preserves/preserves-binary.md

no_site_title	title
true	Preserves: Binary Syntax

Tony Garnock-Jones tonyg@leastfixedpoint.com
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Preserves is a data model, with associated serialization formats. This document defines one of those formats: a binary syntax for Values from the Preserves data model that is easy for computer software to read and write. An equivalent human-readable text syntax also exists.

Machine-Oriented Binary Syntax

A Repr is a binary-syntax encoding, or representation, of a Value. For a value v, we write «v» for the Repr of v.

Type and Length representation.

Each Repr starts with a tag byte, describing the kind of information represented.

However, inspired by argdata, a Repr does not describe its own length. Instead, the surrounding context must supply the length of the Repr.

As a consequence, Reprs for Compound values store the lengths of their contained values. Each contained Value is represented as a length in bytes followed by its own Repr.

Each length is stored as an argdata-compatible big-endian base 128 varint.¹ Each byte of a varint stores seven bits of the length. All bytes have a clear upper bit, except the final byte, which has the upper bit set. We write len(m) for the varint-encoding of a non-negative integer m, defined recursively as follows:

len(m) = e(m, 128)
       where e(v, d) = [v + d]                           if v < 128
                       e(v / 128, 0) ++ [(v % 128) + d]  if v ≥ 128

We write len(|r|) for the varint-encoding of the length of Repr r.

The following table illustrates varint-encoding.

Number, m	m in binary, grouped into 7-bit chunks	len(m) bytes
15	0001111	143
300	0000010 0101100	2 172
1000000000	0000011 1011100 1101011 0010100 0000000	3 92 107 20 128

It is an error for a varint-encoded m in a Repr to be anything other than the unique shortest encoding for that m. That is, a varint-encoding of m MUST NOT start with 0.

Records, Sequences, Sets and Dictionaries.

      «<L F_1...F_m>» = [0xA7] ++ seq(«L», «F_1», ..., «F_m»)
        «[X_1...X_m]» = [0xA8] ++ seq(«X_1», ..., «X_m»)
       «#{E_1...E_m}» = [0xA9] ++ seq(«E_1», ..., «E_m»)
«{K_1:V_1...K_m:V_m}» = [0xAA] ++ seq(«K_1», «V_1», ..., «K_m», «V_m»)

   seq(R_1, ..., R_m) = len(|R_1|) ++ R_1 ++...++ len(|R_m|) ++ R_m

There is no ordering requirement on the E_i elements or K_i/V_i pairs.² They may appear in any order. However, the E_i and K_i MUST be pairwise distinct. In addition, implementations SHOULD default to writing set elements and dictionary key/value pairs in order sorted lexicographically by their Reprs³, and MAY offer the option of serializing in some other implementation-defined order.

SignedIntegers.

«x» when x ∈ SignedInteger = [0xA3] ++ intbytes(x)

The function intbytes(x) gives the big-endian two's-complement binary representation of x, taking exactly as many whole bytes as needed to unambiguously identify the value and its sign. As a special case, intbytes(0) is the empty byte sequence. The most-significant bit in the first byte in intbytes(x) (for x≠0) is the sign bit.⁴ Every SignedInteger MUST be represented with its shortest possible encoding.

For example,

  «87112285931760246646623899502532662132736»
    = A3 01 00 00 00 00 00 00 00
         00 00 00 00 00 00 00 00
         00 00

  «-257» = A3 FE FF        «-3» = A3 FD       «128» = A3 00 80
  «-256» = A3 FF 00        «-2» = A3 FE       «255» = A3 00 FF
  «-255» = A3 FF 01        «-1» = A3 FF       «256» = A3 01 00
  «-254» = A3 FF 02         «0» = A3        «32767» = A3 7F FF
  «-129» = A3 FF 7F         «1» = A3 01     «32768» = A3 00 80 00
  «-128» = A3 80           «12» = A3 0C     «65535» = A3 00 FF FF
  «-127» = A3 81           «13» = A3 0D     «65536» = A3 01 00 00
    «-4» = A3 FC          «127» = A3 7F    «131072» = A3 02 00 00

Strings, ByteStrings and Symbols.

Syntax for these three types varies only in the tag used. For String and Symbol, the data following the tag is a UTF-8 encoding of the Value's code points, while for ByteString it is the raw data contained within the Value unmodified.

«S» = [0xA4] ++ utf8(S)  if S ∈ String
      [0xA5] ++ S        if S ∈ ByteString
      [0xA6] ++ utf8(S)  if S ∈ Symbol

Booleans.

«#f» = [0xA0]
«#t» = [0xA1]

Floats and Doubles.

«F» when F ∈ Float  = [0xA2] ++ binary32(F)
«D» when D ∈ Double = [0xA2] ++ binary64(D)

The functions binary32(F) and binary64(D) yield big-endian 4- and 8-byte IEEE 754 binary representations of F and D, respectively.

Embeddeds.

The Repr of an Embedded is the Repr of a Value chosen to represent the denoted object, prefixed with [0xBF].

«#!V» = [0xBF] ++ «V»

Annotations.

To annotate a Repr r with some sequence of Values [v_1, ..., v_m], surround r as follows:

[0xBE] ++ len(|r|) ++ r ++ len(|«v_1»|) ++ «v_1» ++...++ len(|«v_m»|) ++ «v_m»

The Repr r MUST NOT already have annotations; that is, it must not begin with 0xBE.

For example, the Repr corresponding to textual syntax @a@b[], i.e. an empty sequence annotated with two symbols, a and b, is

«@a @b []»
  = [0xBE] ++ len(|«[]»|) ++ «[]» ++ len(|«a»|) ++ «a» ++ len(|«b»|) ++ «b»
  = [0xBE, 0x81, 0xA8, 0x82, 0xA6, 0x61, 0x82, 0xA6, 0x62]

Security Considerations

Annotations. In modes where a Value is being read while annotations are skipped, an endless sequence of annotations may give an illusion of progress.

Canonical form for cryptographic hashing and signing. No canonical textual encoding of a Value is specified. A canonical form exists for binary encoded Values, and implementations SHOULD produce canonical binary encodings by default; however, an implementation MAY permit two serializations of the same Value to yield different binary Reprs.

Acknowledgements

The exclusion of lengths from Reprs, placing lengths instead ahead of contained values in sequences, is inspired by argdata.

Appendix. Autodetection of textual or binary syntax

Every tag byte in a binary Preserves Repr falls within the range [0x80, 0xBF]. These bytes, interpreted as UTF-8, are continuation bytes, and will never occur as the first byte of a UTF-8 encoded code point. This means no binary-encoded Repr can be misinterpreted as valid UTF-8.

Conversely, a UTF-8 Document must start with a valid codepoint, meaning in particular that it must not start with a byte in the range [0x80, 0xBF]. This means that no UTF-8 encoded textual-syntax Preserves Document can be misinterpreted as a binary-syntax Repr.

Examination of the top two bits of the first byte of an encoded Value gives its syntax: if the top two bits are 10, it should be interpreted as a binary-syntax Repr; otherwise, it should be interpreted as text.

Streaming. Autodetection is still possible when streaming an undetermined number of Values across, say, a TCP/IP connection:

• If the text syntax is to be used for the connection, simply start writing each Document one after the other. Documents for Atoms MUST be separated from their neighbours by whitespace; in general, whitespace SHOULD be used to separate adjacent documents. Specifically, whitespace separating adjacent documents SHOULD be ASCII newline (10).

• If the binary syntax is to be used for the connection, start the connection with byte 0xA8 (sequence). After the initial byte, send each value v as len(|«v»|) ++ «v». A side effect of this approach is that the entire stream, when complete, is a valid Sequence Repr.

Appendix. Table of tag values

(8x)  RESERVED 80-8F
(9x)  RESERVED 90-9F

 A0 - False
 A1 - True
 A2 - Float or Double (length disambiguates)
 A3 - SignedIntegers (0 is encoded with no bytes at all)
 A4 - String (no trailing NUL is added)
 A5 - ByteString
 A6 - Symbol

 A7 - Record
 A8 - Sequence
 A9 - Set
 AA - Dictionary

(Ax)  RESERVED AB-AF

(Bx)  RESERVED B0-BD
 BE - Annotations. {BE Lval val Lann0 ann0 Lann1 ann1 ...}
 BF - Embedded

Appendix. Binary SignedInteger representation

Languages that provide fixed-width machine word types may find the following table useful in encoding and decoding binary SignedInteger values.

Integer range	Bytes required	Encoding (hex)
0	1	A3
-27 ≤ n < 27 (i8)	2	A3 XX
-215 ≤ n < 215 (i16)	3	A3 XX XX
-223 ≤ n < 223 (i24)	4	A3 XX XX XX
-231 ≤ n < 231 (i32)	5	A3 XX XX XX XX
-239 ≤ n < 239 (i40)	6	A3 XX XX XX XX XX
-247 ≤ n < 247 (i48)	7	A3 XX XX XX XX XX XX
-255 ≤ n < 255 (i56)	8	A3 XX XX XX XX XX XX XX
-263 ≤ n < 263 (i64)	9	A3 XX XX XX XX XX XX XX XX

Notes

---

1. Argdata's length representation is very close to Variable-length quantity (VLQ) encoding, differing only in the flipped interpretation of the high bit of each byte. It is big-endian, unlike LEB128 encoding (as used by Google in protobufs). ↩︎

2. In the BitTorrent encoding format, bencoding, dictionary key/value pairs must be sorted by key. This is a necessary step for ensuring serialization of Values is canonical. We do not require that key/value pairs (or set elements) be in sorted order for serialized Values; however, a canonical form for Reprs does exist where a sorted ordering is required. ↩︎

3. It's important to note that the sort ordering for writing out set elements and dictionary key/value pairs is not the same as the sort ordering implied by the semantic ordering of those elements or keys. For example, the Repr of a negative number very far from zero will start with a byte that is greater than the byte which starts the Repr of zero, making it sort lexicographically later by Repr, despite being semantically less than zero.

   Rationale. This is for ease-of-implementation reasons: not all languages can easily represent sorted sets or sorted dictionaries, but encoding and then sorting byte strings is much more likely to be within easy reach. ↩︎

4. The value 0 needs zero bytes to identify the value, so intbytes(0) is the empty byte string. Non-zero values need at least one byte. ↩︎