Lecture #23, Tuesday, November 22nd =================================== - Scheme (and Racket) Macros - Meta Macros - Lazy Constructions in an Eager Language - Recursive Macros - Another example: a simple loop - Yet Another: List Comprehension ------------------------------------------------------------------------ # 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: (define-syntax foo ...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 ...) and `let*' is defined with two transformation rules: 1. (let* () body ...) --> (let () body ...) 2. (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: (syntax-rules () ;*** ignore this "()" for now [(x y) (y x)]) evaluates to a function that is somewhat similar to: (lambda (expr) (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: (lambda (expr) (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`: (define-syntax bind (syntax-rules () [(bind ((x v) ...) body ...) ((lambda (x ...) body ...) v ...)])) and `let*` with its two rules: (define-syntax let* (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: (x y) --> (y x) 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 to `x2`; > > `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 that `x2` 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, and `y` 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 the > `y` 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`: (define-macro (orelse ) (let ((temp (gensym))) `(let ((,temp ,)) (if ,temp ,temp ,)))) Translating this to `define-syntax` and `syntax-rules` we get something simpler: (define-syntax orelse (syntax-rules () [(orelse ) (let ((temp )) (if temp temp ))])) 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: (define-syntax-rule (orelse ) (let ((temp )) (if temp temp ))) 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: (let ([temp 4]) (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): (let ([if +]) (orelse 1 1)) (let ([if +]) (if (orelse 1 1) 10 100)) ; two different `if's here or combining both: (let ([if #f] [temp 4]) (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: (define-syntax-rule (twice x) (+ x x)) 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: (twice (twice (twice (twice (twice (twice (twice (twice 1)))))))) expands to a *lot* of code to compile. Another example is: (define-syntax-rule (with-increment var expr) (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: (define-syntax define-syntax-rule (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: (define-syntax rewrite (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 (define-syntax rewrite (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 ยง37] (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. (define-syntax-rule (cons-stream x y) (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 ones (cons-stream 1 ones)) (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: (define-type promise [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*`: (define-syntax 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: (define-syntax-rule (while condition body ...) (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: (define (while condition-thunk body-thunk) (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: (define-syntax-rule (while condition body ...) (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: (define (while/proc condition-thunk body-thunk) (when (condition-thunk) (body-thunk) (while/proc condition-thunk body-thunk))) (define-syntax-rule (while condition body ...) (while/proc (lambda () condition) (lambda () body ...))) ------------------------------------------------------------------------ ## Another example: a simple loop Here is an implementation of a macro that does a simple arithmetic loop: (define-syntax for (syntax-rules (= to do) [(for x = m to n do body ...) (letrec ([loop (lambda (x) (when (<= x n) body ... (loop (+ x 1))))]) (loop m))])) (Note that this is not complete code: it suffers from the usual problem of multiple evaluations of the `n` expression. We'll deal with it soon.) This macro combines both control flow and lexical scope. Control flow is specified by the loop (done, as usual in Racket, as a tail-recursive function) --- for example, it determines how code is iterated, and it also determines what the `for` form will evaluate to (it evaluates to whatever `when` evaluates to, the void value in this case). Scope is also specified here, by translating the code to a function --- this code makes `x` have a scope that covers the body so this is valid: (for i = 1 to 3 do (printf "i = ~s\n" i)) but it also makes the boundary expression `n` be in this scope, making this: (for i = 1 to (if (even? i) 10 20) do (printf "i = ~s\n" i)) valid. In addition, while evaluating the condition on each iteration might be desirable, in most cases it's not --- consider this example: (for i = 1 to (read) do (printf "i = ~s\n" i)) This is easily solved by using a `let` to make the expression evaluate just once: (define-syntax for (syntax-rules (= to do) [(for x = m to n do body ...) (let ([m* m] ; execution order [n* n]) (letrec ([loop (lambda (x) (when (<= x n*) body ... (loop (+ x 1))))]) (loop m*)))])) which makes the previous use result in a "`reference to undefined identifier: i`" error. Furthermore, the fact that we have a hygienic macro system means that it is perfectly fine to use nested `for` expressions: (for a = 1 to 9 do (for b = 1 to 9 do (printf "~s,~s " a b)) (newline)) The transformation is, therefore, completely specifying the semantics of this new form. Extending this syntax is easy using multiple transformation rules --- for example, say that we want to extend it to have a `step` optional keyword. The standard idiom is to have the step-less pattern translated into one that uses `step 1`: (for x = m to n do body ...) --> (for x = m to n step 1 do body ...) Usually, you should remember that `syntax-rules` tries the patterns one by one until a match is found, but in this case there is no problems because the keywords make the choice unambiguous: (define-syntax for (syntax-rules (= to do step) [(for x = m to n do body ...) (for x = m to n step 1 do body ...)] [(for x = m to n step d do body ...) (let ([m* m] [n* n] [d* d]) (letrec ([loop (lambda (x) (when (<= x n*) body ... (loop (+ x d*))))]) (loop m*)))])) (for i = 1 to 10 do (printf "i = ~s\n" i)) (for i = 1 to 10 step 2 do (printf "i = ~s\n" i)) We can even extend it to do a different kind of iteration, for example, iterate over list: (define-syntax for (syntax-rules (= to do step in) [(for x = m to n do body ...) (for x = m to n step 1 do body ...)] [(for x = m to n step d do body ...) (let ([m* m] [n* n] [d* d]) (letrec ([loop (lambda (x) (when (<= x n*) body ... (loop (+ x d*))))]) (loop m*)))] ;; list [(for x in l do body ...) (for-each (lambda (x) body ...) l)])) (for i in (list 1 2 3 4) do (printf "i = ~s\n" i)) (for i in (list 1 2 3 4) do (for i = 0 to i do (printf "i = ~s " i)) (newline)) ------------------------------------------------------------------------ ## Yet Another: List Comprehension At this point it's clear that macros are a powerful language feature that makes it relatively easy to implement new features, making it a language that is easy to use as a tool for quick experimentation with new language features. As an example of a practical feature rather than a toy, let's see how we can implement [Python's list comprehenions]. These are expressions that conveniently combine `map`, `filter`, and nested uses of both. First, a simple implementation that uses only the `map` feature: (define-syntax list-of (syntax-rules (for in) [(list-of EXPR for ID in LIST) (map (lambda (ID) EXPR) LIST)])) (list-of (* x x) for x in (range 10)) It is a good exercise to see how everything that we've seen above plays a role here. For example, how we get the `ID` to be bound in `EXPR`. Next, add a condition expression with an `if` keyword, and implemented using a `filter`: (define-syntax list-of (syntax-rules (for in if) [(list-of EXPR for ID in LIST if COND) (map (lambda (ID) EXPR) (filter (lambda (ID) COND) LIST))] [(list-of EXPR for ID in LIST) (list-of EXPR for ID in LIST if #t)])) (list-of (* x x) for x in (range 10) if (odd? x)) Again, go over it and see how the binding structure makes the identifier available in both expressions. Note that since we're just playing around we're not paying too much attention to performance etc. (For example, if we cared, we could have implemented the `if`-less case by not using `filter` at all, or we could implement a `filter` that accepts `#t` as a predicate and in that case just returns the list, or even implementing it as a macro that identifies a `(lambda (_) #t)` pattern and expands to just the list (a bad idea in general).) The last step: Python's comprehension accepts multiple `for`-`in`s for nested loops, possibly with `if` filters at each level: (define-syntax list-of (syntax-rules (for in if) [(list-of EXPR for ID in LIST if COND) (map (lambda (ID) EXPR) (filter (lambda (ID) COND) LIST))] [(list-of EXPR for ID in LIST) (list-of EXPR for ID in LIST if #t)] [(list-of EXPR for ID in LIST for MORE ...) (list-of EXPR for ID in LIST if #t for MORE ...)] [(list-of EXPR for ID in LIST if COND for MORE ...) (apply append (map (lambda (ID) (list-of EXPR for MORE ...)) (filter (lambda (ID) COND) LIST)))])) A collection of examples that I found in the Python docs and elsewhere, demonstrating all of these: ;; [x**2 for x in range(10)] (list-of (* x x) for x in (range 10)) ;; [(x, y) for x in [1,2,3] for y in [3,1,4] if x != y] (list-of (list x y) for x in '(1 2 3) for y in '(3 1 4) if (not (= x y))) (define (round-n x n) ; python-like round to n digits (define 10^n (expt 10 n)) (/ (round (* x 10^n)) 10^n)) ;; [str(round(pi, i)) for i in range(1, 6)] (list-of (number->string (round-n pi i)) for i in (range 1 6)) (define matrix '((1 2 3 4) (5 6 7 8) (9 10 11 12))) ;; [[row[i] for row in matrix] for i in range(4)] (list-of (list-of (list-ref row i) for row in matrix) for i in (range 4)) (define text '(("bar" "foo" "fooba") ("Rome" "Madrid" "Houston") ("aa" "bb" "cc" "dd"))) ;; [y for x in text if len(x)>3 for y in x] (list-of y for x in text if (> (length x) 3) for y in x) ;; [y for x in text for y in x if len(y)>4] (list-of y for x in text for y in x if (> (string-length y) 4)) ;; [y.upper() for x in text if len(x) == 3 ;; for y in x if y.startswith('f')] (list-of (string-upcase y) for x in text if (= (length x) 3) for y in x if (regexp-match? #rx"^f" y)) [Python's list comprehenions]: https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions