From 46ff6e3b81d398a25e7a5992ced8cebb2ad05433 Mon Sep 17 00:00:00 2001
From: Marshall Lochbaum <mwlochbaum@gmail.com>
Date: Fri, 5 Nov 2021 19:51:40 -0400
Subject: Extend reference implementation for Join to allow omitted axes

---
 spec/reference.bqn  | 17 +++++++++--------
 test/cases/prim.bqn |  4 ++--
 2 files changed, 11 insertions(+), 10 deletions(-)

diff --git a/spec/reference.bqn b/spec/reference.bqn
index 56ee7318..8d872dad 100644
--- a/spec/reference.bqn
+++ b/spec/reference.bqn
@@ -378,16 +378,17 @@ Replicate ← {0<=𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep𝕩}
 { Identity ↩ 𝕨˙⊸=◶Identity‿𝕩 }´¨ ⟨ ∨‿0 , ∧‿1 ⟩
 
 Join←(0<=)◶{!IsArray𝕩⋄>𝕩}‿{
-  C←(<⟨⟩)⥊⊸∾⌜´⊢  # Cartesian array product
   ! IsArray 𝕩
   s←≢¨𝕩
-  d←≠⊑s
-  ! ∧´⥊d=≠¨s
-  ! d≥=𝕩
-  l←(≢𝕩){(𝕩⊑⟜≢a⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=a←𝕩
-  ! (r↑¨s)≡C l
-  i←C{p←+´¨↑𝕩⋄(↕⊑⌽p)-𝕩/¯1↓p}¨l
-  >i<¨⊸⊏¨l/𝕩
+  a←(≢𝕩){(s⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=𝕩
+  h←(¬⟜(⌈´)≠¨)¨a
+  ! ∧´∧´¨0≤h
+  o←+`⊑¨h
+  t←(¯1⊑o)↓⊑s
+  l←h{𝕎𝕩}¨˜(»o){⊣◶⟨1,𝕨⊸⊑⟩¨⟜𝕩}¨a
+  ! s≡(<t)∾⌜´h⥊¨¨l
+  i←(<⟨⟩)∾⌜´h{((↕¯1⊸⊑)-𝕩/𝕨⥊¨»)+`𝕩}¨l
+  >i<¨⊸⊏⍟(0<≠∘⊣)¨l/𝕩
 }⍟(0<≠∘⥊)
 
 Group←{
diff --git a/test/cases/prim.bqn b/test/cases/prim.bqn
index 697507d1..2858d989 100644
--- a/test/cases/prim.bqn
+++ b/test/cases/prim.bqn
@@ -419,11 +419,11 @@
 (∾´≡∾)"ab"‿"cde"‿""
 ! % ∾"abc"
 ! % ∾≍"ab"‿"cde"‿""
-! % ∾"ab"‿'c'‿""
+"abc"≡∾"ab"‿'c'‿""
 1‿2‿3‿4‿6‿9≡∾(⊢×≠↑↓)1+↕3
 (≡⟜∾∧≡⟜(∾<))<4
 ⟨1‿4,⥊2⟩((∾⋆⌜⌜)≡⋆⌜○∾)⟨2‿3‿4,⟨⟩,⥊5⟩
-! % ∾⟨2‿3,3,3‿3⟩⥊¨0
+(6‿3⥊0)≡∾⟨2‿3,3,3‿3⟩⥊¨0
 ! % ∾⟨2‿3,1‿3,2‿2⟩⥊¨0
 "abcd"≡"abc"∾'d'
 "abcd"≡"abc"∾<'d'
-- 
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