Scheme (and Racket) Macros
Scheme, Racket included (and much extended), has a solution that is
better than defmacro
: it has define-syntax
and syntax-rules
. First
of all, define-syntax
is used to create the “magical connection”
between user code and some macro transformation code that does some
rewriting. This definition:
...something...)
makes foo
be a special syntax that, when used in the head of an
expression, will lead to transforming the expression itself, where the
result of this transformation is what gets used instead of the original
expression. The “...something...
” in this code fragment should be a
transformation function — one that consumes the expression that is to
be transformed, and returns the new expression to run.
Next, syntax-rules
is used to create such a transformation in an easy
way. The idea is that what we thought to be an informal specification of
such rewrites, for example:
-
let
can be defined as the following transformation:(let ((x v) ...) body ...)
--> ((lambda (x ...) body ...) v ...) -
let*
is defined with two transformation rules:- (let* () body …) –> (let () body …)
- (let* ((x1 v1) (x2 v2) …) body …) –> (let ((x1 v1)) (let* ((x2 v2) …) body …))
can actually be formalized by automatically creating a syntax transformation function from these rule specifications. (Note that this example has round parentheses so we don’t fall into the illusion that square brackets are different: the resulting transformation would be the same.) The main point is to view the left hand side as a pattern that can match some forms of syntax, and the right hand side as producing an output that can use some matched patterns.
syntax-rules
is used with such rewrite specifications, and it produces
the corresponding transformation function. For example, this:
[(x y) (y x)])
evaluates to a function that is somewhat similar to:
(if (and (list? expr) (= 2 (length expr)))
(list (second expr) (first expr))
(error "bad syntax")))
but match
is a little closer, since it uses similar input patterns:
(match expr
[(list x y) (list y x)]
[else (error "bad syntax")]))
Such transformations are used in a define-syntax
expression to tie the
transformer back into the compiler by hooking it on a specific keyword.
You can now appreciate how all this work when you see how easy it is to
define macros that are very tedious with define-macro
. For example,
the above bind
:
(syntax-rules ()
[(bind ((x v) ...) body ...)
((lambda (x ...) body ...) v ...)]))
and let*
with its two rules:
(syntax-rules ()
[(let* () body ...)
(let () body ...)]
[(let* ((x v) (xs vs) ...) body ...)
(let ((x v)) (let* ((xs vs) ...) body ...))]))
These transformations are so convenient to follow, that Scheme
specifications (and reference manuals) describe forms by specifying
their definition. For example, the Scheme report, specifies let*
as a
“derived form”, and explains its semantics via this transformation.
The input patterns in these rules are similar to match
patterns, and
the output patterns assemble an s-expression using the matched parts in
the input. For example:
does the thing you expect it to do — matches a parenthesized form with
two sub-forms, and produces a form with the two sub-forms swapped. The
rules for “...
” on the left side are similar to match
, as we have
seen many times, and on the right side it is used to splice a matched
sequence into the resulting expression and it is required to use the
...
for sequence-matched pattern variables. For example, here is a
list of some patterns, and a description of how they match an input when
used on the left side of a transformation rule and how they produce an
output expression when they appear on the right side:
-
(x ...)
LHS: matches a parenthesized sequence of zero or more expressions, and the
x
pattern variable is bound to this whole sequence;match
analogy:(match ? [(list x ...) ?])
RHS: when
x
is bound to a sequence, this will produce a parenthesized expression containing this sequence;match
analogy:(match ? [(list x ...) x])
-
(x1 x2 ...)
LHS: matches a parenthesized sequence of one or more expressions, the first is bound to
x1
and the rest of the sequence is bound tox2
;match
analogy:(match ? [(list x1 x2 ...) ?])
RHS: produces a parenthesized expression that contains the expression bound to
x1
first, then all of the expressions in the sequence thatx2
is bound to;match
analogy:(match ? [(list x1 x2 ...) (cons x1 x2)])
-
((x y) ...)
LHS: matches a parenthesized sequence of 2-form parenthesized sequences, binding
x
to all the first forms of these, andy
to all the seconds of these (so they will both have the same number of items);match
analogy:(match ? [(list (list x y) ...) ?])
RHS: produces a list of forms where each one is made of consecutive forms in the
x
sequence and consecutive forms in they
sequence (both sequences should have the same number of elements);match
analogy:(match ? [(list (list x y) ...)
(map (lambda (x y) (list x y)) x y)])
Some examples of transformations that would be very tedious to write code manually for:
-
((x y) ...) --> ((y x) ...)
Matches a sequence of 2-item sequences, produces a similar sequence with all of the nested 2-item sequences flipped.
-
((x y) ...) --> ((x ...) (y ...))
Matches a similar sequence, and produces a sequence of two sequences, one of all the first items, and one of the second ones.
-
((x y ...) ...) --> ((y ... x) ...)
Similar to the first example, but the nested sequences can have 1 or more items in them, and the nested sequences in the result have the first element moved to the end. Note how the
...
are nested: the rule is that for each pattern variable you count how many...
s apply to it, and that tells you what it holds — and you have to use the same...
nestedness for it in the output template.
This is solving the problems of easy code — no need for list
, cons
etc, not even for quasiquotes and tedious syntax massaging. But there
were other problems. First, there was a problem of bad scope, one that
was previously solved with a gensym
:
(let ((temp (gensym)))
`(let ((,temp ,<expr1>))
(if ,temp ,temp ,<expr2>))))
Translating this to define-syntax
and syntax-rules
we get something
simpler:
(syntax-rules ()
[(orelse <expr1> <expr2>)
(let ((temp <expr1>))
(if temp temp <expr2>))]))
Even simpler, Racket has a macro called define-syntax-rule
that
expands to a define-syntax
combined with a syntax-rules
— using
it, we can write:
(let ((temp <expr1>))
(if temp temp <expr2>)))
This looks like like a function — but you must remember that it is a transformation rule specification which is a very different beast, as we’ll see.
The main thing here is that Racket takes care of making bindings follow the lexical scope rules:
(orelse #f temp))
works fine. In fact, it fully respects the scoping rules: there is no
confusion between bindings that the macro introduces and bindings that
are introduced where the macro is used. (Think about different colors
for bindings introduced by the macro and other bindings.) It’s also fine
with many cases that are much harder to cope with otherwise (eg, cases
where there is no gensym
magic solution):
(orelse 1 1))
(let ([if +])
(if (orelse 1 1) 10 100)) ; two different `if's here
or combining both:
(orelse if temp))
(You can try DrRacket’s macro debugger to see how the various bindings get colored differently.)
define-macro
advocates will claim that it is difficult to make a macro
that intentionally plants a known identifier. Think about a loop
macro that has an abort
that can be used inside its body. Or an
if-it
form that is like if
, but makes it possible to use the
condition’s value in the “then” branch as an it
binding. It is
possible with all Scheme macro systems to “break hygiene” in such ways,
and we will later see how to do this in Racket. However, Racket also
provides a better way to deal with such problems (think about it
being
always “bound to a syntax error”, but locally rebound in an if-it
form).
Scheme macros are said to be hygienic — a term used to specify that
they respect lexical scope. There are several implementations of
hygienic macro systems across Scheme implementations, Racket uses the
one known as “syntax-case system”, named after the syntax-case
construct that we discuss below.
All of this can get much more important in the presence of a module system, since you can write a module that provides transformations rules, not just values and functions. This means that the concept of “a library” in Racket is something that doesn’t exist in other languages: it’s a library that has values, functions, as well as macros (or, “compiler plugins”).
The way that Scheme implementations achieve hygiene in a macro system is by making it deal with more than just raw S-expressions. Roughly speaking, it deals with syntax objects that are sort of a wrapper structure around S-expression, carrying additional information. The important part of this information when it gets to dealing with hygiene is the “lexical scope” — which can roughly be described as having identifiers be represented as symbols plus a “color” which represents the scope. This way such systems can properly avoid confusing identifiers with the same name that come from different scopes.
There was also the problem of making debugging difficult, because a macro can introduce errors that are “coming out of nowhere”. In the implementation that we work with, this is solved by adding yet more information to these syntax objects — in addition to the underlying S-expression and the lexical scope, they also contain source location information. This allows Racket (and DrRacket) to locate the source of a specific syntax error, so locating the offending code is easy. DrRacket’s macro debugger heavily relies on this information to provide a very useful tool — since writing macros can easily become a hard job.
Finally, there was the problem of writing bad macros. For example, it is easy to forget that you’re dealing with a macro definition and write:
just because you want to inline the addition — but in this case you end up duplicating the input expression which can have a disastrous effect. For example:
expands to a lot of code to compile.
Another example is:
(let ([var (add1 var)]) expr))
...
(with-increment (* foo 2)
...code...)
the problem here is that (* foo 2) will be used as an identifier to be
bound by the let
expression — which can lead to a confusing syntax
error.
Racket provides many tools to help macro programmers — in addition to
a user-interface tool like the macro debugger there are also
programmer-level tools where you can reject an input if it doesn’t
contain an identifier at a certain place etc. Still, writing macros is
much harder than writing functions — some of these problems are
inherent to the problem that macros solve; for example, you may want a
twice
macro that replicates an expression. By specifying a
transformation to the core language, a macro writer has full control
over which expressions get evaluated and how, which identifiers are
binding instances, and how is the scope of the given expression is
shaped.
Meta Macros
One of the nice results of syntax-rules
dealing with the subtle points
of identifiers and scope is that things works fine even when we “go up a
level”. For example, the short define-syntax-rule
form that we’ve seen
is itself a defined as a simple macro:
(syntax-rules ()
[(define-syntax-rule (name P ...) B)
(define-syntax name
(syntax-rules ()
[(name P ...) B]))]))
In fact, this is very similar to something that we have already seen:
the rewrite
form that we have used in Schlac is implemented in just
this way. The only difference is that rewrite
requires an actual =>
token to separate the input pattern from the output template. If we just
use it in a syntax rule:
(syntax-rules ()
[(rewrite (name P ...) => B)
(define-syntax name
(syntax-rules ()
[(name P ...) B]))]))
it won’t work. Racket treats the above =>
just like any identifier,
which in this case acts as a pattern variable which matches anything.
The solution to this is to list the =>
as a keyword which is expected
to appear in the macro use as-is — and that’s what the mysterious ()
of syntax-rules
is used for: any identifier listed there is taken to
be such a keyword. This makes the following version
(syntax-rules (=>)
[(rewrite (name P ...) => B)
(define-syntax name
(syntax-rules ()
[(name P ...) B]))]))
do what we want and throw a syntax error unless rewrite
is used with
an actual =>
in the proper place.
Lazy Constructions in an Eager Language
PLAI §37 (has some examples)
This is not really lazy evaluation, but it gets close, and provides the core useful property of easy-to-use infinite lists.
(cons x (lambda () y)))
(define stream? pair?)
(define null-stream null)
(define null-stream? null?)
;; note that there are not proper lists in racket,
;; so we use car and cdr here
(define stream-first car)
(define (stream-rest s) ((cdr s)))
Using it:
(define (stream-map f s)
(if (null-stream? s)
null-stream
(cons-stream (f (stream-first s))
(stream-map f (stream-rest s)))))
(define (stream-map2 f s1 s2)
(if (null-stream? s1)
null-stream
(cons-stream (f (stream-first s1) (stream-first s2))
(stream-map2 f (stream-rest s1)
(stream-rest s2)))))
(define ints (cons-stream 0 (stream-map2 + ones ints)))
Actually, all Scheme implementations come with a generalized tool for
(local) laziness: a delay
form that delays computation of its body
expression, and a force
function that forces such promises. Here is a
naive implementation of this:
[make-promise (-> Any)])
(define-syntax-rule (delay expr)
(make-promise (lambda () expr)))
(define (force p)
(cases p [(make-promise thunk) (thunk)]))
Proper definitions of delay
/force
cache the result — and practical
ones can get pretty complex, for example, in order to allow tail calls
via promises.
Recursive Macros
Syntax transformations can be recursive. For example, we have seen how
let*
can be implemented by a transformation that uses two rules, one
of which expands to another use of let*
:
(syntax-rules ()
[(let* () body ...)
(let () body ...)]
[(let* ((x v) (xs vs) ...) body ...)
(let ((x v)) (let* ((xs vs) ...) body ...))]))
When Racket expands a let*
expression, the result may contain a new
let*
which needs extending as well. An important implication of this
is that recursive macros are fine, as long as the recursive case is
using a smaller expression. This is just like any form of recursion
(or loop), where you need to be looping over a well-founded
set of
values — where each iteration uses a new value that is closer to some
base case.
For example, consider the following macro:
(when condition
body ...
(while condition body ...)))
It seems like this is a good implementation of a while
loop — after
all, if you were to implement it as a function using thunks, you’d write
very similar code:
(when (condition-thunk)
(body-thunk)
(while condition-thunk body-thunk)))
But if you look at the nested while
form in the transformation rule,
you’ll see that it is exactly the same as the input form. This means
that this macro can never be completely expanded — it specifies
infinite code! In practice, this makes the (Racket) compiler loop
forever, consuming more and more memory. This is unlike, for example,
the recursive let*
rule which uses one less binding-value pair than
specified as its input.
The reason that the function version of while
is fine is that it
iterates using the same code, and the condition thunk will depend on
some state that converges to a base case (usually the body thunk will
perform some side-effects that makes the loop converge). But in the
macro case there is no evaluation happening, if the transformed syntax
contains the same input pattern, we end up having a macro that expands
infinitely.
The correct solution for a while
macro is therefore to use plain
recursion using a local recursive function:
(letrec ([loop (lambda ()
(when condition
body ...
(loop)))])
(loop)))
A popular way to deal with macros like this that revolve around a specific control flow is to separate them into a function that uses thunks, and a macro that does nothing except wrap input expressions as thunks. In this case, we get this solution:
(when (condition-thunk)
(body-thunk)
(while/proc condition-thunk body-thunk)))
(define-syntax-rule (while condition body ...)
(while/proc (lambda () condition)
(lambda () body ...)))