First-class (run-time) macros and meta-circular evaluation

First-class macros are macros that can be bound to variables, passed as arguments and returned from functions. First-class macros expand and evaluate syntax at run-time. Meta-circular evaluators support a concise implementation of first-class macros. In fact, first-class macros are easier to implement than traditional compile-time macros. A meta-circular evaluator is an interpreter which (1) can evaluate itself and (2) implements each language construct in terms of itself. This article and the attached implementation explain how to implement first-class macros in a meta-circular evaluator.

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With classical Lisp macros, you could define and in terms of if:

(define-macro (and a b)
 `(if ,a ,b #f))

With first-class (a.k.a. run-time) macros, you would write and as:

(define and (macro (lambda (a b)
                     `(if ,a ,b #f))))

One advantage of the first-class form is that the programmer can pass first-class macros as arguments to procedures; passing a compile-time macro to a procedure causes a compile-time error.

Because of their first-class nature, first-class macros make it easy to add or simulate any degree of laziness.

Of course, run-time macros incur a run-time overhead. Fortunately, my research in static analysis leads me to believe that we will be able to erase that overhead for the common case--where first-class macros are used to do the job of compile-time macros.

The structure of interpretation

SICP teaches (and preaches) the eval/apply model of interpretation. In this model, interpretation toggles between two functions, eval and apply:

  • eval : exp × env → value
  • apply : value × value* → value
The type exp contains expressions, such as numerals, variable references, applications and lambda terms. The type env maps variables to values:

env = variable → value

The type value contains run-time values, such as numbers, lists and closures.

The eval function evaluates an expression in the context of an environment for its free variables. The apply function applies a procedure to a list of arguments.

The foundational principle of Lisp that makes macros so elegant is the unification of code and data through S-Expressions, so that:

  • eval : s-exp × env → s-exp
  • apply : s-exp × s-exp* → s-exp

Clearly, if this approach is to work, then the definition of S-Expressions must also include semantic values like closures; that is, there will be S-Expressions with no literal form.

A typical eval procedure

A meta-circular evaluator with first-class macros differs mostly in the structure of its eval procedure. A typical eval procedure for a meta-circular evaluator looks something like:

(define (eval exp env)
    ((symbol? exp)    (env-lookup env exp))
    ((number? exp)    exp)
    ((boolean? exp)   exp)
    ((string? exp)    exp)
    ((quote? exp)     (eval-quote exp env))

    ((if? exp)        (eval-if exp env))
    ((cond? exp)      (eval-cond exp env))
    ((or? exp)        (eval-or exp env))
    ((and? exp)       (eval-and exp env))
    ((lambda? exp)    (eval-lambda exp env))
    ((let? exp)       (eval (let->app exp) env))
    ((let*? exp)      (eval (let*->let exp) env))
    ((letrec? exp)    (eval (letrec->lets+sets exp) env))
    ((begin? exp)     (eval-begin exp env))
    ((set!? exp)      (eval-set! exp env))
    ((app? exp)       (apply (eval (app->fun exp) env) 
                             (map (lambda (arg) (eval arg env)) 
                                  (app->args exp))))))

A first-class macro eval procedure

The eval procedure in an implementation with first-class macros is shorter:

(define (eval exp env)
    ((symbol? exp)    (env-lookup env exp))
    ((number? exp)    exp)
    ((boolean? exp)   exp)
    ((string? exp)    exp)
    ; 3D-syntax is invoked to produce a captured value:
    ((procedure? exp) (exp))
    ((app? exp)       (perform-apply (eval (app->fun exp) env)
                                     exp env))))

With first-class macros, the core syntactic forms are not privileged; rather, they are defined in the initial environment:

(define initial-environment-amap
  (list (list 'apply      apply)
        (list '+          +)
        (list 'not        not)
        (list 'display    display)
        (list 'newline    newline)
        (list 'cons       cons) 
        (list 'car        car)
        (list 'cdr        cdr)
        (list 'cadr       cadr)
        (list 'caadr      caadr)
        (list 'cadar      cadar)
        (list 'cddr       cddr)
        (list 'cdddr      cdddr)
        (list 'list       list)
        (list 'null?      null?)
        (list 'pair?      pair?)
        (list 'list?      list?)
        (list 'number?    number?)
        (list 'string?    string?)
        (list 'symbol?    symbol?)
        (list 'procedure? procedure?)
        (list 'eq?        eq?)
        (list '=          =)
        (list 'gensym     gensym)
        (list 'void       void)
        (list 'quote    (list 'syntax-primitive eval-quote))
        (list 'if       (list 'syntax-primitive eval-if))
        (list 'cond     (list 'syntax-primitive eval-cond))
        (list 'and      (list 'syntax-primitive eval-and))
        (list 'or       (list 'syntax-primitive eval-or))
        (list 'let      (list 'syntax-primitive eval-let))
        (list 'let*     (list 'syntax-primitive eval-let*))
        (list 'letrec   (list 'syntax-primitive eval-letrec))
        (list 'begin    (list 'syntax-primitive eval-begin))
        (list 'set!     (list 'syntax-primitive eval-set!))
        (list 'lambda   (list 'syntax-primitive eval-lambda))
        (list 'macro    (list 'syntax-primitive eval-macro))))

Interpretation-level primitives are actually bound directly as their meta-level primitives.

The perform-apply procedure must check whether the operator to be applied is a syntactic primitive, a macro or a procedure:

(define (perform-apply fun app-exp env)
  (let ((args (app->args app-exp)))
      ((macro? fun)       (eval (apply (macro->proc fun) args) env))
      ((syntax-prim? fun) ((syntax-primitive->eval fun) app-exp env))
      (else                 (let ((arg-values (eval* args env)))
                              (apply fun arg-values))))))

3D-syntax and hygiene

Some constructs, such as let and letrec, are desugared into other constructs, such as lambda and set!; for example:

 (let ((var exp) ...) body)


 ((lambda (var ...) body) exp ...)

This sort of expansion can cause a problem if we use a let construct in a context where lambda has been redefined. For example, we might define a function to compute the energy of a photon:

(define (energy lambda)
 (let ((c speed-of-light)
       (h plancks-constant))
  (/ (* c h) lambda)))

When the let form expands into a lambda-application this code, the symbol lambda is no longer bound to the syntactic primitive for lambda; rather, it is bound to some numeral representing wavelength. When the evaluator tries to evaluate this code, it will throw a particularly cryptic error about trying to apply a non-function value. This kind of capture is one of the two kinds of "hygiene" violations that Lisp systems worry about, and it is the only one that cannot be solved with gensym.

The provided implementation solves this hygiene problem through 3D syntax. An expression is 3D if a programmer cannot write it down. In other words, it is an expression that must have come from a special syntactic expansion. In Lisp, raw procedures are 3D, because there is no way to write down a literal that the read procedure will pull in as a procedure.

If you examine the eval procedure for the first-class macros implementation, you will find a case not present in the ordinary evaluator: procedure?. When the evaluator hits a procedure, it assumse it takes no arguments and then evaluates it, directly returning whatever that procedure returns.

This behavior provides a way to pass protected values out of first-class macros, since they will be evaluated in whatever scope there was when the closure was born. Consequently, a let from in my implementation (effectively) expands into:

((,(lambda () 3d-lambda) ,@var ,@body) ,@exp)

where 3d-lambda is bound to the syntactic primitive for lambda.

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