From c18e9dd1fe170d2ae8e620f04f98df049594d10d Mon Sep 17 00:00:00 2001
From: Tony Garnock-Jones <tonyg@leastfixedpoint.com>
Date: Tue, 31 Oct 2023 18:06:05 +0100
Subject: [PATCH] Tweaks

---
 preserves-expressions.md | 73 ++++++++++++++++++++++++++--------------
 preserves.css            |  6 ++++
 2 files changed, 53 insertions(+), 26 deletions(-)

diff --git a/preserves-expressions.md b/preserves-expressions.md
index 2adf01e..7901621 100644
--- a/preserves-expressions.md
+++ b/preserves-expressions.md
@@ -67,25 +67,61 @@ documents to directly comprise a sequence of multiple values.
 No changes to [the Preserves semantic model](preserves.html) are made.
 Every Preserves text-syntax term is a valid P-expression, but in general
 P-expressions must be rewritten or otherwise interpreted before a
-meaningful Preserves value can be arrived at.
+meaningful Preserves value can be arrived at ([see
+below](#reading-preserves)).
 
-## Encoding P-expressions as Preserves
+## <a id="encoding-pexprs"></a>Encoding P-expressions as Preserves
+
+We write ⌜*p*⌝ for the encoding into Preserves of P-expression *p*.
+
+{:.pseudocode.equations}
+| ⌜·⌝ | : | **P-expression** ⟶ **Preserves** |
 
 Aside from the special classes `Group`, `Block`, `Comma`, `Semicolon` or
-`Colons`, P-expressions are directly encodable as Preserves data. All
-members of the special classes are encoded as Preserves text
-`Dictionary`[^encoding-rationale] values:
+`Colons`, P-expressions are encoded directly as Preserves data.
+
+{:.pseudocode.equations}
+| ⌜`[`*p* ...`]`⌝  | = | `[`⌜*p*⌝ ...`]`             |
+| ⌜`<`*p* ...`>`⌝  | = | `<`⌜*p*⌝ ...`>`             |
+| ⌜`#{`*p* ...`}`⌝ | = | `#{`⌜*p*⌝ ...`}`            |
+| ⌜`#!`*p*⌝        | = | `#!`⌜*p*⌝                   |
+| ⌜`@`*p* *q*⌝     | = | `@`⌜*p*⌝ ⌜*q*⌝              |
+| ⌜*p*⌝            | = | *p* **when** *p* ∈ **Atom** |
+
+All members of the special classes are encoded as Preserves text
+`Dictionary`[^encoding-rationale] values.
 
 [^encoding-rationale]: In principle, it would be nice to use *records*
     for this purpose, but if we did so we would have to also encode
     usages of records!
 
-{:.pseudocode}
-> ⌜`(`*p* ...`)`⌝ ⟶ `{g:[`⌜*p*⌝ ...`]}`
-> ⌜`{`*p* ...`}`⌝ ⟶ `{b:[`⌜*p*⌝ ...`]}`
-> ⌜`,`⌝ ⟶ `{s:|,|}`
-> ⌜`;`⌝ ⟶ `{s:|;|}`
-> ⌜`:` ...⌝ ⟶ `{s:|:` ...`|}`
+{:.pseudocode.equations}
+| ⌜`(`*p* ...`)`⌝ | = | `{g:[`⌜*p*⌝ ...`]}` |
+| ⌜`{`*p* ...`}`⌝ | = | `{b:[`⌜*p*⌝ ...`]}` |
+| ⌜`,`⌝           | = | `{s:|,|}`           |
+| ⌜`;`⌝           | = | `{s:|;|}`           |
+| ⌜`:` ...⌝       | = | `{s:|:` ...`|}`     |
+
+## <a id="reading-preserves"></a>Interpreting P-expressions as Preserves
+
+The [previous section](#encoding-pexprs) discussed ways of representing
+P-expressions using Preserves. Here, we discuss *interpreting*
+P-expressions *as* Preserves, so that (1) a Preserves datum (2) written
+using Preserves text syntax and then (3) read as a P-expression can be
+(4) interpreted from that P-expression to yield the original datum.
+
+A reader for P-expressions can be adapted to yield a reader for
+Preserves terms by processing (subterms of) each P-expression that the
+reader produces. The only subterms that need processing are the special
+classes mentioned above.
+
+ 1. Every `Group` or `Semicolon` that appears is an error.
+ 2. Every `Colons` with two or more colons in it is an error.
+ 3. Every `Comma` that appears is removed from its container.
+ 4. Every `Block` must contain triplets of `Value`, `Colons` (with a
+    single colon), `Value`. Any `Block` not following this pattern is an
+    error. Each `Block` following the pattern is translated to a
+    `Dictionary` containing a key/value pair for each triplet.
 
 ## Appendix: Examples
 
@@ -146,21 +182,6 @@ text-syntax encodings.
   ]}
 ```
 
-## Appendix: Using a P-expression reader to read Preserves
-
-A reader for P-expressions can be adapted to yield a reader for
-Preserves terms by processing (subterms of) each P-expression that the
-reader produces. The only subterms that need processing are the special
-classes mentioned above.
-
- 1. Every `Group` or `Semicolon` that appears is an error.
- 2. Every `Colons` with two or more colons in it is an error.
- 3. Every `Comma` that appears is removed from its container.
- 4. Every `Block` must contain triplets of `Value`, `Colons` (with a
-    single colon), `Value`. Any `Block` not following this pattern is an
-    error. Each `Block` following the pattern is translated to a
-    `Dictionary` containing a key/value pair for each triplet.
-
 ## Appendix: Reading vs. Parsing
 
 Lisp systems first *read* streams of bytes into S-expressions and then
diff --git a/preserves.css b/preserves.css
index 9c34209..7322cc7 100644
--- a/preserves.css
+++ b/preserves.css
@@ -1,6 +1,7 @@
 :root {
     --sans-font: "Open Sans", -apple-system, BlinkMacSystemFont, avenir next, avenir, segoe ui, helvetica neue, helvetica, Cantarell, Ubuntu, roboto, noto, arial, sans-serif;
     --serif-font: palatino, "Palatino Linotype", "Palatino LT STD", "URW Palladio L", "TeX Gyre Pagella", serif;
+    --blockquote-indent: 40px;
 }
 body {
     font-family: var(--serif-font);
@@ -230,6 +231,7 @@ table.postcard-grammar {
 blockquote {
     padding: 0.5rem 1rem;
     border-left: solid #4f81bd 2px;
+    margin-left: var(--blockquote-indent);
     margin-right: 0;
 }
 blockquote :first-child {
@@ -243,6 +245,10 @@ blockquote :last-child {
     background-color: #e9f0f9;
 }
 
+table.equations { width: auto; margin-left: var(--blockquote-indent); }
+table.equations tr > *:nth-child(1) { text-align: right; }
+table.equations tr > *:nth-child(2) { text-align: center; }
+
 blockquote.pseudocode {
     border-left: none;
     padding: 0;