S-Expressions

Introduction S-expressions are data structures for representing complex data. They are either byte-strings ("octet-strings") or lists of simpler S-expressions. Here is a sample S-expression: (snicker "abc" (#03# |YWJj|)) It is a list of length three:

the octet-string "snicker"
the octet-string "abc"
a sub-list containing two elements: the hexadecimal constant #03# and the base-64 constant |YWJj| (which is the same as "abc")

This note gives a specific proposal for constructing and utilizing S-expressions. The proposal is independent of any particular application.

Here are the design goals for S-expressions:
generality:: S-expressions should be good at representing arbitrary data.
readability:: it should be easy for someone to examine and understand the structure of an S-expression.
economy:: S-expressions should represent data compactly.
tranportability:: S-expressions should be easy to transport over communication media (such as email) that are known to be less than perfect.
flexibility:: S-expressions should make it relatively simple to modify and extend data structures.
canonicalization:: it should be easy to produce a unique "canonical" form of an S-expression, for digital signature purposes.
efficiency:: S-expressions should admit in-memory representations that allow efficient processing.

Section 2 gives an introduction to S-expressions. Section 3 discusses the character sets used. Section 4 presents the various representations of octet-strings. Section 5 describes how to represent lists. Section 6 discusses how S-expressions are represented for various uses. Section 7 gives a BNF syntax for S-expressions. Section 8 talks about how S-expressions might be represented in memory. Section 9 briefly describes implementations for handling S-expressions. Section 10 discusses how applications might utilize S-expressions. Section 11 gives historical notes on S-expressions. Section 12 gives references.

Conventions Used in This Document The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

S-expressions -- informal introduction Informally, an S-expression is either:

an octet-string, or
a finite list of simpler S-expressions.

An octet-string is a finite sequence of eight-bit octets. There may be many different but equivalent ways of representing an octet-string

abc: -- as a token
"abc": -- as a quoted string
#616263#: -- as a hexadecimal string
3:abc: -- as a length-prefixed "verbatim" encoding
{MzphYmM=}: -- as a base-64 encoding of the verbatim encoding (that is, an encoding of "3:abc")
|YWJj|: -- as a base-64 encoding of the octet-string "abc"

These encodings are all equivalent; they all denote the same octet string. We will give details of these encodings later on, and also describe how to give a "display type" to a byte string. A list is a finite sequence of zero or more simpler S-expressions. A list may be represented by using parentheses to surround the sequence of encodings of its elements, as in: (abc (de #6667#) "ghi jkl") As we see, there is variability possible in the encoding of an S-expression. In some cases, it is desirable to standardize or restrict the encodings; in other cases it is desirable to have no restrictions. The following are the target cases we aim to handle:

a "transport" encoding for transporting the S-expression between computers.
a "canonical" encoding, used when signing the S-expression.
an "advanced" encoding used for input/output to people.
an "in-memory" encoding used for processing the S-expression in the computer.

These need not be different; in this proposal the canonical encoding is the same as the transport encoding, for example. In this note we propose (related) encoding techniques for each of these uses.

Character set We will be describing encodings of S-expressions. Except when giving "verbatim" encodings, the character set used is limited to the following characters in US-ASCII:

Alphabetic:: A B ... Z a b ... z
numeric:: 0 1 ... 9
whitespace:: space, horizontal tab, vertical tab, form-feed carriage-return, line-feed
The following graphics characters, which we call "pseudo-alphabetic":: - hyphen or minus . period / slash _ underscore : colon * asterisk + plus = equal
The following graphics characters, which are "reserved punctuation":
The following characters are unused and unavailable, except in "verbatim" encodings:: greater than ? question mark ]]>

Octet string representations This section describes in detail the ways in which an octet-string may be represented. We recall that an octet-string is any finite sequence of octets, and that the octet-string may have length zero.

Verbatim representation A verbatim encoding of an octet string consists of four parts:

the length (number of octets) of the octet-string, given in decimal most significant digit first, with no leading zeros.
a colon ":"
the octet string itself, verbatim.

There are no blanks or whitespace separating the parts. No "escape sequences" are interpreted in the octet string. This encoding is also called a "binary" or "raw" encoding. Here are some sample verbatim encodings: 3:abc 7:subject 4::::: 12:hello world! 10:abcdefghij 0:

Quoted-string representation The quoted-string representation of an octet-string consists of:

an optional decimal length field
an initial double-quote (")
the octet string with "C" escape conventions (\n, etc)
a final double-quote (")

The specified length is the length of the resulting string after any escape sequences have been handled. The string does not have any "terminating NULL" that C includes, and the length does not count such a character. The length is optional. The escape conventions within the quoted string are as follows (these follow the "C" programming language conventions, with an extension for ignoring line terminators of just LF or CRLF): \b -- backspace \t -- horizontal tab \v -- vertical tab \n -- new-line \f -- form-feed \r -- carriage-return \" -- double-quote \' -- single-quote \\ -- back-slash \ooo -- character with octal value ooo (all three digits must be present) \xhh -- character with hexadecimal value hh (both digits must be present) \<carriage-return> -- causes carriage-return to be ignored. \<line-feed> -- causes linefeed to be ignored \<carriage-return><line-feed> -- causes CRLF to be ignored. \<line-feed><carriage-return> -- causes LFCR to be ignored. Here are some examples of quoted-string encodings: "subject" "hi there" 7"subject" 3"\n\n\n" "This has\n two lines." "This has\ one." ""

Token representation An octet string that meets the following conditions may be given directly as a "token".

it does not begin with a digit
it contains only characters that are: alphabetic (upper or lower case); numeric; or one of the eight "pseudo-alphabetic" punctuation marks:

- . / _ : * + = (Note: upper and lower case are not equivalent.) (Note: A token may begin with punctuation, including ":"). Here are some examples of token representations: subject not-before class-of-1997 //microsoft.com/names/smith *

Hexadecimal representation An octet-string may be represented with a hexadecimal encoding consisting of:

an (optional) decimal length of the octet string
a sharp-sign "#"
a hexadecimal encoding of the octet string, with each octet represented with two hexadecimal digits, most significant digit first.
a sharp-sign "#"

There may be whitespace inserted in the midst of the hexadecimal encoding arbitrarily; it is ignored. It is an error to have characters other than whitespace and hexadecimal digits. Here are some examples of hexadecimal encodings: #616263# -- represents "abc" 3#616263# -- also represents "abc" # 616 263 # -- also represents "abc"

Base-64 representation An octet-string may be represented in a base-64 coding consisting of:

an (optional) decimal length of the octet string
a vertical bar "|"
the rfc 1521 base-64 encoding of the octet string.
a final vertical bar "|"

The base-64 encoding uses only the characters A-Z a-z 0-9 + / = It produces four characters of output for each three octets of input. If the input has one or two left-over octets of input, it produces an output block of length four ending in two or one equals signs, respectively. Output routines compliant with this standard MUST output the equals signs as specified. Input routines MAY accept inputs where the equals signs are dropped. There may be whitespace inserted in the midst of the base-64 encoding arbitrarily; it is ignored. It is an error to have characters other than whitespace and base-64 characters. Here are some examples of base-64 encodings: |YWJj| -- represents "abc" | Y W J j | -- also represents "abc" 3|YWJj| -- also represents "abc" |YWJjZA==| -- represents "abcd" |YWJjZA| -- also represents "abcd"

Display hint Any octet string may be preceded by a single "display hint". The purposes of the display hint is to provide information on how to display the octet string to a user. It has no other function. Many of the MIME types work here. A display-hint is an octet string surrounded by square brackets. There may be whitespace separating the octet string from the surrounding brackets. Any of the legal formats may be used for the octet string. Here are some examples of display-hints: [image/gif] [URI] [charset=unicode-1-1] [text/richtext] [application/postscript] [audio/basic] ["http://abc.com/display-types/funky.html"] In applications an octet-string that is untyped may be considered to have a pre-specified "default" mime type. The mime type "text/plain; charset=iso-8859-1" is the standard default.

Equality of octet-strings Two octet strings are considered to be "equal" if and only if they have the same display hint and the same data octet strings. Note that octet-strings are "case-sensitive"; the octet-string "abc" is not equal to the octet-string "ABC". An untyped octet-string can be compared to another octet-string (typed or not) by considering it as a typed octet-string with the default mime-type.

Lists Just as with octet-strings, there are several ways to represent an S-expression. Whitespace may be used to separate list elements, but they are only required to separate two octet strings when otherwise the two octet strings might be interpreted as one, as when one token follows another. Also, whitespace may follow the initial left parenthesis, or precede the final right parenthesis. Here are some examples of encodings of lists: (a b c) ( a ( b c ) ( ( d e ) ( e f ) ) ) (11:certificate(6:issuer3:bob)(7:subject5:alice)) ({3Rt=} "1997" murphy 3:{XC++})

Representation types There are three "types" of representations:

canonical
basic transport
advanced transport

The first two MUST be supported by any implementation; the last is optional.

Canonical representation This canonical representation is used for digital signature purposes, transmission, etc. It is uniquely defined for each S-expression. It is not particularly readable, but that is not the point. It is intended to be very easy to parse, to be reasonably economical, and to be unique for any S-expression. The "canonical" form of an S-expression represents each octet-string in verbatim mode, and represents each list with no blanks separating elements from each other or from the surrounding parentheses. Here are some examples of canonical representations of S-expressions: (6:issuer3:bob) (4:icon[12:image/bitmap]9:xxxxxxxxx) (7:subject(3:ref5:alice6:mother))

Basic transport representation There are two forms of the "basic transport" representation:

the canonical representation
an base-64 representation of the canonical representation, surrounded by braces.

The transport mechanism is intended to provide a universal means of representing S-expressions for transport from one machine to another. Here are some examples of an S-expression represented in basic transport mode: (1:a1:b1:c) {KDE6YTE6YjE6YykA} The second example above is the same S-expression as the first encoded in base-64. There is a difference between the brace notation for base-64 used here and the || notation for base-64'd octet-strings described above. Here the base-64 contents are converted to octets, and then re-scanned as if they were given originally as octets. With the || notation, the contents are just turned into an octet-string.

Advanced transport representation The "advanced transport" representation is intended to provide more flexible and readable notations for documentation, design, debugging, and (in some cases) user interface. The advanced transport representation allows all of the representation forms described above, include quoted strings, base-64 and hexadecimal representation of strings, tokens, representations of strings with omitted lengths, and so on.

BNF for syntax We give separate BNF's for canonical and advanced forms of S-expressions. We use the following notation: * means 0 or more occurrences of + means 1 or more occurrences of ? means 0 or 1 occurrences of parentheses are used for grouping, as in ( | )* ]]> For canonical and basic transport: :: | :: ? ; :: ; :: "[" "]" ; :: ":" ; :: + ; -- decimal numbers should have no unnecessary leading zeros -- any string of bytes, of the indicated length :: "(" * ")" ; :: "0" | ... | "9" ; ]]> For advanced transport: :: | :: ? ; :: | | | | ; :: "[" "]" ; :: ":" ; :: + ; -- decimal numbers should have no unnecessary leading zeros -- any string of bytes, of the indicated length :: + ; :: ? "|"( | )* "|" ; :: "#" ( | )* "#" ; :: ?

:: "\"" "\"" :: "(" ( | )* ")" ; :: * ; :: | | ; :: | | ; :: "a" | ... | "z" ; :: "A" | ... | "Z" ; :: "0" | ... | "9" ; :: | "A" | ... | "F" | "a" | ... | "f" ; :: "-" | "." | "/" | "_" | ":" | "*" | "+" | "=" ; :: " " | "\t" | "\r" | "\n" ; :: | | "+" | "/" | "=" ; :: "" ; ]]>

In-memory representations For processing, the S-expression would typically be parsed and represented in memory in a more more amenable to efficient processing. We suggest two alternatives:

"list-structure"
"array-layout"

We only sketch these here, as they are only suggestive. The code referenced below illustrates these styles in more detail.

List-structure memory representation Here there are separate records for simple-strings, strings, and lists. An S-expression of the form ("abc" "de") would require two records for the simple strings, two for the strings, and two for the list elements. This is a fairly conventional representation, and details are omitted here.

Array-layout memory representation Here each S-expression is represented as a contiguous array of bytes. The first byte codes the "type" of the S-expression: 01 octet-string 02 octet-string with display-hint 03 beginning of list (and 00 is used for "end of list") Each of the three types is immediately followed by a k-byte integer indicating the size (in bytes) of the following representation. Here k is an integer that depends on the implementation, it might be anywhere from 2 to 8, but would be fixed for a given implementation; it determines the size of the objects that can be handled. The transport and canonical representations are independent of the choice of k made by the implementation. Although the length of lists are not given in the usual S-expression notations, it is easy to fill them in when parsing; when you reach a right-parenthesis you know how long the list representation was, and where to go back to fill in the missing length.

Octet string This is represented as follows:

]]>

For example (here k = 2) 01 0003 a b c

Octet-string with display-hint This is represented as follows: 01

/* for display-type */ 01

/* for octet-string */ ]]>

For example, the S-expression [gif] #61626364# would be represented as (with k = 2) 02 000d 01 0003 g i f 01 0004 61 62 63 64

List This is represented as ... 00 ]]> For example, the list (abc [d]ef (g)) is represented in memory as (with k=2) 03 001b 01 0003 a b c 02 0009 01 0001 d 01 0002 e f 03 0005 01 0001 g 00 00

Code There is code available for reading and parsing the various S-expression formats proposed here. See http://theory.lcs.mit.edu/~rivest/sexp.html

Utilization of S-expressions This note has described S-expressions in general form. Application writers may wish to restrict their use of S-expressions in various ways. Here are some possible restrictions that might be considered:

no display-hints
no lengths on hexadecimal, quoted-strings, or base-64 encodings
no empty lists
no empty octet-strings
no lists having another list as its first element
no base-64 or hexadecimal encodings
fixed limits on the size of octet-strings

Historical note The S-expression technology described here was originally developed for "SDSI" (the Simple Distributed Security Infrastructure by Lampson and Rivest ) in 1996, although the origins clearly date back to McCarthy's LISP programming language. It was further refined and improved during the merger of SDSI and SPKI during the first half of 1997. S-expressions are similar to, but more readable and flexible than, Bernstein's "net-strings" . Although made publicly available as a file named draft-rivest-sexp-00.txt on 4 May 1997, this document was not actually submitted to the IETF as that time. This is a modernized version of that file.

IANA Considerations This document requires no IANA actions.

Security Consideration TBD