From 960c96cd2e7cf5bcf1adf97e677bbda911313b7a Mon Sep 17 00:00:00 2001
From: Marshall Lochbaum <mwlochbaum@gmail.com>
Date: Sat, 6 Nov 2021 22:18:36 -0400
Subject: Specify Join of empty using fills

---
 spec/reference.bqn | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

(limited to 'spec/reference.bqn')

diff --git a/spec/reference.bqn b/spec/reference.bqn
index 8d872dad..d3f84ec9 100644
--- a/spec/reference.bqn
+++ b/spec/reference.bqn
@@ -377,7 +377,9 @@ Replicate ← {0<=𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep𝕩}
 
 { Identity ↩ 𝕨˙⊸=◶Identity‿𝕩 }´¨ ⟨ ∨‿0 , ∧‿1 ⟩
 
-Join←(0<=)◶{!IsArray𝕩⋄>𝕩}‿{
+JoinEmpty ← ({!𝕨≤○≠𝕩⋄𝕨≠⊸((𝕨×≠⊸↑)∾↓)𝕩}○≢⥊⊢)⟜Fill
+
+Join←(0<≠∘⥊)◶⟨JoinEmpty, (0<=)◶{!IsArray𝕩⋄>𝕩}‿{
   ! IsArray 𝕩
   s←≢¨𝕩
   a←(≢𝕩){(s⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=𝕩
@@ -389,7 +391,7 @@ Join←(0<=)◶{!IsArray𝕩⋄>𝕩}‿{
   ! s≡(<t)∾⌜´h⥊¨¨l
   i←(<⟨⟩)∾⌜´h{((↕¯1⊸⊑)-𝕩/𝕨⥊¨»)+`𝕩}¨l
   >i<¨⊸⊏⍟(0<≠∘⊣)¨l/𝕩
-}⍟(0<≠∘⥊)
+}⟩
 
 Group←{
   ! IsArray 𝕩
-- 
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