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Updated SRFI-105



Here's an updated draft SRFI-105, per mailing list discussion.

I've also sent this to the SRFI editors, but I'm sure they're busy, so we can start looking at it now.  I tried to respond to most of the comments.

--- David A. Wheeler
Title: Draft SRFI 105: Curly-infix-expressions

Title

Curly-infix-expressions

Authors 

David A. Wheeler

Alan Manuel K. Gloria

Status

This is a draft Scheme Request for Implementation (SRFI) for SRFI 105. To see an explanation of each status that a SRFI can hold, see here.

To provide input on this SRFI, please mail to <srfi minus 105 at srfi dot schemers dot org>. See instructions here to subscribe to the list. You can access previous messages via the archive of the mailing list. This SRFI contains all the required sections, including an abstract, rationale, specification, and reference implementation.

Related SRFIs

None

Abstract

Lisp-based languages, like Scheme, are almost the only programming languages in modern use that do not support infix notation. In addition, most languages allow infix expressions to be combined with function call notation of the form f(x). This SRFI provides these capabilities, both for developers who already use Scheme and want these conveniences, and also for other developers who may choose to use other languages in part because they miss these conveniences. Scheme currently reserves {...} “for possible future extensions to the language”. We propose that {...} be used to support “curly-infix” notation as a homoiconic infix abbreviation, as a modification of the Scheme reader. It is an abbreviation in much the same way that 'x is an abbreviation for (quote x).

A curly-infix list introduces a list whose visual presentation is in infix order instead of prefix order. For example, {n > 2}(> n 2), and {a + b + c}(+ a b c). By intent, there is no precedence, but e.g., {x + {y * z}} maps cleanly to (+ x (* y z)). Forms with mixed infix operators and other complications have “nfx” prepended to enable later macro processing, e.g., {2 + 3 * 5}(nfx 2 + 3 * 5). Also, inside a curly-infix list (recursively), expressions of the form f(...) are simply an abbreviation for (f ...).

Note that this is derived from the “readable” project. We intend to later submit at least one additional SRFI that will build on top of this SRFI, but curly-infix-expressions are useful on their own.

Rationale

Lisp-based languages, like Scheme, are almost the only programming languages in modern use that do not support infix notation. Even some Lisp advocates, like Paul Graham, admit that they “don’t find prefix math expressions natural” (http://www.paulgraham.com/pypar.html) even after decades of experience with Lisp-based languages. Paul Prescod has said, “I have more faith that you could convince the world to use Esperanto than prefix notation” (http://people.csail.mit.edu/gregs/ll1-discuss-archive-html/msg01571.html). Infix is not going away; standard mathematical notation uses infix, infix notation is taught to most people (programmers or not) in school, and nearly all new programming languages include infix.

Adding infix support to Scheme would be a useful convenience for some existing developers who use Scheme, and it would also eliminate a common complaint by developers who currently choose to use other languages instead.

Scheme currently reserves {...} “for possible future extensions to the language”. We propose that {...} be used to support “curly-infix” notation as a reader abbreviation, just as 'x is an abbreviation for (quote x) and (x y z) is an abbreviation for (x . (y . (z . ()))).

This proposal is an extremely simple and straightforward technique for supporting infix notation. There is no complex precedence system, all other Scheme capabilities (including macros and quasiquoting) work unchanged, any symbol can be used as an infix operation where desired, and Scheme remains general and homoiconic. Curly-infix-expressions (also known as c-expressions) are just a convenient reader abbreviation for infix notation.

At its core, this SRFI provides the simple curly-infix list that a list of expressions, with the difference that values are written in a different order. The simple curly-infix list {operand-1 operator operand-2 operator operand-3 operator ...} is mapped to (operator operand-1 operand-2 operand-3 ...) so that more than two operands are handled cleanly. E.g., {a + b + c}(+ a b c).

Why not macros? Why replace the reader?

Many previous systems have implemented “infix” systems as a named macro or procedure (e.g., INFIX). This looks ugly, and it does the wrong thing — the resulting list always has INFIX at the beginning, not the actual infix operator, so this approach can interfere with quoting, macros, and other capabilities. In particular, consider the following syntax-rules macro for function composition:

(define-syntax o
  (syntax-rules ()
    ({f o g}
     (lambda args
       (f (apply g args))))
    ({f o g o h o ...}
     {(lambda (x)
        (f (g x))) o h o ...})))

This example takes advantage of the fact that {f o g o h o ...}(o f g h ...). Infix cannot be implemented as a macro alone, as the syntax-rules form has a particular treatment for the pattern. A macro for infix would very likely confuse the syntax-rules form.

Why not a completely different notation for infix?

Other systems build notations into the reader, but the infix notation are often a notation radically different from normal Lisp notation. The result, in some cases, would be that these notations would simultaneously lose Lisp’s abilities for quoting, quasiquoting, and so on, and these notations were not homoiconic.

In contrast, this curly-infix-_expression_ proposal avoids these problems. For example, in curly-infix, `{,a + ,b} maps cleanly to `(+ ,a ,b), which works as expected with all macros.

Why isn’t precedence part of this SRFI?

Many past “infix” systems for Lisp build in precedence. However, Lisp systems often process other languages, and they may freely mix these different languages. Thus, the same symbol may have different meanings and precedence levels in different contexts. The symbol might not even be defined where it is being used, and allowing precedence definitions would create subtle errors if files are read in a different order. If users hook in their own precedence system into a reader, it could even become difficult to combine code written for different precedence systems. In short, building precedence into a Lisp reader creates many complexities.

Yet the complexity of precedence systems is often unnecessary. In practice, we’ve found that simple infix is all that’s needed most of the time in Lisp-based languages. Even in other languages, many developers unnecessarily use grouping symbols with infix operators to make their order clear. Thus, requiring grouping symbols is less of a hardship than it might appear.

By intentionally not building a precedence system into the reader, a very simple yet useful infix system results. We don’t need to register procedures, ensure that declarations of precedence precede their use, or anything like it. We also ensure that the notation is clearly homoiconic.

Instead, where precedence is desired, application and library writers can implement precedence by defining and controlling the scope of an “nfx” macro or procedure, or by later postprocessing of that symbol. Scheme macros are already quite powerful and capable of handling this; in these cases, {...} provides a more convenient notation. The curly-infix approach, instead of trying to manage both infix and precedence, handles simple cases and then takes advantage of the existing Scheme scoping rules and macro system for more complex cases (in the rare cases where they are needed).

It would be possible to extend curly-infix to provide a full fixed precedence system (e.g., if an _expression_ is mixed, attempt to use various precedence rules). However, such capabilities would be extensions beyond this SRFI.

Note that curly-infix includes support for unary operators, but again, they are without precedence. As a result, they must be grouped separately. This does not lead to hard-to-read expressions, however. Examples of simple curly-infix lists combining infix and unary operations include {-(x) * -(y)} and {-{x} * -{y}} (the notation is designed so that both work).

At first David A. Wheeler, who started this project, considered reporting an error if a simple infix _expression_ isn’t provided. However, prepending “nfx” is much more flexible.

Why not autodetect infix?

Some past efforts tried to automatically detect infix operators, but this turns out to not work well. It’s hard to express good rules for detecting infix operators, and the rules become too complex for users (e.g., “punctuation-only symbols” doesn’t detect “and” or “or”). And in any case, if they were automatically detected, an escape mechanism would be needed anyway - consider (map - ns) for getting a new list with the numbers in ns negated. Allowing the user to expressly notate when infix was intended, using {...}, turns out to be far more clearer and more intuitive. In particular, curly-infix allows the use of infix with any symbol, whenever you want... and where it’s not convenient, you don’t need to use it. It is also very backwards-compatible: Normal lists work normally, and if you want infix, use {...}.

Why are 0, 1, and 2 parameters special?

The empty curly-infix list {} is intentionally mapped to (), as it is an empty list, and this is the likely user meaning (reducing unnecessary errors).

The one and two parameter cases are defined in part to reduce user error, and in part to provide better support:

  1. An “escaping” {e} is mapped to e so that {...} can conceptually be used for grouping: {{{a} + {b}}} is equivalent to (+ a b). It ensures that the neoteric-_expression_ f{x} becomes the likely-intended (f x), and also makes it easy to use prefix notation; e.g., { f(x) } is just another way to write ( f x). Finally, it also provides an easy escape mechanism in sweet-expressions for symbols that would otherwise have other meanings.
  2. The “unary-operation” curly-infix list {e f}(e f), so that {- x}(- x), the likely interpretation, and also so that the neoteric-expressions like f{- x}(f (- x)).

Why use equal? to compare operators in a “simple” curly-infix-list for equality?

Operators are compared using equal? so that constructs like ,op are legal operators, e.g., {x ,op y ,op z}. Note that unfortunately if the operator construct contains a cycle, it might not terminate if equal? does not terminate in the presence of cycles. This was specified this way so that implementors could use the normal Scheme equal? comparison instead of having to implement a special comparison operator just for this particular case.

Why must infix operators be delimited?

Curly-infix requires that the infix operators be delimited (e.g., by spaces). This is consistent with Lisp history and current practice. Currently, in Lisp, operators are always delimited in traditional s-expressions (typically by left parentheses on the left, and by whitespace on the right). It’s impractical to do otherwise today; most Lisps, including Scheme, allow and predefine symbols that include characters (like “-”) that are typically used for infix operators. Many developers put space around infix operators even in languages that don’t require them, so syntactically requiring them is no burden. In short, it is difficult to allow infix operators without delimiters, and the visual results are the same as many real-world uses in other languages, so the result appears quite customary to typical software developers.

Why the curly-foo convention?

We would like to have a convention for users to easily enable curly-infix everywhere, e.g., for the default reader (e.g., read), read-eval-print loop (REPL), and loader (e.g., load). Our ideal would be that implementations would enable curly-infix in their normal invocation, but some implementors may not want to do that. For example, if an implementation already uses braces for a different local extension, they may not want to immediately switch to curly-infix in their default invocation. Thus, if implementors choose to not enable curly-infix in their default reader, a conventional command line name “curly-foo” is defined for each implementation foo that enables it.

There is simply no single option flag (for example) that everyone could agree on to enable this. In practice, we expect that implementations will build this capability into their default readers and then control it via some special flag, but we do not want to mandate exactly how it is turned on or passed.

Why the marker #!srfi-105?

We would like implementations to always have curly-infix enabled. However, some implementations may have other extensions that use {...}. We want a simple, standard way to identify code that uses curly-infix so that readers will switch to curly-infix if they need to switch. This marker was recommended during discussion of SRFI-105. After all, R6RS and R7RS (draft 6) already use #!fold-case and #!no-fold-case as special markers to control the reader. Using #!srfi-105 is a simple, similar-looking marker for a similar situation. What’s more, it implies a reasonable convention for reader extensions: markers that begin with #!, followed by an ASCII letter, should have the rest read as an identifier (up to a whitespace) and use that to control the reader, and srfi- should be the namespace for SRFIs.

This marker need not interfere with other uses of #!. SRFI-22 supports #! followed by space as a comment to the end of the line; this is supported by several implementations, but this is easily distinguished from this marker by the space. Guile, clisp, and several other Lisps support #!...!# as a multi-line comment, enabling scripts with mixed languages and multi-line arguments. But in practice the #! is almost always followed immediately by / or ., and other scripts could be trivially fixed to make that so. R6RS had a non-normative recommendation to ignore a line that began with #!/usr/bin/env, as well as a #! /usr/bin/env, but this is non-normative; an implementation could easily implement #! followed by space as an ignored line, and treat #! followed by / or . differently. Thus, implementations could trivially support simultaneously markers such as #!srfi-105 to identify curly-infix, the SRFI-22 #!+space marker as an ignored line, and support #!/ ...!# and #!. ...!# as a multi-line comment. Note that this SRFI does not mandate support or any particular semantics for #!fold-case, #!no-fold-case, the SRFI-22 #!+space convention, or #! followed by a slash or period; it is merely designed so that implementations could implement them all simultaneously. We recommend that #!srfi-105 not be the first two characters in a file (e.g., put a newline in front of it). If the file were made executable, and execution was attempted, this might confuse some systems into trying to run the program srfi-105.

By intent, this SRFI (including the enabling mechanism) doesn’t use or interact with any module system at all (including the R6RS and R7RS module systems). This is because some implementations won’t have a module system (or at least not a standard one). Curly-infix is an intentionally simple mechanism that can be built into even trivial Scheme implementations. Mandating module support is unnecessary and might inhibit its adoption.

What about the Racket “infix convention”?

Racket allows a notation called the “infix convention” with the form “(a . operation . b). An advantage of this alternative is that it does not use the braces, so it might be easier to implement in Schemes which already define {...} in a local extension. However, the Racket “infix convention” has many problems:

In short, cases where infix notation would be useful are extremely common, so its notation should be convenient. The Racket “infix convention” may be the next-best notation for infix notation after curly-infix, but it’s next-best, and we should strive for the best available notation for such a common need. Curly-infix does not conflict with the Racket infix convention; implementations could implement both. We recommend that an implementation that implements the Racket infix convention should also allow multiple operands and use curly-infix semantics for them, pretending that . op . is a single parameter. In that case, (a . + . b . + . c) would map to (+ a b c), and (a . + . b . * . c) would map to (nfx a + b * c). Note that the existence of the Racket “infix convention” is additional evidence of the need for a standard infix convention; many have separately created mechanisms to try to provide infix support.

What about Gambit’s “Scheme Infix eXtension (SIX)”?

The Gambit reader includes a notation called the “Scheme Infix eXtension (SIX)” that supports infix notation. SIX expressions begin with a backslash.

Like curly-infix, SIX is a reader extension. But SIX has a number of problems compared to curly-infix:

Like Racket, SIX does demonstrate that there is a need for an infix notation that can be used in Scheme.

A system could simultaneously implement curly-infix and SIX. However, curly-infix is far simpler, is more flexible (e.g., by allowing arbitrary symbols), and works much more easily with macros and quoting. Thus, we believe that curly-infix is the better system and more appropriate for standardization across Scheme implementations.

What about Guile 1.4’s “reading infix” module?

Guile 1.4.x at gnuvola.org is self-described as a “(somewhat amicable) fork from the official Guile”. It includes support for reading infix expressions. Once activated, infix expressions are surrounded by #[ and ]. Infix are surrounded by whitespace. It supports precedence, which sounds like an advantage, but operators must be registered before use (and few are predefined), creating an opportunity for terrible errors if the _expression_ is read first. There is also the opportunity for serious problems if different programs are written assuming different precedence levels. Inside the infix notation a very different language is used (e.g., parentheses are used for grouping instead of necessarily creating lists, and parameters are separated by commas), so it is unclear how well it would work with other Scheme features such as quasiquotation.

The guile 1.4 reading infix module has a more complex grammar requiring a more complex implementation and understanding. Its registration system creates serious problems when trying to use it for larger systems. This infix notation has not been accepted into the version of guile used by most people, so it is very much not portable. But perhaps the biggest problem is that this notation is fundamentally not homoiconic; it is harder to determine where lists begin and end with it.

Like Racket and SIX, this module does demonstrate that there is a need for an infix notation that can be used in Scheme.

In contrast, curly-infix is simpler, requires no registration system or other complexities, works more clearly with macros and quasiquotation, and has the general advantage of being homoiconic.

Why neoteric-expressions?

Lisp’s standard notation is different from “normal” notation in that the parentheses precede the function name, rather than follow it. Others have commented that it’d be valueable to be able to say name(x) instead of (name x):

Neoteric-expressions allow users to use a more traditional-looking notation for function calls. Again, quoting rules and macros continue to work as usual.

The (. e) rule handles expressions like read(. port), ensuring that they map to (read . port). If (. x) didn’t mean x, then it would be easy to get this case wrong. Also, if someone wanted to build on top of an existing reader, they would have to reimplement parts of the list-processing system if this wasn’t handled. It is already true that (. x) is x in guile, so there was already a working example that this is a reasonable extension. In fact, in a typical implementation of a list reader, it takes extra effort to prevent this extension, so this is a relatively easy extension to include.

Comma-separated parameters

It would be possible to define neoteric-expressions to have comma-separated values in a function call; this would make it even more similar to traditional function call notation. A simple way would be to simply remove all commas, but this would interfere with ,-lifting, and thus was immediately rejected.

A better rule, that would indeed work, would be to require each parameter to end with a comma, and then remove that ending comma. However, this rule:

Many other languages do use commas, but they are required in those languages because infix operators are not surrounded by any marker. Since infix operations are already surrounded by {...} in our notation, there is no need for the additional commas for parameter separation.

Experimentation found that separating parameters solely by whitespace worked well, so that approach was selected.

Other comments on neoteric-expressions

Originally the prefix had to be a symbol or list. The theory was that by ignoring others, the sweet-reader would be backwards-compatible with some badly-formatted code, and some errors might not result in incorrectly-interpreted expressions. But this was an odd limitation, and in some cases other prefixes made sense (e.g., for strings). This was changed to eliminate the inconsistency.

Neoteric-expressions used to be called “modern-expressions”. But some people didn’t like that name, and the obvious abbreviation (“m-_expression_”) was easily confused with the original Lisp M-_expression_ language. So the name was changed to neoteric, which has a similar meaning and abbreviates nicely. It wasn’t called “function-expressions” because “f-expressions” are previously used (and can sound bad if said quickly), and they weren’t called “prefix-expressions” because “p-expressions” sound like “pee-expressions”. It’s not called “name-prefix” because the prefix need not be a name. There is absolutely no truth to the rumor that the notation was developed by a secret technologically advanced species, so pay no attention to “Microcosmic God” by Theodore Sturgeon :-).

The neoteric rules do introduce the risk of someone inserting a space between the function name and the opening (. But whitespace is already significant as a parameter separator, so this is consistent with how the system works anyway... this is not really a change at all.

Obviously, this is trivial to parse. We don’t lose any power, because this is completely optional -- we only use it when we want to, and we can switch back to the traditional s-_expression_ notation if we want to. It’s trivially quoted... if you quote a symbol followed by (, just keep going until its matching ), which is essentially the same rule as before!

Other details

There is no requirement that writers (e.g., “write” or a pretty-printer) write out curly-infix-expressions. They may choose to do so, e.g., for lists of length 3-6 whose car is the symbol “and”, the symbol “or”, or a punctuation-only symbol. However, it would probably be wise to wait until many implementations can handle c-expressions.

Curly-infix is designed so that it can work on other Lisps as well. We even have a working implementation in Common Lisp.

Curly-infix is an unusually simple mechanism, but like much of any Lisp-based language, its power comes from its simplicity.

Specification

Curly-infix-expressions” or “c-expressions” are s-expressions with an additional notation: The curly-infix list. A curly-infix list is syntactically almost identical to a regular list, but it is surrounded by braces instead of by parentheses, and instead of a sequence of s-expressions it contains a sequence of neoteric-expressions (which add support for formats like f(x)). Once a curly-infix list is read, it is mapped differently than a regular list by a curly-infix reader:

  1. A simple curly-infix list has an odd number of parameters, at least three parameters, and all even parameters are “equal?”. If there is more than one even parameter, and an even parameter contains a cycle, then the equal? comparison must terminate if equal? terminates (otherwise the comparison may terminate). A simple curly-infix list is mapped by the reader into a list with the first even parameter followed by the odd parameters. E.g., {n <= 2}(<= n 2), and {2 * 3 * 4}(* 2 3 4).
  2. The empty curly-infix list {} is mapped to the empty list ().
  3. An escaping curly-infix list {e} is mapped to e. E.g., {5} is mapped to 5.
  4. A unary-operation curly-infix list {e1 e2} is mapped to (e1 e2). E.g., {- x}(- x).
  5. The mapping of a curly-infix list beginning with the symbol “.” is unspecified. (Note: the reference implementation maps {. e} to e.)
  6. Any other curly-infix list (including all other improper lists) is mixed. A mixed curly-infix list must be mapped to that list with “nfx” added to its front. E.g., {q + r * s} is mapped to (nfx q + r * s), and {q + r . s} is mapped to (nfx q + r . s).

Here is the precise definition of a curly-infix list (which is nearly identical to a traditional list):

curly-infix-list → {” <whitespace>* [ <n-_expression_> [ <whitespace>+ <n-_expression_> ]* [ <whitespace>+ . <whitespace>+ <n-_expression_> ] <whitespace>* ] “}

A “neoteric-_expression_” or “n-_expression_” is a curly-infix-_expression_, with the following modifications where e is any datum _expression_:

  1. e(...)(e ...). E.g., f(1 2)(f 1 2), exit()(exit), and read(. port)(read . port).
  2. e{}(e) when there are zero or more whitespace characters within the braces; otherwise, e{...}(e {...}). E.g., f{n - 1}(f {n - 1})(f (- n 1)), and g{- x}(g (- x)).
  3. e[...](bracketaccess e ...)
  4. There must be no whitespace between e and the open paired character.
  5. An unprefixed ( . e) must evaluate as e.
  6. These recurse within lists, so lists contains sequences of zero or more neoteric expressions, not s-expressions.
  7. These recurse left-to-right. E.g., f{n - 1}(x)f({n - 1})(x)(f (- n 1))(x)((f (- n 1)) x)

Here are some examples of c-expressions (note all operators in curly-infix are delimited):

A curly-infix reader is a datum reader that can correctly read and map curly-infix-expressions. A curly-infix reader must include the braces “{” and “}” as delimiters.

An implementation of this SRFI must accept the marker #!srfi-105 followed by a whitespace character. This marker (including the trailing whitespace character) is consumed and considered whitespace; after reading this marker, the reader must accept curly-infix expressions in subsequent datums until it reaches an end-of-file or some other conflicting marker (no conflicting marker is specified here). We encourage implementations to always implement curly-infix expressions, even when the marker is not received. However, portable applications must include this marker before any curly-infix expressions. We recommend that portable applications not use this marker as the first characters of a file (e.g., they should precede it with a newline).

The “standard readers” are the datum reader used by the REPL, the datum readers defined by the relevant Scheme standards (such as “read” and where applicable “get-datum”), and the readers used to load user-supplied code as defined by the relevant Scheme standards (e.g., the reader used by “load” and module-loading mechanisms for user code). The standard readers are curly-infix enabled if the standard readers are curly-infix readers.

An implementation of this SRFI must have its standard readers be curly-infix enabled. We encourage implementations’ default invocation to have their standard readers be curly-infix enabled, but this is not required. If the standard readers are not curly-infix enabled in an implementation’s default invocation, then if it can be invoked from a command line via the command “foo”, the implementation must provide an alternative command “curly-foo” (the command prefixed with “curly-”) in which its standard readers are curly-infix enabled. In addition, if the implementation is invokable as a graphical user interface (GUI), it must provide a documented means to ensure that its standard readers are curly-infix enabled.

An implementation must not, by default, bind the symbol “nfx” to a procedure, macro, or syntax that cannot be overridden. This symbol is reserved for use by library writers (in the case of a library-based implementation of this SRFI, this symbol is reserved for use by other libraries) and application writers.

However, an implementation may provide a default library that binds the “nfx” symbol (as it is then a library, this case actually falls under the “reserved for use by library writers” clause above). Application writers and other library writers using that implementation are then free to use or not use the implementation’s provided “nfx”. An implementation may even provide more than one, if they so desire. For a library-based implementation of this SRFI, any “nfx” implementation or implementations may be provided, as long as the “nfx” symbol can be rebound by users of that library.

Implementations may provide the procedure (curly-infix-read . port) as a curly-infix reader.

Note that, by definition, this SRFI modifies lexical syntax.

Reference implementation

The implementation below is portable, with the exception that Scheme provides no standard mechanism to override {...} in its built-in reader. Thus, implementations will typically have a modified reader that detects “{“, starts reading a list until its matching “}”, and then calls process-curly defined below. We recommend that implementations always do this, but an implementation must at least activate this behavior when “curly-foo” is invoked or when they read #!srfi-105.

This reference implementation is SRFI type 2: “A mostly-portable solution that uses some kind of hooks provided in some Scheme interpreter/compiler. In this case, a detailed specification of the hooks must be included so that the SRFI is self-contained.”

  ; Return true if lyst has an even # of parameters, and the (alternating)
  ; first parameters are "op".  Used to determine if a longer lyst is infix.
  ; If passed empty list, returns true (so recursion works correctly).
  (define (even-and-op-prefix? op lyst)
    (cond
      ((null? lyst) #t)
      ((not (pair? lyst)) #f)
      ((not (equal? op (car lyst))) #f) ; fail - operators not the same
      ((not (pair? (cdr lyst)))  #f) ; Wrong # of parameters or improper
      (#t   (even-and-op-prefix? op (cddr lyst))))) ; recurse.


  ; Return true if the lyst is in simple infix format
  ; (and thus should be reordered at read time).
  (define (simple-infix-list? lyst)
    (and
      (pair? lyst)           ; Must have list;  '() doesn't count.
      (pair? (cdr lyst))     ; Must have a second argument.
      (pair? (cddr lyst))    ; Must have a third argument (we check it
                             ; this way for performance)
      (even-and-op-prefix? (cadr lyst) (cdr lyst)))) ; true if rest is simple

  ; Return alternating parameters in a list (1st, 3rd, 5th, etc.)
  (define (alternating-parameters lyst)
    (if (or (null? lyst) (null? (cdr lyst)))
      lyst
      (cons (car lyst) (alternating-parameters (cddr lyst)))))

  ; Not a simple infix list - transform it.  Written as a separate procedure
  ; so that future experiments or SRFIs can easily replace just this piece.
  (define (transform-mixed-infix lyst)
     (cons 'nfx lyst))

  ; Given curly-infix lyst, map it to its final internal format.
  (define (process-curly lyst)
    (cond
     ((not (pair? lyst)) lyst) ; E.G., map {} to ().
     ((null? (cdr lyst)) ; Map {a} to a.
       (car lyst))
     ((and (pair? (cdr lyst)) (null? (cddr lyst))) ; Map {a b} to (a b).
       lyst)
     ((simple-infix-list? lyst) ; Map {a OP b [OP c...]} to (OP a b [c...])
       (cons (cadr lyst) (alternating-parameters lyst)))
     (#t  (transform-mixed-infix lyst))))


  ; ------------------------------------------------
  ; Key procedures to implement neoteric-expressions
  ; ------------------------------------------------

  ; Read the "inside" of a list until its matching stop-char, returning list.
  ; stop-char needs to be closing paren, closing bracket, or closing brace.
  ; This is like read-delimited-list of Common Lisp.
  ; This implements a useful extension: (. b) returns b.
  (define (my-read-delimited-list stop-char port)
    (let*
      ((c   (peek-char port)))
      (cond
        ((eof-object? c) (read-error "EOF in middle of list") '())
        ((eqv? c #\;)
          (consume-to-eol port)
          (my-read-delimited-list stop-char port))
        ((my-char-whitespace? c)
          (read-char port)
          (my-read-delimited-list stop-char port))
        ((char=? c stop-char)
          (read-char port)
          '())
        ((or (eq? c #\)) (eq? c #\]) (eq? c #\}))
          (read-char port)
          (read-error "Bad closing character"))
        (#t
          (let ((datum (neoteric-read port)))
            (cond
               ((eq? datum '.)
                 (let ((datum2 (neoteric-read port)))
                   (consume-whitespace port)
                   (cond
                     ((eof-object? datum2)
                      (read-error "Early eof in (... .)\n")
                      '())
                     ((not (eqv? (peek-char port) stop-char))
                      (read-error "Bad closing character after . datum"))
                     (#t
                       (read-char port)
                       datum2))))
               (#t
                   (cons datum
                     (my-read-delimited-list stop-char port)))))))))


  ; Implement neoteric-_expression_'s prefixed (), [], and {}.
  ; At this point, we have just finished reading some _expression_, which
  ; MIGHT be a prefix of some longer _expression_.  Examine the next
  ; character to be consumed; if it's an opening paren, bracket, or brace,
  ; then the _expression_ "prefix" is actually a prefix.
  ; Otherwise, just return the prefix and do not consume that next char.
  ; This recurses, to handle formats like f(x)(y).
  (define (neoteric-process-tail port prefix)
      (let* ((c (peek-char port)))
        (cond
          ((eof-object? c) prefix)
          ((char=? c #\( ) ; Implement f(x).
            (read-char port)
            (neoteric-process-tail port
                (cons prefix (my-read-delimited-list #\) port))))
          ((char=? c #\[ )  ; Implement f[x]
            (read-char port)
            (neoteric-process-tail port
                  (cons 'bracketaccess
                    (cons prefix
                      (my-read-delimited-list #\] port)))))
          ((char=? c #\{ )  ; Implement f{x}. Balance }
            (neoteric-process-tail port
              (let ((tail (neoteric-read port)))
                (if (eqv? tail '())
                  (list prefix) ; Map f{} to (f), not (f ()).
                  (list prefix tail)))))
          (#t prefix))))

  (define (neoteric-read . port)
    (if (null? port)
      (neoteric-read-real (current-input-port))
      (neoteric-read-real (car port))))
  
  ; This is the "real" implementation of neoteric-read
  ; (neoteric-read just figures out the port and calls neoteric-read-real).
  ; It implements an entire reader, as a demonstration, but if you can
  ; update your existing reader you should just update that instead.
  ; This is a simple R5RS reader, with a few minor (common) extensions.
  ; The key part is that it implements [] and {} as delimiters, and
  ; after it reads in some datum (the "prefix"), it calls
  ; neoteric-process-tail to see if there's a "tail".
  (define (neoteric-read-real port)
    (let*
      ((c (peek-char port))
       (prefix
         ; This cond is a normal Scheme reader, puts result in "prefix"
         ; This implements "read-_expression_-as-usual" as described above.
        (cond
          ((eof-object? c) c)
          ((char=? c #\;)
            (consume-to-eol port)
            (neoteric-read-real port))
          ((my-char-whitespace? c)
            (read-char port)
            (neoteric-read-real port))
          ((char=? c #\( )
             (read-char port)
             (my-read-delimited-list #\) port))
          ((char=? c #\) )
             (read-char port)
             (read-error "Closing parenthesis without opening")
             (neoteric-read-real port))
          ((char=? c #\[ )
             (read-char port)
             (my-read-delimited-list #\] port))
          ((char=? c #\] )
             (read-char port)
             (read-error "Closing bracket without opening")
             (neoteric-read-real port))
          ((char=? c #\{ )
            (read-char port)
            (process-curly
                (my-read-delimited-list #\} port)))
          ((char=? c #\} )
             (read-char port)
             (read-error "Closing brace without opening")
             (neoteric-read-real port))
          ((char=? c #\") ; Strings are delimited by ", so can call directly
            (default-scheme-read port))
          ((char=? c #\')
            (read-char port)
            (list 'quote (neoteric-read-real port)))
          ((char=? c #\`)
            (read-char port)
            (list 'quasiquote (neoteric-read-real port)))
          ((char=? c #\,)
            (read-char port)
              (cond
                ((char=? #\@ (peek-char port))
                  (read-char port)
                  (list 'unquote-splicing (neoteric-read-real port)))
               (#t
                (list 'unquote (neoteric-read-real port)))))
          ((ismember? c digits) ; Initial digit.
            (read-number port '()))
          ((char=? c #\#) (process-sharp port))
          ((char=? c #\.) (process-period port))
          ((or (char=? c #\+) (char=? c #\-))  ; Initial + or -
             (read-char port)
             (if (ismember? (peek-char port) digits)
               (read-number port (list c))
               (string->symbol (fold-case-maybe port
                 (list->string (cons c
                    (read-until-delim port neoteric-delimiters)))))))
          (#t ; Nothing else.  Must be a symbol start.
            (string->symbol (fold-case-maybe port
              (list->string
                (read-until-delim port neoteric-delimiters))))))))
      ; Here's the big change to implement neoteric-expressions:
      (if (eof-object? prefix)
        prefix
        (neoteric-process-tail port prefix))))


  ; Modify the main reader so that [] and {} are also delimiters, and so
  ; that when #\{ is detected, read using my-read-delimited-list
  ; any list from that port until its matching #\}, then process
  ; that list with "process-curly", like this:
  ;   (process-curly (my-read-delimited-list #\} port))

References

The readable project website has more information: http://readable.sourceforge.net

Acknowledgments

We thank all the participants on the “readable-discuss” mailing list.

Copyright

Copyright (C) 2012 David A. Wheeler and Alan Manuel K. Gloria. All Rights Reserved.

Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use, copy,
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of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY
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NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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