1 Motivation🔗

Shrubbery notation is a vehicle for using a programming language in much the same way that S-expression notation is a vehicle. Like Racket’s macro system as built on S-expressions, this proposal introduces an expander layer that is built on shrubberies.

Here’s an example of the kind of language that the expander is meant to support:




class Posn(x, y)


def home :: Posn:

  Posn(3, 7)


fun abs(n): if n < 0 | -n | n


fun manhattan_distance(p :: Posn):

  abs(home.x - p.x) + 5 * abs(home.y - p.y)


fun another_manhattan_distance(Posn(x, y)):

  abs(home.x - x) + 5 * abs(home.y - y)



| should_take_cab(Posn(0, 0)): #false

| should_take_cab(p :: Posn):

    manhattan_distance(p) > 10 || weather.currently_raining()

| should_take_cab(#false): #false

The intent here is that def and fun are macro-implemented and recognize various forms of definitions, including simple binding, functions, and functions that have pattern-matching cases. The def and fun forms are not meant to know about :: specifically; the :: is meant to be a binding operator that checks whether the value flowing to the binding satisfies a predicate, and it may also associate compile-time information to a binding, such as the information that p is a Posn instance. The name Posn works in an expression to construct a position value, while in a binding position, Posn works to construct a pattern-matching binding (again, without def or fun knowing anything specific about Posn). Meanwhile, ., -, +, *, <, and || are the obvious operators with the usual precedence. Unlike the other operators, the . operator’s right-hand side is not an expression; it must always be an identifier. The weather.currently_raining form looks like a use of the . operator, but it’s meant here to be a use of the namer weather that is bound by import and recognizes . to access the imported currently_raining binding, which might be a macro instead of a variable that is bound to a function.

The Rhombus expander is further meant to a support a language where new operators can be defined in a function-like way, like this:

operator (x <> y):

  Posn(x, y)


1 <> 2 // same as Posn(1, 2)

Alternatively, operators can be defined in a more general, macro-like way. For example, defining -> as an alias for . requires a macro, since the right-hand side of . is not an expression. Using '' for “quote” and $ for “unquote,” the -> operator might be implemented in a pattern-matching macro as

expr.macro '$x -> $y $tail ...':

  values('$x . $y', '$tail ...')


home->x + 1 // same as home.x + 1

The intent here is that expr.macro (the . there is like using an import, accessing the macro form within an expr group of bindings) allows a macro to consume as many terms after the operator as it wants, and the macro must return two values: a quoted expression for the expansion plus leftover terms for further expression parsing (i.e., tail in the example use will hold + 1). Macros can work for other contexts, too, such as binding positions. Here’s a definition that extends the <> operator to make it work in binding positions:

bind.macro '$x <> $y $tail ...':

  values('Posn($x, $y)', '$tail ...')


// uses <> both for argument binding and result expression:

fun flip(x <> y):

  y <> x


flip(1 <> 2) // produces 2 <> 1

The above examples run in Rhombus, but the examples are meant only to illustrate some of the ingredients that the expander supports. This proposal does not intended to specify a language with specific definition forms, expression forms, and so on.

To define a new expander layer for shrubbery notation, we take Racket’s primitives as given: syntax objects, scopes, modules, and more. We also recycle some variant of Racket as the target for shrubbery expansion. In principle, the variant could be minimal, corresponding to the core forms that all Racket modules expand into, but some larger variant (including keyword arguments, for example) is likely a better choice of interoperability with Racket modules. The enforestation and expansion processes here are defined in terms of the S-expression form of parsed shrubbery notation (really, syntax-object form, so it can include scopes to determine a mapping for identifiers and operators). The <> and -> examples above use operator- and macro-definition forms in terms of shrubbery notation, but this proposal focuses on the lower-level mechanisms that allow such shrubbery-native forms to be implemented.

Since shrubbery notation is intended to be used with less grouping than is normally present in S-expressions, a key goal of this proposal is to specify an extensible traversal of shrubberies to turn them into Racket terms. In particular, the proposal addresses the problem of parsing a mixture of operators and other terms within a shrubbery group, allowing the definition of infix, prefix, and postfix operators for expressions, bindings, and other contexts. The handling of operators is directly based on Honu, but with several refinements—including a framework for relative and non-transitive operator precedence that is more like Fortress than Honu.

Although this proposal does not specify definition forms, we assume some way of mapping an identifier or operator to a compile-time entity, such as a macro transformer. (Throughout this proposal, we use “mapping” to refer to this binding in the sense of define-syntax, as opposed to binding positions in a language that is built with the Rhombus expander.) We also assume that mappings can be local, so that delaying the expansion of nested groups is useful while compile-time mappings are created by surrounding terms.