From e65f5b2410330220d2b136f9ba8c4e86bd5a4dfc Mon Sep 17 00:00:00 2001
From: Marshall Lochbaum <mwlochbaum@gmail.com>
Date: Mon, 7 Sep 2020 08:39:42 -0400
Subject: Don't require inverses for derived functions that happen to be
 constant

---
 docs/spec/inferred.html | 13 ++++---------
 spec/inferred.md        |  9 ++++-----
 2 files changed, 8 insertions(+), 14 deletions(-)

diff --git a/docs/spec/inferred.html b/docs/spec/inferred.html
index ee325c5b..401a0e60 100644
--- a/docs/spec/inferred.html
+++ b/docs/spec/inferred.html
@@ -187,7 +187,7 @@
 </tbody>
 </table>
 <h3 id="required-modifiers">Required modifiers</h3>
-<p>The following cases of Self/Swap must be supported. In the table below, a number (n) in parentheses indicates that the function in question is equivalent to the constant function <code><span class='Value'>n</span><span class='Modifier'>˙</span></code>, and should be inverted accordingly (check that the argument matches <code><span class='Value'>n</span></code>, then return it).</p>
+<p>The following cases of Self/Swap must be supported.</p>
 <table>
 <thead>
 <tr>
@@ -204,7 +204,7 @@
 </tr>
 <tr>
 <td><code><span class='Function'>-</span><span class='Modifier'>˜</span></code></td>
-<td>(0)</td>
+<td></td>
 <td><code><span class='Function'>+</span></code></td>
 </tr>
 <tr>
@@ -214,7 +214,7 @@
 </tr>
 <tr>
 <td><code><span class='Function'>÷</span><span class='Modifier'>˜</span></code></td>
-<td>(1)</td>
+<td></td>
 <td><code><span class='Function'>×</span></code></td>
 </tr>
 <tr>
@@ -239,7 +239,7 @@
 </tr>
 <tr>
 <td><code><span class='Function'>¬</span><span class='Modifier'>˜</span></code></td>
-<td>(1)</td>
+<td></td>
 <td><code><span class='Function'>+-</span><span class='Number'>1</span><span class='Modifier'>˙</span></code></td>
 </tr>
 </tbody>
@@ -255,11 +255,6 @@
 </thead>
 <tbody>
 <tr>
-<td><code><span class='Modifier'>˙</span></code></td>
-<td><code><span class='Brace'>{</span><span class='Value'>𝕗</span><span class='Function'>⊢</span><span class='Modifier'>⁼</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code></td>
-<td></td>
-</tr>
-<tr>
 <td><code><span class='Modifier'>¨</span></code></td>
 <td><code><span class='Brace'>{</span><span class='Function'>!</span><span class='Number'>0</span><span class='Function'>&lt;≡</span><span class='Value'>𝕩</span><span class='Separator'>⋄</span><span class='Value'>𝕨</span><span class='Function'>𝔽</span><span class='Modifier'>⁼¨</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code></td>
 <td></td>
diff --git a/spec/inferred.md b/spec/inferred.md
index 79bbcac3..058710e5 100644
--- a/spec/inferred.md
+++ b/spec/inferred.md
@@ -66,25 +66,24 @@ Several primitives are easily undone, but doing so is not important for BQN prog
 
 ### Required modifiers
 
-The following cases of Self/Swap must be supported. In the table below, a number (n) in parentheses indicates that the function in question is equivalent to the constant function `n˙`, and should be inverted accordingly (check that the argument matches `n`, then return it).
+The following cases of Self/Swap must be supported.
 
 | Fn   | 1     | 2
 |------|-------|-------
 | `+˜` | `÷⟜2` | `+⁼`
-| `-˜` | (0)   | `+`
+| `-˜` |       | `+`
 | `ט` | `√`   | `×⁼`
-| `÷˜` | (1)   | `×`
+| `÷˜` |       | `×`
 | `⋆˜` |       | `√`
 | `√˜` |       | `÷⋆⁼`
 | `∧˜` | `√`   | `∧⁼`
 | `∨˜` | `√⌾¬` | `∨⁼`
-| `¬˜` | (1)   | `+-1˙`
+| `¬˜` |       | `+-1˙`
 
 Inverses of other modifiers and derived functions or modifiers obtained from them are given below. Here the "inverse" of a modifier is another modifier that, if applied to the same operands as the original operator, gives its inverse function. A constant is either a data value or `𝔽˙` for an arbitrary value `𝔽`.
 
 | Mod     | Inverse              | Requirements
 |---------|----------------------|--------------
-| `˙`     | `{𝕗⊢⁼𝕩}`             |
 | `¨`     | `{!0<≡𝕩⋄𝕨𝔽⁼¨𝕩}`      |
 | `⌜`     | `{!0<≡𝕩⋄ 𝔽⁼⌜𝕩;}`     | Monadic case only
 | `˘`     | `{!0<=𝕩⋄𝕨𝔽⁼˘𝕩}`      |
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