An example: building the equivalent of a switch statement, but that compares (via string equality) with a set of strings. The macro would translate this into code that would do something like a decision tree on string length or particular characters at particular positions.
Basically anything that's done with a preprocessor in another language can be done with macros in Lisp family languages.
(foo (+ 2 3) (* 3 4))
($bar (+ 2 3) (* 3 4))
`$bar` however, receives its operands verbatim. It receives (+ 2 3) as its first operand and (* 3 4) as its second - unevaluated.
The operative/FEXPR body decides how to evaluate the operands - if at all.
The difference between an operative/FEXPR and a macro is that macros are second-class objects which must appear in their own name - we cannot assign them to variables, pass them or return them from functions. Operatives and FEXPRs are first-class objects that can be treated like any other.
The difference between FEXPRs and Operatives is to do with scoping and environments. FEXPRs were around before Scheme - when Lisps were dynamically scoped. This meant we could have unpredictable behavior and so called "spooky action at distance". They were problematic and basically abandoned almost entirely in the 1980s.
Shutt introduced Operatives as a more hygienic version - based on statically scoped Scheme. Instead of the operative being able to mutate the dynamic environment arbitrarily, there are limitations. The first part of this is that environments are made into first-class objects - so we can assign them to a symbol and pass them around. The final part is that an operative receives a reference to the dynamic environment of its caller - which we bind to a symbol using the operative constructor, `$vau`.
($vau (operands) dynamic-env . body)
($lambda (arguments) . body)
The body can decide to evaluate the operands using the environment of the caller - essentially behaving as if the caller had evaluated them
(eval operands dynamic-env)
This also allows the operative to mutate the environment of its callee - but only the locals of that environment. The parent environments cannot be mutated through the reference `dynamic-env`.
Technically, `$lambda` is not primitive in Kernel - though it is the main constructor of applicatives (functions) - the primitive constructor is called `wrap` - and it takes another combiner (an operative or applicative) as its parameter. Wrapping a combiner simply forces the evaluation of its arguments when called - so functions are just wrappers around operatives - and the underlying operative of any function can be extracted with `unwrap`.
There's a lot more to them. They're conceptually quite simple in terms of implementation, but they have enormous potential use cases that are unexplored.
Read more on the Kernel page[1]. In particular, the Kernel report[2]. There's also a formal calculus describing them, called the vau calculus[3].
[1]:https://web.cs.wpi.edu/~jshutt/kernel.html
[2]:https://ftp.cs.wpi.edu/pub/techreports/pdf/05-07.pdf
[3]:https://web.archive.org/web/20150224035948/http://www.wpi.ed...
I use C preprocessor macros extensively and don't have the typical dislike for them that many people have - though I clearly understand their limitations and the advantage Scheme macros have over them.
Since learning Kernel, the boundary of "compile time" and "runtime" is more blurry - I can write operatives which behave somewhat like a macro, and I do more "multi-stage" programming, where one operative optimizes its argument to produce something more efficient which is later evaluated - though there are still limitations due to the inability to fully compile Kernel.
As one example, I've used a kind of operative I call a "template", which evaluates its free symbols ahead of time but doesn't actually evaluate the body. When we later apply the some operands it replaces the bound symbols with the operands, looking up any symbols to produce an expression which we don't need to immediately evaluate either - but this expression has all symbols fully resolved. This is somewhere between a macro and regular operative.
Consider:
($define! z 10)
($define! @add-z
($template (x y)
(+ x y z)))
([#applicative: +] x y 10)
> ($let ((x 9)
(y 7))
(@add-z (* x 3) (- y 13)))
([#applicative: +] ([#applicative: *] 9 3) ([#applicative: -] 7 13) 10)
---
The $template form above isn't too difficult to implement. I've iterated several forms of this - some which only partially resolved the bound symbols, but lost them in a RAID failure. An earlier version which has some issues I still have because I put it online:
($provide! ($template)
($define! $resolve-free-symbols
($vau (params expr) env
($cond
((null? expr) ())
((pair? expr)
(cons (apply (wrap $resolve-free-symbols)
(list params (car expr))
env)
(apply (wrap $resolve-free-symbols)
(list params (cdr expr))
env)))
((symbol? expr)
($if (member? expr params)
expr
(eval expr env)))
(#t expr))))
($define! $resolve-bound-symbols
($vau (params expr) env
($cond
((null? expr) ())
((pair? expr)
(cons (apply (wrap $resolve-bound-symbols)
(list params (car expr))
env)
(apply (wrap $resolve-bound-symbols)
(list params (cdr expr))
env)))
((symbol? expr)
($if (member? expr params)
(eval expr env)
expr))
(#t expr))))
($define! zip
($lambda (fst snd)
($cond
(($and? (null? fst) (null? snd)) ())
(($and? (pair? fst) (pair? snd))
(cons (list (car fst)
(list* (($vau #ignore #ignore list)) (car snd)))
(zip (cdr fst) (cdr snd)))))))
($define! $template
($vau (params body) senv
($let ((newbody
(eval (list $resolve-free-symbols params body) senv)))
($vau args denv
(eval (list $resolve-bound-symbols params newbody)
(eval (list* $bindings->environment
(zip params args))
denv)))))))
At present the best interpreter is klisp, and the fastest is bronze-age-lisp, which uses klisp - with parts of hand-written 32-bit x86 assembly.
I've been working on a faster interpreter for a number of years as a side project, optimized for x86_64 with some parts C and some parts assembly. It has diverged in some parts from the Kernel report, but still retains what I see are the key ingredients.
My modified Kernel has optional types, and we have operatives to `$typecheck` complex expressions ahead of evaluating them. I intend to go all in on the "multi-stage" aspect and have operatives to JIT-compile expressions in a manner similar to the above template.