From 71ead5abb7bff04b4ef09547e44fdaf9c52d48bf Mon Sep 17 00:00:00 2001
From: Tony Garnock-Jones <tonyg@leastfixedpoint.com>
Date: Tue, 17 Oct 2023 01:34:21 +0200
Subject: [PATCH] Further small improvements

---
 _includes/cheatsheet-binary.md |  7 ++++---
 preserves-binary.md            | 35 +++++++++++++++-------------------
 2 files changed, 19 insertions(+), 23 deletions(-)

diff --git a/_includes/cheatsheet-binary.md b/_includes/cheatsheet-binary.md
index 35b49c8..9abec85 100644
--- a/_includes/cheatsheet-binary.md
+++ b/_includes/cheatsheet-binary.md
@@ -31,9 +31,10 @@ class="postcard-grammar binarysyntax">*V*</span>.
 | | <span class="outputish">(*n* &amp; 127) &#124; 128</span> **varint**(*n* &gt;&gt; 7) | if *n* ≥ 128
 
 {:.postcard-grammar.binarysyntax}
-**intbytes**(*n*) | = | <span class="roman">(the empty sequence)</span> | if *n* = 0
-| | **signedBigEndian**(*n*) | otherwise
-**signedBigEndian**(*n*) | = | <span class="outputish">*n* &amp; 255</span> | if -128 ≤ *n* ≤ 127
+**intbytes**(*n*) | = | <span class="roman">the empty sequence if</span> *n* = 0<span class="roman">, otherwise</span> **signedBigEndian**(*n*)
+
+{:.postcard-grammar.binarysyntax}
+**signedBigEndian**(*n*) | = | <span class="outputish">*n* &amp; 255</span> | if −128 ≤ *n* ≤ 127
 | | **signedBigEndian**(*n* &gt;&gt; 8) <span class="outputish">*n* &amp; 255</span> | otherwise
 
 The functions <span class="postcard-grammar binarysyntax">**binary32**(*F*)</span> and <span
diff --git a/preserves-binary.md b/preserves-binary.md
index 55fc01f..4790834 100644
--- a/preserves-binary.md
+++ b/preserves-binary.md
@@ -92,17 +92,23 @@ serializing in some other implementation-defined order.
     but encoding and then sorting byte strings is much more likely to
     be within easy reach.
 
-### SignedIntegers.
+### SignedIntegers, Strings, ByteStrings and Symbols.
 
-    «x» = [0xB0] ++ varint(|intbytes(x)|) ++ intbytes(x)  if x ∈ SignedInteger
+    «S» = [0xB0] ++ varint(|intbytes(S)|) ++ intbytes(S)  if S ∈ SignedInteger
+          [0xB1] ++ varint(|utf8(S)|) ++ utf8(S)          if S ∈ String
+          [0xB2] ++ varint(|S|) ++ S                      if S ∈ ByteString
+          [0xB3] ++ varint(|utf8(S)|) ++ utf8(S)          if S ∈ Symbol
 
-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. `intbytes(0)`
-is special-cased to be the empty byte
-sequence;[^empty-intbytes-sequence] otherwise, the most-significant
-bit of the first byte is the sign bit. See the [examples in the
-appendix below](#signedinteger-examples).
+For `String` and `Symbol`, the data following the tag and length is a
+UTF-8 encoding of the `Value`. For `ByteString`, it is the raw data
+contained within the `Value` unmodified. For `SignedInteger`, it is
+the big-endian two's-complement binary representation of the number,
+taking exactly as many whole bytes as needed to unambiguously identify
+the value and its sign. `intbytes(0)` is special-cased to be the empty
+byte sequence;[^empty-intbytes-sequence] otherwise, the
+most-significant bit of the first byte is the sign bit. (See
+[SignedInteger examples](#signedinteger-examples) in the appendix
+below.)
 
   [^empty-intbytes-sequence]: Without the special case of
     `intbytes(0)` yielding the empty byte sequence, no input to
@@ -110,17 +116,6 @@ appendix below](#signedinteger-examples).
     `0` or `-1` could be special-cased to the empty sequence; here, we
     arbitrarily choose `0`.
 
-### Strings, ByteStrings and Symbols.
-
-    «S» = [0xB1] ++ varint(|utf8(S)|) ++ utf8(S)  if S ∈ String
-          [0xB2] ++ varint(|S|) ++ S              if S ∈ ByteString
-          [0xB3] ++ varint(|utf8(S)|) ++ utf8(S)  if S ∈ Symbol
-
-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`, while for `ByteString` it is the raw data contained within the
-`Value` unmodified.
-
 ### Booleans.
 
     «#f» = [0x80]