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Operatives are based on FEXPRS from older lisps - they're basically a function-like form, but where the operands are not implicitly reduce at the time of call.

    (foo (+ 2 3) (* 3 4))
    ($bar (+ 2 3) (* 3 4))

`foo` is a function, when it is combined with the arguments, it receives the values 5 and 7.

`$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)

Compare to:

    ($lambda (arguments) . body)

So operatives are called in the same way a function is called - but the operands are not reduced, and the environment is passed implicitly.

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)

But it can chose other evaluation strategies for the operands - such as evaluating them in a custom created environment which we can make with (make-environment) or ($bindings->environment).

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...