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<title>Preserves: an Expressive Data Language</title>
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# Preserves: an Expressive Data Language

Tony Garnock-Jones <tonyg@leastfixedpoint.com>  
September 2018. Version 0.0.2.

  [sexp.txt]: http://people.csail.mit.edu/rivest/Sexp.txt
  [spki]: http://world.std.com/~cme/html/spki.html
  [varint]: https://developers.google.com/protocol-buffers/docs/encoding#varints
  [erlang-map]: http://erlang.org/doc/reference_manual/data_types.html#map

This document proposes a data model and serialization format called
*Preserves*.

Preserves supports *records* with user-defined *labels*. This makes it
more expressive[^macro-expressiveness] than most data languages in use
on the web and allows it to easily represent the *labelled sums of
products* as seen in many functional programming languages.

Preserves also supports the usual suite of atomic and compound data
types, in particular including *binary* data as a distinct type from
text strings.

Finally, Preserves defines precisely how to *compare* two values.
Comparison is based on the data model, not on syntax or on data
structures of any particular implementation language.

  [^macro-expressiveness]: By "expressive" I mean *macro-expressive*
    in the sense of Felleisen's 1991 paper, "On the Expressive Power
    of Programming Languages".

    Roughly speaking, there's no way in a JSON document to introduce a
    new kind of information (such as binary data, or a date-stamp, or
    a "person" object) in an *unambiguous way* without *global
    agreement* from every potential consumer of the document. With an
    extensible labelled record type, there is.

    Felleisen, Matthias. “On the Expressive Power of Programming
    Languages.” Science of Computer Programming 17, no. 1--3 (1991):
    35–75.

## Starting with Semantics

Taking inspiration from functional programming, we start with a
definition of the *values* that we want to work with and give them
meaning independent of their syntax. We will treat syntax separately,
later in this document.

Our `Value`s fall into two broad categories: *atomic* and *compound*
data.

                          Value = Atom
                                | Compound

                           Atom = Boolean
                                | Float
                                | Double
                                | SignedInteger
                                | String
                                | ByteString
                                | Symbol

                       Compound = Record
                                | Sequence
                                | Set
                                | Dictionary

**Total order.**<a name="total-order"></a> As we go, we will
incrementally specify a total order over `Value`s. Two values of the
same kind are compared using kind-specific rules. The ordering among
values of different kinds is essentially arbitrary, but having a total
order is convenient for many tasks, so we define it as
follows:[^ordering-by-syntax]

            (Values)        Atom < Compound

            (Compounds)     Record < Sequence < Set < Dictionary

            (Atoms)         Boolean < Float < Double < SignedInteger
                              < String < ByteString < Symbol

  [^ordering-by-syntax]: The observant reader may note that the
    ordering here is (almost) the same as that implied by the tagging
    scheme used in the concrete binary syntax for `Value`s. (The
    exception is the syntax for small integers near zero.)

**Equivalence.**<a name="equivalence"></a> Two `Value`s are equal if
neither is less than the other according to the total order.

### Signed integers.

A `SignedInteger` is a signed integer of arbitrary width.
`SignedInteger`s are compared as mathematical integers. We will write
examples of `SignedInteger`s using standard mathematical notation.

**Examples.** 10; -6; 0.

**Non-examples.** NaN (the clue is in the name!); ∞ (not finite); 0.2
(not an integer); 1/7 (likewise); 2+*i*3 (likewise); √2 (likewise).

### Unicode strings.

A `String` is a sequence of Unicode
[code-point](http://www.unicode.org/glossary/#code_point)s. `String`s
are compared lexicographically, code-point by
code-point.[^utf8-is-awesome] We will write examples of `String`s as
text surrounded by quotes “`"`”.

  [^utf8-is-awesome]: Happily, the design of UTF-8 is such that this
    gives the same result as a lexicographic byte-by-byte comparison
    of the UTF-8 encoding of a string!

**Examples.** `"Hello world"`, an eleven-code-point string; `"z水𝄞"`,
the string containing the three Unicode code-points `z` (0x7A), `水`
(0x6C34) and `𝄞` (0x1D11E); `""`, the empty string.

### Binary data.

A `ByteString` is an ordered sequence of zero or more eight-bit bytes.
`ByteString`s are compared lexicographically. We will only write
examples of `ByteString`s that contain bytes denoting printable ASCII
characters, using “`#"`” as an open-quote and “`"`” as a close-quote
mark.

**Examples.** The `ByteString` containing the integers 65, 66 and 67
(corresponding to ASCII characters `A`, `B` and `C`) is written as
`#"ABC"`. The empty `ByteString` is written as `#""`. **N.B.** Despite
appearances, these are *binary* data.

### Symbols.

Programming languages like Lisp and Prolog frequently use string-like
values called *symbols*. Here, a `Symbol` is, like a `String`, a
sequence of Unicode code-points representing an identifier of some
kind. `Symbol`s are also compared lexicographically by code-point. We
will write examples including only non-empty sequences of
non-whitespace characters, using a monospace font without quotation
marks.

**Examples.** `hello-world`; `utf8-string`; `exact-integer?`.

### Booleans.

There are exactly two `Boolean` values, “false” and “true”. The
“false” value compares less-than the “true” value. We write `#f` for
“false”, and `#t` for “true”.

### IEEE floating-point values.

A `Float` is a single-precision IEEE 754 floating-point value; a
`Double` is a double-precision IEEE 754 floating-point value.
`Float`s, `Double`s and `SignedInteger`s are considered disjoint, and
so by the rules [above](#total-order), every `Float` is less than
every `Double`, and every `SignedInteger` is greater than both. Two
`Float`s or two `Double`s are to be ordered by the `totalOrder`
predicate defined in section 5.10 of
[IEEE Std 754-2008](https://dx.doi.org/10.1109/IEEESTD.2008.4610935).
We write examples using standard mathematical notation, avoiding NaN
and infinities, using a suffix `f` or `d` to indicate `Float` or
`Double`, respectively.

**Examples.** 10f; -6d; 0f; 0.5d; -1.202e300d.

**Non-examples.** 10, -6, and 0, because writing them this way
indicates `SignedInteger`s, not `Float`s or `Double`s.

### Records.

A `Record` is a *labelled* tuple of zero or more `Value`s, called the
record's *fields*. A record's label is, itself, a `Value`, though it
will usually be a `Symbol`.[^extensibility] [^iri-labels] `Record`s
are compared lexicographically as if they were just tuples; that is,
first by their labels, and then by the remainder of their fields. We
will write examples of `Record`s as a parenthesised, space-separated
sequence of their label `Value` followed by their field `Value`s.

  [^extensibility]: The [Racket](https://racket-lang.org/) programming
    language defines
    [“prefab”](http://docs.racket-lang.org/guide/define-struct.html#(part._prefab-struct))
    structure types, which map well to our `Record`s. Racket supports
    record extensibility by encoding record supertypes into record
    labels as specially-formatted lists.

  [^iri-labels]: It is occasionally (but seldom) necessary to
    interpret such `Symbol` labels as UTF-8 encoded IRIs. Where a
    label can be read as a relative IRI, it is notionally interpreted
    with respect to the IRI
    `urn:uuid:6bf094a6-20f1-4887-ada7-46834a9b5b34`; where a label can
    be read as an absolute IRI, it stands for that IRI; and otherwise,
    it cannot be read as an IRI at all, and so the label simply stands
    for itself—for its own `Value`.

**Examples.** The `Record` with label `foo` and fields 1, 2 and 3 is
written `(foo 1 2 3)`; the `Record` with label `void` and no fields is
written `(void)`.

**Non-examples.** `()`, because it lacks a label.

### Sequences.

A `Sequence` is a general-purpose, variable-length ordered sequence of
zero or more `Value`s. `Sequence`s are compared lexicographically. We
write examples space-separated, surrounded with square brackets.

**Examples.** `[]`, the empty sequence; `[1 2 3]`, the sequence of
`SignedInteger`s 1, 2 and 3.

### Sets.

A `Set` is an unordered finite set of `Value`s. It contains no
duplicate values, following the [equivalence relation](#equivalence)
induced by the total order on `Value`s. Two `Set`s are compared by
sorting their elements ascending using the [total order](#total-order)
and comparing the resulting `Sequence`s. We write examples
space-separated, surrounded with curly braces, prefixed by `#set`.

**Examples.** `#set{}`, the empty set; `#set{#set{}}`, the set
containing only the empty set; `#set{4 "hello" (void) 9.0f}`, the set
containing 4, the string `"hello"`, the record with label `void` and
no fields, and the `Float` denoting the number 9.0; `#set{1 1.0f}`,
the set containing a `SignedInteger` and a `Float`; `#set{(mime
application/xml #"<x/>") (mime application/xml #"<x />")}`, a set
containing two different type-labelled byte
arrays.[^mime-xml-difference]

  [^mime-xml-difference]: The two XML documents `<x/>` and `<x />`
    differ by bytewise comparison, and thus yield different record
    values, even though under the semantics of XML they denote
    identical XML infoset.

**Non-examples.** `#set{1 1 1}`, because it contains multiple
equivalent `Value`s.

### Dictionaries.

A `Dictionary` is an unordered finite collection of pairs of `Value`s.
Each pair comprises a *key* and a *value*. Keys in a `Dictionary` must
be pairwise distinct. Instances of `Dictionary` are compared by
lexicographic comparison of the sequences resulting from ordering each
`Dictionary`'s pairs in ascending order by key. Examples are written
as a `#dict`-prefixed, curly-brace-surrounded sequence of
space-separated key-value pairs, each written with a colon between the
key and value.

**Examples.** `#dict{}`, the empty dictionary; `#dict{a:1}`, the
dictionary mapping the `Symbol` `a` to the `SignedInteger` 1;
`#dict{[1 2 3]:a}`, mapping `[1 2 3]` to `a`; `#dict{"hi":0 hi:0
there:[]}`, having a `String` and two `Symbol` keys, and
`SignedInteger` and `Sequence` values.

**Non-examples.** `#dict{a:1 b:2 a:3}`, because it contains duplicate
keys; `#dict{[7 8]:[] [7 8]:99}`, for the same reason.

## Syntax

Now we have discussed `Value`s and their meanings, we may turn to
techniques for *representing* `Value`s for communication or storage.

For now, we limit our attention to an easily-parsed, easily-produced
machine-readable syntax.

A `Repr` is an encoding, or representation, of a specific `Value`.
Each `Repr` comprises one or more bytes describing first the kind of
represented `Value` and the length of the representation, and then the
encoded details of the `Value` itself.

For a value `v`, we write `[[v]]` for the `Repr` of v.

### Type and Length representation

Each `Repr` takes one of three possible forms:

 - (A) a fixed-length form, used for simple values such as `Boolean`s
   or `Float`s.

 - (B) a variable-length form with length specified up-front, used for
   almost all `Record`s as well as for most `Sequence`s and `String`s,
   when their sizes are known at the time serialization begins.

 - (C) a variable-length streaming form with unknown or unpredictable
   length, used only seldom for `Record`s, since the number of fields
   in a `Record` is usually statically known, but sometimes used for
   `Sequence`s, `String`s etc., such as in cases when serialization
   begins before the number of elements or bytes in the corresponding
   `Value` is known.

Applications may choose between formats B and C depending on their
needs at serialization time.

#### The lead byte

Every `Repr` starts with a *lead byte*, constructed by
`leadbyte(t,n,m)`, where `t`,`n`∈{0,1,2,3} and 0≤`m`<16:

    leadbyte(t,n,m) = [t*64 + n*16 + m]

The arguments `t` and `n` describe the rest of the
representation:[^some-encodings-unused]

  [^some-encodings-unused]: Some encodings are unused. All such
    encodings are reserved for future versions of this specification.

 - `t`=0, `n`=0 (format A) represents an `Atom` with fixed-length binary representation.
 - `t`=0, `n`=1 (format A) represents certain small `SignedInteger`s.
 - `t`=0, `n`=2 (format C) is a Stream Start byte.
 - `t`=0, `n`=3 (format C) is a Stream End byte.
 - `t`=1 (format B) represents an `Atom` with variable-length binary representation.
 - `t`=2 (format B) represents a `Record`.
 - `t`=3 (format B) represents a `Sequence`, `Set` or `Dictionary`.

#### Encoding data of fixed length (format A)

Each specific type of data defines its own rules for this format.

---

#### Encoding data of known length (format B)

A `Repr` where the length of the `Value` to be encoded is variable but
known uses the value of `m` in `leadbyte` to encode its length. The
length counts *bytes* for atomic `Value`s, but counts *contained
values* for compound `Value`s.

 - A length `l` between 0 and 14 is represented using `leadbyte` with
   `m=l`.
 - A length of 15 or greater is represented by `m=15` and additional
   bytes describing the length following the lead byte.

The function `header(t,n,m)` yields an appropriate sequence of bytes
describing a `Repr`'s type and length when `t`, `n` and `m` are
appropriate non-negative integers:

    header(t,n,m) =    leadbyte(t,n,m)                 when m < 15
                    or leadbyte(t,n,15) ++ varint(m)   otherwise

The additional length bytes are formatted as
[base 128 varints][varint]. We write `varint(m)` for the
varint-encoding of `m`. Quoting the [Google Protocol Buffers][varint]
definition,

> Each byte in a varint, except the last byte, has the most
> significant bit (msb) set – this indicates that there are further
> bytes to come. The lower 7 bits of each byte are used to store the
> two's complement representation of the number in groups of 7 bits,
> least significant group first.

**Examples.**

 - The varint representation of 15 is just the byte 15.
 - 300 (binary, grouped into 7-bit chunks, `10 0101100`) varint-encodes to the two bytes 172 and 2.
 - 1000000000 (binary `11 1011100 1101011 0010100 0000000`) varint-encodes to bytes 128, 148, 235, 220, and 3.

#### Streaming data of unknown length (format C)

A `Repr` where the length of the `Value` to be encoded is variable and
not known at the time serialization of the `Value` starts is encoded
by a single Stream Start (“open”) byte, followed by zero or more
*chunks*, followed by a matching Stream End (“close”) byte:

     open(t,n) = leadbyte(0,2, t*4 + n)
    close(t,n) = leadbyte(0,3, t*4 + n)

For a `Repr` of a `Value` containing binary data, each chunk is to be
a format B `Repr` of the same type as the overall `Repr`.

For a `Repr` of a `Value` containing other `Value`s, each chunk is to
be a single `Repr`.

### Records

Format B (known length):

    [[ (L F_1...F_m) ]] = header(2,3,m+1) ++ [[L]] ++ [[F_1]] ++...++ [[F_m]]

For `m` fields, `m+1` is supplied to `header`, to account for the
encoding of the record label.

Format C (streaming):

    [[ (L F_1...F_m) ]] = open(2,3) ++ [[L]] ++ [[F_1]] ++...++ [[F_m]] ++ close(2,3)

Applications *SHOULD* prefer the known-length format for encoding
`Record`s.

#### Application-specific short form for labels

Any given protocol using Preserves may additionally define an
interpretation for `n`∈{0,1,2}, mapping each *short form label
number* `n` to a specific record label. When encoding `m` fields with
short form label number `n`, format B becomes

    header(2,n,m) ++ [[F_1]] ++...++ [[F_m]]

and format C becomes

    open(2,n) ++ [[F_1]] ++...++ [[F_m]] ++ close(2,n)

**Examples.** For example, a protocol may choose to map records
labelled `void` to `n=0`, making

    [[(void)]] = header(2,0,0) = [0x80]

or it may map records labelled `person` to short form label number 1,
making

    [[(person "Dr" "Elizabeth" "Blackwell")]]
        = header(2,1,3) ++ [["Dr"]] ++ [["Elizabeth"]] ++ [["Blackwell"]]
        =        [0x93] ++ [["Dr"]] ++ [["Elizabeth"]] ++ [["Blackwell"]]

for format B, or

        = open(2,1) ++ [["Dr"]] ++ [["Elizabeth"]] ++ [["Blackwell"]] ++ close(2,1)
        =    [0x29] ++ [["Dr"]] ++ [["Elizabeth"]] ++ [["Blackwell"]] ++ [0x39]

for format C.

### Sequences, Sets and Dictionaries

Format B (known length):

                 [[ [X_1...X_m] ]] = header(3,0,m)   ++ [[X_1]] ++...++ [[X_m]]
             [[ #set{X_1...X_m} ]] = header(3,1,m)   ++ [[X_1]] ++...++ [[X_m]]
    [[ #dict{K_1:V_1...K_m:V_m} ]] = header(3,2,m*2) ++ [[K_1]] ++ [[V_1]] ++...
                                                     ++ [[K_m]] ++ [[V_m]]

Note that `m*2` is given to `header` for a `Dictionary`, since there
are two `Value`s in each key-value pair.

Format C (streaming):

                 [[ [X_1...X_m] ]] = open(3,0) ++ [[X_1]] ++...++ [[X_m]] ++ close(3,0)
             [[ #set{X_1...X_m} ]] = open(3,1) ++ [[X_1]] ++...++ [[X_m]] ++ close(3,1)
    [[ #dict{K_1:V_1...K_m:V_m} ]] = open(3,2) ++ [[K_1]] ++ [[V_1]] ++...
                                               ++ [[K_m]] ++ [[V_m]] ++ close(3,2)

Applications may use whichever format suits their needs on a
case-by-case basis.

There is *no* ordering requirement on the `X_i` elements or
`K_i`/`V_i` pairs.[^no-sorting-rationale] They may appear in any
order.

  [^no-sorting-rationale]: In the BitTorrent encoding format,
    [bencoding](http://www.bittorrent.org/beps/bep_0003.html#bencoding),
    dictionary key/value pairs must be sorted by key. This is a
    necessary step for ensuring serialization of `Value`s is
    canonical. We do not require that key/value pairs (or set
    elements) be in sorted order for serialized `Value`s, because (a)
    where canonicalization is used for cryptographic signatures, it is
    more reliable to simply retain the exact binary form of the signed
    document than to depend on canonical de- and re-serialization, and
    (b) sorting keys or elements makes no sense in streaming
    serialization formats.

    However, a quality implementation may wish to offer the programmer
    the option of serializing with set elements and dictionary keys in
    sorted order.

Note that `header(3,3,m)` and `open(3,3)`/`close(3,3)` is unused and reserved.

### SignedIntegers

Format B/A (known length/fixed-size):

    [[ x ]] when x ∈ SignedInteger = header(1,0,m) ++ intbytes(x)  if x<-3 ∨ 13≤x
                                     header(0,1,x+16)              if -3≤x<0
                                     header(0,1,x)                 if 0≤x<13

Integers in the range [-3,12] are compactly represented using format A
because they are so frequently used. Other integers are represented
using format B.

Format C *MUST NOT* be used for `SignedInteger`s.

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, and `m =
|intbytes(x)|`. The most-significant bit in the first byte in
`intbytes(x)` <!-- for `x`≠0 --> is the sign bit.[^zero-intbytes]

  [^zero-intbytes]: 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.

For example,

    [[   -257 ]] = 42 FE FF    [[     -3 ]] = 1D       [[    128 ]] = 42 00 80
    [[   -256 ]] = 42 FF 00    [[     -2 ]] = 1E       [[    255 ]] = 42 00 FF
    [[   -255 ]] = 42 FF 01    [[     -1 ]] = 1F       [[    256 ]] = 42 01 00
    [[   -254 ]] = 42 FF 02    [[      0 ]] = 10       [[  32767 ]] = 42 7F FF
    [[   -129 ]] = 42 FF 7F    [[      1 ]] = 11       [[  32768 ]] = 43 00 80 00
    [[   -128 ]] = 41 80       [[     12 ]] = 1C       [[  65535 ]] = 43 00 FF FF
    [[   -127 ]] = 41 81       [[     13 ]] = 41 0D    [[  65536 ]] = 43 01 00 00
    [[     -4 ]] = 41 FC       [[    127 ]] = 41 7F    [[ 131072 ]] = 43 02 00 00

### Strings, ByteStrings and Symbols

Syntax for these three types varies only in the value of `n` supplied
to `header`, `open`, and `close`. In each case, the payload following
the header is a binary sequence; for `String` and `Symbol`, it is a
UTF-8 encoding of the `Value`'s code points, while for `ByteString` it
is the raw data contained within the `Value` unmodified.

Format B (known length):

              [[ S ]] = header(1,n,m) ++ encode(S)
              where m = |encode(S)|
    and (n,encode(S)) = (1,utf8(S))  if S ∈ String
                        (2,S)        if S ∈ ByteString
                        (3,utf8(S))  if S ∈ Symbol

To stream a `String`, `ByteString` or `Symbol`, emit `open(1,n)` and
then a sequence of zero or more format B chunks, followed by
`close(1,n)`. For a `String`, every chunk must be a `String`;
likewise, for `ByteString` and `Symbol`.

While the overall content of a streamed `String` or `Symbol` must be
valid UTF-8, individual chunks do not have to conform to UTF-8.

### Fixed-length Atoms

Fixed-length atoms all use format A, and do not have a length
representation. They repurpose the bits that format B `Repr`s use to
specify lengths. Applications *MUST NOT* use format C with
`open(0,n)` or `close(0,n)` for any `n`.

#### Booleans

    [[ #f ]] = header(0,0,0) = [0x00]
    [[ #t ]] = header(0,0,1) = [0x01]

#### Floats and Doubles

    [[ F ]] when F ∈ Float  = header(0,0,2) ++ binary32(F)
    [[ D ]] when D ∈ Double = header(0,0,3) ++ 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.

## Examples

<!-- TODO: Give some examples of large and small Preserves, perhaps -->
<!-- translated from various JSON blobs floating around the internet. -->

For the following examples, imagine an application that maps `Record`
short form label number 0 to label `discard`, 1 to `capture`, and 2 to
`observe`.

| Value                                                              | Encoded hexadecimal byte sequence                  |
|--------------------------------------------------------------------|----------------------------------------------------|
| `(capture (discard))`                                              | 91 80                                              |
| `(observe (speak (discard) (capture (discard))))`                  | A1 B3 75 73 70 65 61 6B 80 91 80                   |
| `[1 2 3 4]` (format B)                                             | C4 11 12 13 14                                     |
| `[1 2 3 4]` (format C)                                             | 2C 11 12 13 14 3C                                  |
| `[-2 -1 0 1]`                                                      | C4 1E 1F 10 11                                     |
| `"hello"` (format B)                                               | 55 68 65 6C 6C 6F                                  |
| `"hello"` (format C, 2 chunks)                                     | 25 52 68 65 53 6C 6C 6F 35                         |
| `"hello"` (format C, 5 chunks)                                     | 25 52 68 65 52 6C 6C 50 50 51 6F 35                |
| `["hello" there #"world" [] #set{} #t #f]`                         | C7 55 68 65 6C 6C 6F 75 74 68 65 72 65 C0 D0 01 00 |
| `-257`                                                             | 42 FE FF                                           |
| `-1`                                                               | 1F                                                 |
| `0`                                                                | 10                                                 |
| `1`                                                                | 11                                                 |
| `255`                                                              | 42 00 FF                                           |
| `1f`                                                               | 02 3F 80 00 00                                     |
| `1d`                                                               | 03 3F F0 00 00 00 00 00 00                         |
| `-1.202e300d`                                                      | 03 FE 3C B7 B7 59 BF 04 26                         |

Finally, a larger example, using a non-`Symbol` label for a record.[^extensibility2] The `Record`

    ([titled person 2 thing 1]
       101
       "Blackwell"
       (date 1821 2 3)
       "Dr")

encodes to

    B5                              ;; Record, generic, 4+1
      C5                              ;; Sequence, 5
        76 74 69 74 6C 65 64            ;; Symbol, "titled"
        76 70 65 72 73 6F 6E            ;; Symbol, "person"
        12                              ;; SignedInteger, "2"
        75 74 68 69 6E 67               ;; Symbol, "thing"
        11                              ;; SignedInteger, "1"
      41 65                           ;; SignedInteger, "101"
      59 42 6C 61 63 6B 77 65 6C 6C   ;; String, "Blackwell"
      B4                              ;; Record, generic, 3+1
        74 64 61 74 65                  ;; Symbol, "date"
        42 07 1D                        ;; SignedInteger, "1821"
        12                              ;; SignedInteger, "2"
        13                              ;; SignedInteger, "3"
      52 44 72                        ;; String, "Dr"

  [^extensibility2]: It happens to line up with Racket's
    representation of a record label for an inheritance hierarchy
    where `titled` extends `person` extends `thing`:

        (struct date (year month day) #:prefab)
        (struct thing (id) #:prefab)
        (struct person thing (name date-of-birth) #:prefab)
        (struct titled person (title) #:prefab)

## Conventions for Common Data Types

The `Value` data type is essentially an S-Expression, able to
represent semi-structured data over `ByteString`, `String`,
`SignedInteger` atoms and so on.[^why-not-spki-sexps]

  [^why-not-spki-sexps]: Rivest's S-Expressions are in many ways
    similar to Preserves. However, while they include binary data and
    sequences, and an obvious equivalence for them exists, they lack
    numbers *per se* as well as any kind of unordered structure such
    as sets or maps. In addition, while "display hints" allow
    labelling of binary data with an intended interpretation, they
    cannot be attached to any other kind of structure, and the "hint"
    itself can only be a binary blob.

However, users need a wide variety of data types for representing
domain-specific values such as various kinds of encoded and normalized
text, calendrical values, machine words, and so on.

Appropriately-labelled `Record`s denote these domain-specific data
types.[^why-dictionaries]

  [^why-dictionaries]: Given `Record`'s existence, it may seem odd
    that `Dictionary`, `Set`, `Float`, etc. are given special
    treatment. Preserves aims to offer a useful basic equivalence
    predicate to programmers, and so if a data type demands a special
    equivalence predicate, as `Dictionary`, `Set` and `Float` all do,
    then the type should be included in the base language. Otherwise,
    it can be represented as a `Record` and treated separately. Both
    `Boolean` and `String` are seeming exceptions: they merit
    inclusion because of their cultural importance.

All of these conventions are optional. They form a layer atop the core
`Value` structure. Non-domain-specific tools do not in general need to
treat them specially.

**Validity.** Many of the labels we will describe in this section come
  with side-conditions on the contents of labelled `Record`s. It is
  possible to construct an instance of `Value` that violates these
  side-conditions without ceasing to be a `Value` or becoming
  unrepresentable. However, we say that such a `Value` is *invalid*
  because it fails to honour the necessary side-conditions.
  Implementations *SHOULD* allow two modes of working: one which
  treats all `Value`s identically, without regard for side-conditions,
  and one which enforces validity (i.e. side-conditions) when reading,
  writing, or constructing `Value`s.

### MIME-type tagged binary data

Many internet protocols use
[media types](https://tools.ietf.org/html/rfc6838) (a.k.a MIME types)
to indicate the format of some associated binary data. For this
purpose, we define `MIMEData` to be a record labelled `mime` with two
fields, the first being a `Symbol`, the media type, and the second
being a `ByteString`, the binary data.

While each media type may define its own rules for comparing
documents, we define ordering among `MIMEData` *representations* of
such media types following the general rules for ordering of
`Record`s.

**Examples.**

| Value                                      | Encoded hexadecimal byte sequence                                                                                 |
|--------------------------------------------|-------------------------------------------------------------------------------------------------------------------|
| `(mime application/octet-stream #"abcde")` | B3 74 6D 69 6D 65 7F 18 61 70 70 6C 69 63 61 74 69 6F 6E 2F 6F 63 74 65 74 2D 73 74 72 65 61 6D 65 61 62 63 64 65 |
| `(mime text/plain #"ABC")`                 | B3 74 6D 69 6D 65 7A 74 65 78 74 2F 70 6C 61 69 6E 63 41 42 43                                                    |
| `(mime application/xml #"<xhtml/>")`       | B3 74 6D 69 6D 65 7F 0F 61 70 70 6C 69 63 61 74 69 6F 6E 2F 78 6D 6C 68 3C 78 68 74 6D 6C 2F 3E                   |
| `(mime text/csv #"123,234,345")`           | B3 74 6D 69 6D 65 78 74 65 78 74 2F 63 73 76 6B 31 32 33 2C 32 33 34 2C 33 34 35                                  |

Applications making heavy use of `mime` records may choose to use a
short form label number for the record type. For example, if short
form label number 1 were chosen, the second example above, `(mime
text/plain "ABC")`, would be encoded with "92" in place of "B3 74 6D
69 6D 65".

### Unicode normalization forms

Unicode defines multiple
[normalization forms](http://unicode.org/reports/tr15/) for text.
While no particular normalization form is required for `String`s,
users may need to unambiguously signal or require a particular
normalization form. A `NormalizedString` is a `Record` labelled with
`unicode-normalization` and having two fields, the first of which is a
`Symbol` specifying the normalization form used (e.g. `nfc`, `nfd`,
`nfkc`, `nfkd`), and the second of which is a `String` whose
underlying code point representation *MUST* be normalized according to
the named normalization form.

### IRIs (URIs, URLs, URNs, etc.)

An `IRI` is a `Record` labelled with `iri` and having one field, a
`String` which is the IRI itself and which *MUST* be a valid absolute
or relative IRI.

### Machine words

The definition of `SignedInteger` captures all integers. However, in
certain circumstances it can be valuable to assert that a number
inhabits a particular range, such as a fixed-width machine word.

A family of labels `i`*n* and `u`*n* for *n* ∈ {16,32,64} denote
*n*-bit-wide signed and unsigned range restrictions, respectively.
Records with these labels *MUST* have one field, a `SignedInteger`,
which *MUST* fall within the appropriate range. That is, to be valid,
 - in `(i16 `*x*`)`, -32768 <= *x* <= 32767.
 - in `(u16 `*x*`)`, 0 <= *x* <= 65535.
 - in `(i32 `*x*`)`, -2147483648 <= *x* <= 2147483647.
 - etc.

### Anonymous Tuples and Unit

A `Tuple` is a `Record` with label `tuple` and zero or more fields,
denoting an anonymous tuple of values.

The 0-ary tuple, `(tuple)`, denotes the empty tuple, sometimes called
"unit" or "void" (but *not* e.g. JavaScript's "undefined" value).

### Null and Undefined

Tony Hoare's
"[billion-dollar mistake](https://en.wikipedia.org/wiki/Tony_Hoare#Apologies_and_retractions)"
can be represented with the 0-ary `Record` `(null)`. An "undefined"
value can be represented as `(undefined)`.

### Dates and Times

Dates, times, moments, and timestamps can be represented with a
`Record` with label `rfc3339` having a single field, a `String`, which
*MUST* conform to one of the `full-date`, `partial-time`, `full-time`,
or `date-time` productions of
[section 5.6 of RFC 3339](https://tools.ietf.org/html/rfc3339#section-5.6).

## Security Considerations

**Empty chunks.** Streamed (format C) `String`s, `ByteString`s and
`Symbol`s may include chunks of zero length. This opens up a
possibility for denial-of-service: an attacker may begin streaming a
string, sending an endless sequence of zero length chunks, appearing
to make progress but not actually doing so. Implementations may place
optional reasonable restrictions on the number of consecutive empty
chunks that may appear in a stream, and may even supply an optional
mode that rejects empty chunks entirely.

**Canonical form for cryptographic hashing and signing.** As
specified, the encoding rules for `Value`s do not force canonical
serializations for `Set` or `Dictionary` values. Two serializations of
the same `Value` may yield different binary `Repr`s.

## Appendix. Table of lead byte values

     00 - False
     01 - True
     02 - Float
     03 - Double
    (0x)  RESERVED 04-0F
     1x - Small integers 0..12,-3..-1
     2x - Start Stream
     3x - End Stream

     4x - SignedInteger
     5x - String
     6x - ByteString
     7x - Symbol

     8x - short form Record label index 0
     9x - short form Record label index 1
     Ax - short form Record label index 2
     Bx - Record

     Cx - Sequence
     Dx - Set
     Ex - Dictionary
    (Fx)  RESERVED F0-FF

## Appendix. Bit fields within lead byte values

     tt nn mmmm  contents
     ---------- ---------

     00 00 0000  False
     00 00 0001  True
     00 00 0010  Float, 32 bits big-endian binary
     00 00 0011  Double, 64 bits big-endian binary

     00 01 xxxx  Small integers 0..12,-3..-1

     00 10 ttnn  Start Stream <tt,nn>
                   When tt = 00 --> error
                             01 --> each chunk is a <tt,nn> piece
                             1x --> each chunk is a single encoded Value
     00 11 ttnn  End Stream <tt,nn> (must match preceding Start Stream)

     01 00 mmmm  SignedInteger, big-endian binary
     01 01 mmmm  String, UTF-8 binary
     01 10 mmmm  ByteString
     01 11 mmmm  Symbol, UTF-8 binary

     10 00 mmmm  application-specific Record
     10 01 mmmm  application-specific Record
     10 10 mmmm  application-specific Record
     10 11 mmmm  Record

     11 00 mmmm  Sequence
     11 01 mmmm  Set
     11 10 mmmm  Dictionary

     If mmmm = 1111, a varint(m) follows, giving the length, before
     the body; otherwise, m is the length of the body to follow.

## Appendix. Representing Values in Programming Languages

We have given a definition of `Value` and its semantics, and proposed
a concrete syntax for communicating and storing `Value`s. We now turn
to **suggested** representations of `Value`s as *programming-language
values* for various programming languages.

When designing a language mapping, an important consideration is
roundtripping: serialization after deserialization, and vice versa,
should both be identities.

### JavaScript

 - `SignedInteger` ↔ numbers or `BigInt` [[1](https://developers.google.com/web/updates/2018/05/bigint), [2](https://github.com/tc39/proposal-bigint)]
 - `String` ↔ strings
 - `ByteString` ↔ `Uint8Array`
 - `Symbol` ↔ `Symbol.for(...)`
 - `Boolean` ↔ `Boolean`
 - `Float` and `Double` ↔ numbers,
 - `Record` ↔ `{ "_label": theLabel, "_fields": [field0, ..., fieldN] }`, plus convenience accessors
    - `(undefined)` ↔ the undefined value
    - `(rfc3339 F)` ↔ `Date`, if `F` matches the `date-time` RFC 3339 production
 - `Sequence` ↔ `Array`
 - `Set` ↔ `{ "_set": M }` where `M` is a `Map` from the elements of the set to `true`
 - `Dictionary` ↔ a `Map`

### Scheme/Racket

 - `SignedInteger` ↔ exact numbers
 - `String` ↔ strings
 - `ByteString` ↔ byte vector (Racket: "Bytes")
 - `Symbol` ↔ symbols
 - `Boolean` ↔ booleans
 - `Float` and `Double` ↔ inexact numbers (Racket: single- and double-precision floats)
 - `Record` ↔ structures (Racket: prefab struct)
 - `Sequence` ↔ lists
 - `Set` ↔ Racket: sets
 - `Dictionary` ↔ Racket: hash-table

### Java

 - `SignedInteger` ↔ `Integer`, `Long`, `BigInteger`
 - `String` ↔ `String`
 - `ByteString` ↔ `byte[]`
 - `Symbol` ↔ a simple data class wrapping a `String`
 - `Boolean` ↔ `Boolean`
 - `Float` and `Double` ↔ `Float` and `Double`
 - `Record` ↔ in a simple implementation, a generic `Record` class; else perhaps a bean mapping?
 - `Sequence` ↔ an implementation of `java.util.List`
 - `Set` ↔ an implementation of `java.util.Set`
 - `Dictionary` ↔ an implementation of `java.util.Map`

### Erlang

 - `SignedInteger` ↔ integers
 - `String` ↔ tuple of `utf8` and a binary
 - `ByteString` ↔ a binary
 - `Symbol` ↔ the underlying string converted to an Erlang atom, if
   some kind of an "unsafe" mode is set on the decoder (because Erlang
   atoms are not GC'd); otherwise perhaps a tuple of `symbol` and a
   binary of the utf-8
 - `Boolean` ↔ `true` and `false`
 - `Float` and `Double` ↔ floats (unsure how Erlang deals with single-precision)
 - `Record` ↔ a tuple with the label in the first position, and the fields in subsequent positions
 - `Sequence` ↔ a list
 - `Set` ↔ a `sets` set (is this unambiguous? Maybe a [map][erlang-map] from elements to `true`?)
 - `Dictionary` ↔ a [map][erlang-map] (new in Erlang/OTP R17)

## Appendix. Why not Just Use JSON?

<!-- JSON lacks semantics: JSON syntax doesn't denote anything -->

JSON offers *syntax* for numbers, strings, booleans, null, arrays and
string-keyed maps. However, it suffers from two major problems. First,
it offers no *semantics* for the syntax: it is left to each
implementation to determine how to treat each JSON term. This causes
[interoperability](http://seriot.ch/parsing_json.php) and even
[security](http://web.archive.org/web/20180906202559/http://docs.couchdb.org/en/stable/cve/2017-12635.html)
issues. Second, JSON's lack of support for type tags leads to awkward
and incompatible *encodings* of type information in terms of the fixed
suite of constructors on offer.

There are other minor problems with JSON having to do with its syntax.
Examples include its relative verbosity and its lack of support for
binary data.

### JSON syntax doesn't *mean* anything

When are two JSON values the same? When are they different?
<!-- When is one JSON value "less than" another? -->

The specifications are largely silent on these questions. Different
JSON implementations give different answers.

Specifically, JSON does not:

 - assign any meaning to numbers,[^meaning-ieee-double]
 - determine how strings are to be compared,[^string-key-comparison]
 - determine whether object key ordering is significant,[^json-member-ordering] or
 - determine whether duplicate object keys are permitted, what it
   would mean if they were, or how to determine a duplicate in the
   first place.[^json-key-uniqueness]

In short, JSON syntax doesn't *denote* anything.[^xml-infoset] [^other-formats]

  [^meaning-ieee-double]:
    [Section 6 of RFC 7159](https://tools.ietf.org/html/rfc7159#section-6)
    does go so far as to indicate “good interoperability can be
    achieved” by imagining that parsers are able reliably to
    understand the syntax of numbers as denoting an IEEE 754
    double-precision floating-point value.

  [^string-key-comparison]:
    [Section 8.3 of RFC 7159](https://tools.ietf.org/html/rfc7159#section-8.3)
    suggests that *if* an implementation compares strings used as
    object keys “code unit by code unit”, then it will interoperate
    with *other such implementations*, but neither requires this
    behaviour nor discusses comparisons of strings used in other
    contexts.

  [^json-member-ordering]:
    [Section 4 of RFC 7159](https://tools.ietf.org/html/rfc7159#section-4)
    remarks that “[implementations] differ as to whether or not they
    make the ordering of object members visible to calling software.”

  [^json-key-uniqueness]:
    [Section 4 of RFC 7159](https://tools.ietf.org/html/rfc7159#section-4)
    is the only place in the specification that mentions the issue. It
    explicitly sanctions implementations supporting duplicate keys,
    noting only that “when the names within an object are not unique,
    the behavior of software that receives such an object is
    unpredictable.” Implementations are free to choose any behaviour
    at all in this situation, including signalling an error, or
    discarding all but one of a set of duplicates.

  [^xml-infoset]: The XML world has the concept of
    [XML infoset](https://www.w3.org/TR/xml-infoset/). Loosely
    speaking, XML infoset is the *denotation* of an XML document; the
    *meaning* of the document.

  [^other-formats]: Most other recent data languages are like JSON in
    specifying only a syntax with no associated semantics. While some
    do make a sketch of a semantics, the result is often
    underspecified (e.g. in terms of how strings are to be compared),
    overly machine-oriented (e.g. treating 32-bit integers as
    fundamentally distinct from 64-bit integers and from
    floating-point numbers), overly fine (e.g. giving visibility to
    the order in which map entries are written), or all three.

Some examples:

 - are the JSON values `1`, `1.0`, and `1e0` the same or different?
 - are the JSON values `1.0` and `1.0000000000000001` the same or different?
 - are the JSON strings `"päron"` (UTF-8 `70c3a4726f6e`) and `"päron"`
   (UTF-8 `7061cc88726f6e`) the same or different?
 - are the JSON objects `{"a":1, "b":2}` and `{"b":2, "a":1}` the same
   or different?
 - which, if any, of `{"a":1, "a":2}`, `{"a":1}` and `{"a":2}` are the
   same? Are all three legal?
 - are `{"päron":1}` and `{"päron":1}` the same or different?

### JSON can multiply nicely, but it can't add very well

JSON includes a fixed set of types: numbers, strings, booleans, null,
arrays and string-keyed maps. Domain-specific data must be *encoded*
into these types. For example, dates and email addresses are often
represented as strings with an implicit internal structure.

There is no convention for *labelling* a value as belonging to a
particular category. This makes it difficult to extract, say, all
email addresses, or all URLs, from an arbitrary JSON document.

Instead, JSON-encoded data are often labelled in an ad-hoc way.
Multiple incompatible approaches exist. For example, a "money"
structure containing a `currency` field and an `amount` may be
represented in any number of ways:

    { "_type": "money", "currency": "EUR", "amount": 10 }
    { "type": "money", "value": { "currency": "EUR", "amount": 10 } }
    [ "money", { "currency": "EUR", "amount": 10 } ]
    { "@money": { "currency": "EUR", "amount": 10 } }

This causes particular problems when JSON is used to represent *sum*
or *union* types, such as "either a value or an error, but not both".
Again, multiple incompatible approaches exist.

For example, imagine an API for depositing money in an account. The
response might be either a "success" response indicating the new
balance, or one of a set of possible errors.

Sometimes, a *pair* of values is used, with `null` marking the option
not taken.[^interesting-failure-mode]

    { "ok": { "balance": 210 }, "error": null }
    { "ok": null, "error": "Unauthorized" }

  [^interesting-failure-mode]: What is the meaning of a document where
    both `ok` and `error` are non-null? What might happen when a
    program is presented with such a document?

The branch not chosen is sometimes present, sometimes omitted as if it
were an optional field:

    { "ok": { "balance": 210 } }
    { "error": "Unauthorized" }

Sometimes, an array of a label and a value is used:

    [ "ok", { "balance": 210 } ]
    [ "error", "Unauthorized" ]

Sometimes, the shape of the data is sufficient to distinguish among
the alternatives, and the label is left implicit:

    { "balance": 210 }
    "Unauthorized"

JSON itself does not offer any guidance for which of these options to
choose. In many real cases on the web, poor choices have led to
encodings that are irrecoverably ambiguous.

# Open questions

Q. Should "symbols" instead be URIs? Relative, usually; relative to
what? Some domain-specific base URI?

Q. Are the language mappings reasonable? How about one for Python?

Q. Literal small integers: are they pulling their weight? They're not
absolutely necessary. They mess up the connection between
value-ordering and repr-ordering!

## Notes