: usize = count_exprs!();
    const _1: usize = count_exprs!(x);
    const _2: usize = count_exprs!(x, y);
    assert_eq!(_0, 0);
    assert_eq!(_1, 1);
    assert_eq!(_2, 2);
}

This is fine since Rust can fold 1 + 1 into a constant value. What if we have three expressions?

macro_rules! count_exprs {
    () => (0);
    ($e:expr) => (1);
    ($e0:expr, $e1:expr) => (1 + count_exprs!($e1));
    ($e0:expr, $e1:expr, $e2:expr) => (1 + count_exprs!($e1, $e2));
//  ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ added
}
fn main() {
    const _0: usize = count_exprs!();
    const _1: usize = count_exprs!(x);
    const _2: usize = count_exprs!(x, y);
    const _3: usize = count_exprs!(x, y, z);
    assert_eq!(_0, 0);
    assert_eq!(_1, 1);
    assert_eq!(_2, 2);
    assert_eq!(_3, 3);
}

Aside: You might be wondering if we could reverse the order of these rules. In this particular case, yes, but the macro system can sometimes be picky about what it is and is not willing to recover from. If you ever find yourself with a multi-rule macro that you swear should work, but gives you errors about unexpected tokens, try changing the order of the rules.

Hopefully, you can see the pattern here. We can always reduce the list of expressions by matching one expression, followed by zero or more expressions, expanding that into 1 + a count.

macro_rules! count_exprs {
    () => (0);
    ($head:expr) => (1);
    ($head:expr, $($tail:expr),*) => (1 + count_exprs!($($tail),*));
//  ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ changed
}
fn main() {
    const _0: usize = count_exprs!();
    const _1: usize = count_exprs!(x);
    const _2: usize = count_exprs!(x, y);
    const _3: usize = count_exprs!(x, y, z);
    assert_eq!(_0, 0);
    assert_eq!(_1, 1);
    assert_eq!(_2, 2);
    assert_eq!(_3, 3);
}

JFTE: this is not the only, or even the best way of counting things. You may wish to peruse the Counting section later for a more efficient way.

With this, we can now modify recurrence to determine the necessary size of mem.

// added:
macro_rules! count_exprs {
    () => (0);
    ($head:expr) => (1);
    ($head:expr, $($tail:expr),*) => (1 + count_exprs!($($tail),*));
}

macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
        {
            use std::ops::Index;

            const MEM_SIZE: usize = count_exprs!($($inits),+);
//          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ added

            struct Recurrence {
                mem: [$sty; MEM_SIZE],
//                          ^~~~~~~~ changed
                pos: usize,
            }

            struct IndexOffset<'a> {
                slice: &'a [$sty; MEM_SIZE],
//                                ^~~~~~~~ changed
                offset: usize,
            }

            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = $sty;

                #[inline(always)]
                fn index<'b>(&'b self, index: usize) -> &'b $sty {
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(MEM_SIZE);
//                                        ^~~~~~~~ changed

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }

            impl Iterator for Recurrence {
                type Item = $sty;

                #[inline]
                fn next(&mut self) -> Option<$sty> {
                    if self.pos < MEM_SIZE {
//                                ^~~~~~~~ changed
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let n = self.pos;
                            let a = IndexOffset { slice: &self.mem, offset: n };
                            (a[n-1] + a[n-2])
                        };

                        {
                            use std::mem::swap;

                            let mut swap_tmp = next_val;
                            for i in (0..MEM_SIZE).rev() {
//                                       ^~~~~~~~ changed
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }

                        self.pos += 1;
                        Some(next_val)
                    }
                }
            }

            Recurrence { mem: [$($inits),+], pos: 0 }
        }
    };
}
/* ... */

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1; ...; a[n-1] + a[n-2]];

    for e in fib.take(10) { println!("{}", e) }
}

With that done, we can now substitute the last thing: the recur expression.

macro_rules! count_exprs {
    () => (0);
    ($head:expr $(, $tail:expr)*) => (1 + count_exprs!($($tail),*));
}
macro_rules! recurrence {
    ( a[n]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
        {
            use std::ops::Index;

            const MEM_SIZE: usize = count_exprs!($($inits),+);
            struct Recurrence {
                mem: [$sty; MEM_SIZE],
                pos: usize,
            }
            struct IndexOffset<'a> {
                slice: &'a [$sty; MEM_SIZE],
                offset: usize,
            }
            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = $sty;

                #[inline(always)]
                fn index<'b>(&'b self, index: usize) -> &'b $sty {
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(MEM_SIZE);

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }
            impl Iterator for Recurrence {
              type Item = $sty;
/* ... */
                #[inline]
                fn next(&mut self) -> Option<u64> {
                    if self.pos < MEM_SIZE {
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let n = self.pos;
                            let a = IndexOffset { slice: &self.mem, offset: n };
                            $recur
//                          ^~~~~~ changed
                        };
                        {
                            use std::mem::swap;
                            let mut swap_tmp = next_val;
                            for i in (0..MEM_SIZE).rev() {
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }
                        self.pos += 1;
                        Some(next_val)
                    }
                }
/* ... */
            }
            Recurrence { mem: [$($inits),+], pos: 0 }
        }
    };
}
fn main() {
    let fib = recurrence![a[n]: u64 = 1, 1; ...; a[n-1] + a[n-2]];
    for e in fib.take(10) { println!("{}", e) }
}

And, when we compile our finished macro_rules! macro...

error[E0425]: cannot find value `a` in this scope
  --> src/main.rs:68:50
   |
68 |     let fib = recurrence![a[n]: u64 = 1, 1; ...; a[n-1] + a[n-2]];
   |                                                  ^ not found in this scope

error[E0425]: cannot find value `n` in this scope
  --> src/main.rs:68:52
   |
68 |     let fib = recurrence![a[n]: u64 = 1, 1; ...; a[n-1] + a[n-2]];
   |                                                    ^ not found in this scope

error[E0425]: cannot find value `a` in this scope
  --> src/main.rs:68:59
   |
68 |     let fib = recurrence![a[n]: u64 = 1, 1; ...; a[n-1] + a[n-2]];
   |                                                           ^ not found in this scope

error[E0425]: cannot find value `n` in this scope
  --> src/main.rs:68:61
   |
68 |     let fib = recurrence![a[n]: u64 = 1, 1; ...; a[n-1] + a[n-2]];
   |                                                             ^ not found in this scope

... wait, what? That can't be right... let's check what the macro is expanding to.

$ rustc -Z unstable-options --pretty expanded recurrence.rs

The --pretty expanded argument tells rustc to perform macro expansion, then turn the resulting AST back into source code. Because this option isn't considered stable yet, we also need -Z unstable-options. The output (after cleaning up some formatting) is shown below; in particular, note the place in the code where $recur was substituted:

#![feature(no_std)]
#![no_std]
#[prelude_import]
use std::prelude::v1::*;
#[macro_use]
extern crate std as std;
fn main() {
    let fib = {
        use std::ops::Index;
        const MEM_SIZE: usize = 1 + 1;
        struct Recurrence {
            mem: [u64; MEM_SIZE],
            pos: usize,
        }
        struct IndexOffset<'a> {
            slice: &'a [u64; MEM_SIZE],
            offset: usize,
        }
        impl <'a> Index<usize> for IndexOffset<'a> {
            type Output = u64;
            #[inline(always)]
            fn index<'b>(&'b self, index: usize) -> &'b u64 {
                use std::num::Wrapping;
                let index = Wrapping(index);
                let offset = Wrapping(self.offset);
                let window = Wrapping(MEM_SIZE);
                let real_index = index - offset + window;
                &self.slice[real_index.0]
            }
        }
        impl Iterator for Recurrence {
            type Item = u64;
            #[inline]
            fn next(&mut self) -> Option<u64> {
                if self.pos < MEM_SIZE {
                    let next_val = self.mem[self.pos];
                    self.pos += 1;
                    Some(next_val)
                } else {
                    let next_val = {
                        let n = self.pos;
                        let a = IndexOffset{slice: &self.mem, offset: n,};
                        a[n - 1] + a[n - 2]
                    };
                    {
                        use std::mem::swap;
                        let mut swap_tmp = next_val;
                        {
                            let result =
                                match ::std::iter::IntoIterator::into_iter((0..MEM_SIZE).rev()) {
                                    mut iter => loop {
                                        match ::std::iter::Iterator::next(&mut iter) {
                                            ::std::option::Option::Some(i) => {
                                                swap(&mut swap_tmp, &mut self.mem[i]);
                                            }
                                            ::std::option::Option::None => break,
                                        }
                                    },
                                };
                            result
                        }
                    }
                    self.pos += 1;
                    Some(next_val)
                }
            }
        }
        Recurrence{mem: [0, 1], pos: 0,}
    };
    {
        let result =
            match ::std::iter::IntoIterator::into_iter(fib.take(10)) {
                mut iter => loop {
                    match ::std::iter::Iterator::next(&mut iter) {
                        ::std::option::Option::Some(e) => {
                            ::std::io::_print(::std::fmt::Arguments::new_v1(
                                {
                                    static __STATIC_FMTSTR: &'static [&'static str] = &["", "\n"];
                                    __STATIC_FMTSTR
                                },
                                &match (&e,) {
                                    (__arg0,) => [::std::fmt::ArgumentV1::new(__arg0, ::std::fmt::Display::fmt)],
                                }
                            ))
                        }
                        ::std::option::Option::None => break,
                    }
                },
            };
        result
    }
}

But that looks fine! If we add a few missing #![feature(...)] attributes and feed it to a nightly build of rustc, it even compiles! ... what?!

Aside: You can't compile the above with a non-nightly build of rustc. This is because the expansion of the println! macro depends on internal compiler details which are not publicly stabilized.

Being Hygienic

The issue here is that identifiers in Rust syntax extensions are hygienic. That is, identifiers from two different contexts cannot collide. To show the difference, let's take a simpler example.

macro_rules! using_a {
    ($e:expr) => {
        {
            let a = 42i;
            $e
        }
    }
}

let four = using_a!(a / 10);
fn main() {}

This macro simply takes an expression, then wraps it in a block with a variable a defined. We then use this as a round-about way of computing 4. There are actually two syntax contexts involved in this example, but they're invisible. So, to help with this, let's give each context a different colour. Let's start with the unexpanded code, where there is only a single context:

macro_rules! using_a {
    ($e:expr) => {
        {
            let a = 42;
            $e
        }
    }
}

let four = using_a!(a / 10);

Now, let's expand the invocation.

let four = {
    let a = 42;
    a / 10
};

As you can see, the a that's defined by the macro invocation is in a different context to the a we provided in our invocation. As such, the compiler treats them as completely different identifiers, even though they have the same lexical appearance.

This is something to be really careful of when working on macro_rules! macros, syntax extensions in general even: they can produce ASTs which will not compile, but which will compile if written out by hand, or dumped using --pretty expanded.

The solution to this is to capture the identifier with the appropriate syntax context. To do that, we need to again adjust our macro syntax. To continue with our simpler example:

macro_rules! using_a {
    ($a:ident, $e:expr) => {
        {
            let $a = 42;
            $e
        }
    }
}

let four = using_a!(a, a / 10);

This now expands to:

let four = {
    let a = 42;
    a / 10
};

Now, the contexts match, and the code will compile. We can make this adjustment to our recurrence! macro by explicitly capturing a and n. After making the necessary changes, we have:

macro_rules! count_exprs {
    () => (0);
    ($head:expr) => (1);
    ($head:expr, $($tail:expr),*) => (1 + count_exprs!($($tail),*));
}

macro_rules! recurrence {
    ( $seq:ident [ $ind:ident ]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
//    ^~~~~~~~~~   ^~~~~~~~~~ changed
        {
            use std::ops::Index;

            const MEM_SIZE: usize = count_exprs!($($inits),+);

            struct Recurrence {
                mem: [$sty; MEM_SIZE],
                pos: usize,
            }

            struct IndexOffset<'a> {
                slice: &'a [$sty; MEM_SIZE],
                offset: usize,
            }

            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = $sty;

                #[inline(always)]
                fn index<'b>(&'b self, index: usize) -> &'b $sty {
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(MEM_SIZE);

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }

            impl Iterator for Recurrence {
                type Item = $sty;

                #[inline]
                fn next(&mut self) -> Option<$sty> {
                    if self.pos < MEM_SIZE {
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let $ind = self.pos;
//                              ^~~~ changed
                            let $seq = IndexOffset { slice: &self.mem, offset: $ind };
//                              ^~~~ changed
                            $recur
                        };

                        {
                            use std::mem::swap;

                            let mut swap_tmp = next_val;
                            for i in (0..MEM_SIZE).rev() {
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }

                        self.pos += 1;
                        Some(next_val)
                    }
                }
            }

            Recurrence { mem: [$($inits),+], pos: 0 }
        }
    };
}

fn main() {
    let fib = recurrence![a[n]: u64 = 0, 1; ...; a[n-1] + a[n-2]];

    for e in fib.take(10) { println!("{}", e) }
}

And it compiles! Now, let's try with a different sequence.

macro_rules! count_exprs {
    () => (0);
    ($head:expr) => (1);
    ($head:expr, $($tail:expr),*) => (1 + count_exprs!($($tail),*));
}

macro_rules! recurrence {
    ( $seq:ident [ $ind:ident ]: $sty:ty = $($inits:expr),+ ; ... ; $recur:expr ) => {
        {
            use std::ops::Index;

            const MEM_SIZE: usize = count_exprs!($($inits),+);

            struct Recurrence {
                mem: [$sty; MEM_SIZE],
                pos: usize,
            }

            struct IndexOffset<'a> {
                slice: &'a [$sty; MEM_SIZE],
                offset: usize,
            }

            impl<'a> Index<usize> for IndexOffset<'a> {
                type Output = $sty;

                #[inline(always)]
                fn index<'b>(&'b self, index: usize) -> &'b $sty {
                    use std::num::Wrapping;

                    let index = Wrapping(index);
                    let offset = Wrapping(self.offset);
                    let window = Wrapping(MEM_SIZE);

                    let real_index = index - offset + window;
                    &self.slice[real_index.0]
                }
            }

            impl Iterator for Recurrence {
                type Item = $sty;

                #[inline]
                fn next(&mut self) -> Option<$sty> {
                    if self.pos < MEM_SIZE {
                        let next_val = self.mem[self.pos];
                        self.pos += 1;
                        Some(next_val)
                    } else {
                        let next_val = {
                            let $ind = self.pos;
                            let $seq = IndexOffset { slice: &self.mem, offset: $ind };
                            $recur
                        };

                        {
                            use std::mem::swap;

                            let mut swap_tmp = next_val;
                            for i in (0..MEM_SIZE).rev() {
                                swap(&mut swap_tmp, &mut self.mem[i]);
                            }
                        }

                        self.pos += 1;
                        Some(next_val)
                    }
                }
            }

            Recurrence { mem: [$($inits),+], pos: 0 }
        }
    };
}

fn main() {
for e in recurrence!(f[i]: f64 = 1.0; ...; f[i-1] * i as f64).take(10) {
    println!("{}", e)
}
}

Which gives us:

1
1
2
6
24
120
720
5040
40320
362880

Success!