---
title: "Canonical Form for Binary Syntax"
---

  [spec]: preserves.html

When two `Value`s are written down in *canonical form*, comparing
their *syntax* for equivalence gives the same result as comparing them
*semantically* according to the equivalence defined in the
[Preserves specification][spec].[^equivalence-not-ordering]

  [^equivalence-not-ordering]: However, canonical form does *not*
    induce a match between lexicographic ordering on syntax and
    semantic ordering [as specified][spec]. It *only* induces a
    connection between equivalences.

That is, canonical forms are equal if and only if the encoded `Value`s
are equal.

This document specifies canonical form for the Preserves compact
binary syntax.

**General rules.**
Streaming formats ("format C") MUST NOT be used.
Annotations MUST NOT be present.
Placeholders MUST NOT be used.
Where possible, fixed-length ("format A") MUST be used in preference
to variable-length ("format B") formats.

**Signed integers.**
When a `SignedInteger` *n* is greater than or equal to -3 and less
than 13 (i.e. -3≤*n*<13), it MUST be represented using the single-byte
encoding with initial nibble equal to 3.
Otherwise (i.e. when *n*<-3 or *n*≥13), it MUST be represented using
the multi-byte encoding with initial nibble equal to 4, and the
variable-length part must be as short as possible while remaining
unambiguous.[^signed-integer-examples]

  [^signed-integer-examples]: The following examples from
    [the specification][spec] are all in canonical form:

        [[   -257 ]] = 42 FE FF    [[     -3 ]] = 3D       [[    128 ]] = 42 00 80
        [[   -256 ]] = 42 FF 00    [[     -2 ]] = 3E       [[    255 ]] = 42 00 FF
        [[   -255 ]] = 42 FF 01    [[     -1 ]] = 3F       [[    256 ]] = 42 01 00
        [[   -254 ]] = 42 FF 02    [[      0 ]] = 30       [[  32767 ]] = 42 7F FF
        [[   -129 ]] = 42 FF 7F    [[      1 ]] = 31       [[  32768 ]] = 43 00 80 00
        [[   -128 ]] = 41 80       [[     12 ]] = 3C       [[  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


**Sets.**
The elements of a `Set` MUST be serialized sorted in ascending order
following the total order relation defined in the
[Preserves specification][spec].

**Dictionaries.**
The key-value pairs in a `Dictionary` MUST be serialized sorted in
ascending order by key, following the total order relation defined in
the [Preserves specification][spec].

**Other kinds of `Value`.**
There are no special canonicalization restrictions on `String`s,
`ByteString`s, `Symbol`s, `Boolean`s, `Float`s, `Double`s, `Record`s,
or `Sequence`s.

<!-- Heading to visually offset the footnotes from the main document: -->
## Notes