Test layer 6 structural and search functions

3 files changed, 99 insertions, 60 deletions

diff --git a/spec/dzref b/spec/dzref
index 6034fa78..db98ef89 100755
--- a/spec/dzref
+++ b/spec/dzref
@@ -64,20 +64,7 @@ _perv←{ ⍝ Pervasion
 Int←IsArray◶⟨⌊⊸=,0⟩
 Nat←IsArray◶⟨0⊸≤∧⌊⊸=,0⟩
 
-Pick1←{
-  ! 1=≠≢𝕨
-  ! 𝕨=○≠s←≢𝕩
-  ! ∧´Int¨𝕨
-  ! ∧´𝕨(≥⟜-∧<)s
-  𝕨↩𝕨+s×𝕨<0
-  (⥊𝕩)⊑˜0(⊑⟜𝕨+⊑⟜s×⊢)´-↕⊸¬≠𝕨
-}
-Pickd←(0∨´⟜⥊IsArray¨∘⊣)◶Pick1‿{Pickd⟜𝕩¨𝕨}
-Pick←IsArray◶⥊‿⊢⊸Pickd
-
 Depth←IsArray◶0‿{1+0⌈´Depth¨⥊𝕩}
-
-⊑ ↩ (0¨∘≢)⊸Pick    ⊘ Pick
 ≡ ← Depth          ⊘ ≡
 
 
@@ -223,11 +210,11 @@ Join←{
   C←(<⟨⟩)⥊⊸∾⌜´⊢  ⍝ Cartesian array product
   ! IsArray 𝕩
   s←≢¨𝕩
-  c←≠⊑s
-  ! ∧´c=≠¨s
-  ! c≥≠≢𝕩
-  l←(≢𝕩){(𝕩⊑a⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕≠≢a←𝕩
-  ! s≡C l
+  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
 }⍟(0<≠∘⥊)
@@ -238,43 +225,47 @@ Group←{
   l←(1<≡)◶Chk‿{!1=≠≢𝕩⋄Chk¨𝕩}𝕨
   ! l≤○≠≢𝕩
   ! ∧´l=l≠⊸↑≢𝕩
-  (𝕨⊸=/𝕩˜)¨↕1+0⌈´⚇1𝕨
+  (𝕨⊸=/𝕩˜)¨↕1+¯1⌈´⚇1𝕨
 }
 
-ReorderAxes←{
-  𝕩↩<⍟(0=≡)𝕩
-  ! 𝕨≤○≠≢𝕩
-  r←(≠≢𝕩)-+´¬∊𝕨
-  ! ∧´𝕨<r
-  𝕨↩𝕨∾𝕨(¬∘∊˜/⊢)↕r
-  (𝕨⊸⊏⊑𝕩˜)¨↕1×´¨𝕨⊔≢𝕩
-}
-Transpose←(≠∘≢-1˜)⊸ReorderAxes⍟(0<≠∘≢)
-
 ∾ ↩ Join           ⊘ JoinTo
-⊔ ← ⊔⟜(↕∘≠⚇1)      ⊘ Group
-⍉ ← Transpose      ⊘ ReorderAxes
+⊔ ← Group⟜(↕≠⚇1)   ⊘ Group
 
 ⍝ Searching
 IndexOf←{
   c←1-˜≠≢𝕨
   ! 0≤c
-  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,((+´<˘)∧`)≢⎉c⎉∞‿c⟩ 𝕩
+  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,((+´<˘)∧`)≢⎉c⎉c‿∞⟩ 𝕩
 }
 UniqueMask←{
   ! 1≤≠≢𝕩
   u←0↑𝕩
-  {𝕩∊u}⊘{u↩u∾𝕩⋄1}‿0˘𝕩
+  {(≠u)>⊑u IndexOf 𝕩}◶{u↩u∾𝕩⋄1}‿0˘𝕩
 }
 Find←{
   r←≠s←≢𝕨
-  𝕨≡⎉r s↕⎉r 𝕩
+  ! r≤≠≢𝕩
+  𝕨 ≡⎉r s ↕⎉r 𝕩
 }
 
 ⊐ ← !∘0            ⊘ IndexOf
 ∊ ← UniqueMask     ⊘ (⊐˜<≠∘⊢)
 ⍷ ← ∊⊸/            ⊘ Find
 
+ReorderAxes←{
+  𝕩↩<⍟(0=≡)𝕩
+  ! 1≥≠≢𝕨
+  𝕨↩⥊𝕨
+  ! 𝕨≤○≠≢𝕩
+  ! ∧´Nat¨⥊𝕨
+  r←(≠≢𝕩)-+´¬∊𝕨
+  ! ∧´𝕨<r
+  𝕨↩𝕨∾𝕨(¬∘∊˜/⊢)↕r
+  (𝕨⊸⊏⊑𝕩˜)¨↕⌊´¨𝕨⊔≢𝕩
+}
+Transpose←(≠∘≢-1˜)⊸ReorderAxes⍟(0<≠∘≢)
+⍉ ← Transpose      ⊘ ReorderAxes
+
 ⍝ Sorting
 Cmp ← ∨○IsArray◶{ ⍝ No arrays
   𝕨(>-<)𝕩 ⍝ Assume they're numbers
@@ -292,7 +283,7 @@ Cmp ← ∨○IsArray◶{ ⍝ No arrays
 
 _grade←{
   ! 1≤≠≢𝕩
-  i⊐+´˘(𝔽⎉∞‿¯1⎉¯1‿∞˜𝕩)(⌈⟜0+=⟜0⊸×)>⌜˜i←↕≠𝕩
+  i⊐˜+´˘(𝔽⎉∞‿¯1⎉¯1‿∞˜𝕩)(⌈⟜0+=⟜0⊸×)>⌜˜i←↕≠𝕩
 }
 _bins←{
   r←1-˜≠≢𝕨
@@ -314,7 +305,7 @@ ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩}
 
 {
   chrs←⟨
-    "!√∧∨|≡∾↑↓↕⌽⍉/⍋⍒⊏⊑⊐⊒∊⍷⊔"
+    "!√∧∨|≡∾↑↓↕⌽⍉/⍋⍒⊏⊐⊒∊⍷⊔"
     "˘¨⌜´`"
     "⎉⚇⍟◶"
   ⟩
@@ -345,7 +336,6 @@ ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩}
   ⍎"Type    ← ⟨⟩⥊0⊸⥊"
 
   '!' Mod "{𝕩 ⋄ ≤1}⍟¬"
-  '⊑' Mod "⊑"
   '↕' Mod "↕"
   '≡' Mod "≡"
 
diff --git a/spec/reference.bqn b/spec/reference.bqn
index 9c82cda1..241be28a 100644
--- a/spec/reference.bqn
+++ b/spec/reference.bqn
@@ -317,7 +317,7 @@ Replicate ← {0<≠≢𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep
 ⍝ LAYER 6: Everything else
 
 ∾ ↩ Join           ⊘ JoinTo
-⊔ ← ⊔⟜(↕∘≠⚇1)      ⊘ Group
+⊔ ← ⊔⟜(↕≠⚇1)       ⊘ Group
 ⍉ ← Transpose      ⊘ ReorderAxes
 ⊐ ← !∘0            ⊘ IndexOf
 ∊ ← UniqueMask     ⊘ (⊐˜<≠∘⊢)
@@ -332,11 +332,11 @@ Join←{
   C←(<⟨⟩)⥊⊸∾⌜´⊢  ⍝ Cartesian array product
   ! IsArray 𝕩
   s←≢¨𝕩
-  c←≠⊑s
-  ! ∧´c=≠¨s
-  ! c≥≠≢𝕩
-  l←(≢𝕩){(𝕩⊑a⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕≠≢a←𝕩
-  ! s≡C l
+  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
 }⍟(0<≠∘⥊)
@@ -347,35 +347,39 @@ Group←{
   l←(1<≡)◶Chk‿{!1=≠≢𝕩⋄Chk¨𝕩}𝕨
   ! l≤○≠≢𝕩
   ! ∧´l=l≠⊸↑≢𝕩
-  (𝕨⊸=/𝕩˜)¨↕1+0⌈´⚇1𝕨
+  (𝕨⊸=/𝕩˜)¨↕1+¯1⌈´⚇1𝕨
 }
 
-ReorderAxes←{
-  𝕩↩<⍟(0=≡)𝕩
-  ! 𝕨≤○≠≢𝕩
-  r←(≠≢𝕩)-+´¬∊𝕨
-  ! ∧´𝕨<r
-  𝕨↩𝕨∾𝕨(¬∘∊˜/⊢)↕r
-  (𝕨⊸⊏⊑𝕩˜)¨↕×´¨𝕨⊔≢𝕩
-}
-Transpose←(≠∘≢-1˜)⊸ReorderAxes⍟(0<≠∘≢)
-
 ⍝ Searching
 IndexOf←{
   c←1-˜≠≢𝕨
   ! 0≤c
-  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,((+´<˘)∧`)≢⎉c⎉∞‿c⟩ 𝕩
+  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,((+´<˘)∧`)≢⎉c⎉c‿∞⟩ 𝕩
 }
 UniqueMask←{
   ! 1≤≠≢𝕩
   u←0↑𝕩
-  {𝕩∊u}⊘{u↩u∾𝕩⋄1}‿0˘𝕩
+  {⊑𝕩∊u}⊘{u↩u∾𝕩⋄1}‿0˘𝕩
 }
 Find←{
   r←≠s←≢𝕨
-  𝕨≡⎉r s↕⎉r 𝕩
+  ! r≤≠≢𝕩
+  𝕨 ≡⎉r s ↕⎉r 𝕩
 }
 
+ReorderAxes←{
+  𝕩↩<⍟(0=≡)𝕩
+  ! 1≥≠≢𝕨
+  𝕨↩⥊𝕨
+  ! 𝕨≤○≠≢𝕩
+  ! ∧´Nat¨⥊𝕨
+  r←(≠≢𝕩)-+´¬∊𝕨
+  ! ∧´𝕨<r
+  𝕨↩𝕨∾𝕨(¬∘∊˜/⊢)↕r
+  (𝕨⊸⊏⊑𝕩˜)¨↕⌊´¨𝕨⊔≢𝕩
+}
+Transpose←(≠∘≢-1˜)⊸ReorderAxes⍟(0<≠∘≢)
+
 ⍝ Sorting
 Cmp ← ∨○IsArray◶{ ⍝ No arrays
   𝕨(>-<)𝕩 ⍝ Assume they're numbers
@@ -393,7 +397,7 @@ Cmp ← ∨○IsArray◶{ ⍝ No arrays
 
 _grade←{
   ! 1≤≠≢𝕩
-  i⊐+´˘(𝔽⎉∞‿¯1⎉¯1‿∞˜𝕩)(⌈⟜0+=⟜0⊸×)>⌜˜i←↕≠𝕩
+  i⊐˜+´˘(𝔽⎉∞‿¯1⎉¯1‿∞˜𝕩)(⌈⟜0+=⟜0⊸×)>⌜˜i←↕≠𝕩
 }
 _bins←{
   r←1-˜≠≢𝕨
diff --git a/test/testref.bqn b/test/testref.bqn
index 62758027..59313beb 100644
--- a/test/testref.bqn
+++ b/test/testref.bqn
@@ -1,8 +1,8 @@
 ⍝ Tests of primitive functionality
 ⍝ Ordering matches the reference implementations
 
-•←/¬⟨
-  ⍝ LAYER 0
+•←/¬∾⟨
+⟨ ⍝ LAYER 0
   ⍝ [0,34)
   0≡¯2+2
   1e4≡5e3+5e3
@@ -251,4 +251,49 @@
   3‿3‿3‿2‿2‿1≡/˜3‿2‿1
   (≍1∾¨1‿2‿2)≡(↕¨/↕)2‿3
   ⟨⟩(/≡⊢)≍"ab"
+
+⟩
+⟨ ⍝ LAYER 6
+  ⍝ [230,270)
+  ≡⟜(∾⥊¨)"abc"
+  (∾´≡∾)"ab"‿"cde"‿""
+  1‿2‿3‿4‿6‿9≡∾(⊢×≠↑↓)1+↕3
+  ≡⟜∾⟨⟩
+  ⟨1‿4,⥊2⟩((∾⋆⌜⌜)≡⋆⌜○∾)⟨2‿3‿4,⟨⟩,⥊5⟩
+  "abcd"≡"abc"∾'d'
+  "abcd"≡"abc"∾<'d'
+  (↕4‿3)≡(↕3‿3)∾3∾¨↕3
+  (∾˜≡·¯1⊸(×´∘↓∾↑)∘≢⊸⥊≍˜)2‿3⥊"abcdef"
+  (∾´≡∾)⟨3‿2‿1,0‿2‿1⟩⥊¨<↕6
+  ⟨1‿2,⥊0,⥊3⟩≡⊔1‿0‿0‿2
+  4‿3‿2(≍○<≡·(≠¨≍○<∾)/⊸⊔)"abcdefghi"
+  ⟨⟩≡(3⥊¯1)⊔"abc"
+  (≍˘1‿1‿4<∘⥊⎉1 16‿4+⌜↕4)≡2↓⟨3‿2,¯1‿0‿¯1⟩⊔2‿3‿4⥊↕24
+  ⥊⚇0⊸≡○⊔⟜(⥊<)1‿2‿2‿¯1‿0
+  (⊔≡·≍⍟2∘<·∾⌜´/∘(0⊸=)¨)⟨0‿¯1‿0‿0,¯1‿0‿0⟩
+  2‿0‿4≡"abcd"⊐"cae"
+  ⟨1⟩≡"abcd"⊐"b"
+  (<3)≡⊐⟜(3⊸⊏)"abcd"
+  (5⌊3+↕5)≡⊐⟜(3‿0‿0+⚇1⊢)↕5‿2‿1
+  1‿0‿0‿1≡"acef"∊"adf"
+  (∊⟜(↕2)≡<⟜2)3⋆⌜○↕5
+  (<1)≡3‿4‿5∊4+⌜○↕3
+  ('0'≠"11010001")≡∊"abacbacd"
+  (↑⟜1≡⟜∊⥊⟜∞)9
+  (⥊⟜1≡∊∘↕)6
+  ≡⟜∊⟨⟩
+  ≡○∊⟜(≍˜˘)"abcadbba"
+  ≡⟜⍷⟨⟩
+  "ba"≡⍷"baa"
+  0‿1‿0‿0≡"abc"⍷"aabcba"
+  (0‿1≍0‿0)≡(1‿2≍4‿5)⍷3‿3⥊↕9
+  (⌽¨≡⍉)↕2⥊3
+  ∧´⍉⊸≡¨⟨'a',<'a',"a","abc",""⟩
+  (↕4)(-˜⌜˜≡·⍉-⌜)↕3‿2
+  (2×↕3)≡0‿0⍉6+⌜○↕3
+  ⟨⟩(⍉≡⊢)<4
+  (2‿0‿1⥊⟨⟩)≡1‿2‿0‿1⍉↕↕4
+  2‿0‿3‿1‿4≡⍋"bdace"
+  "edcba"≡∨"bdace"
+⟩
 ⟩