Move dzref_full implementations to a separate file

2 files changed, 406 insertions, 406 deletions

diff --git a/dzref_full b/dzref_full
index beaf39c2..cccbc58e 100755
--- a/dzref_full
+++ b/dzref_full
@@ -5,411 +5,7 @@
 # BQN runtime; use plain dzref if you just want to run BQN as it's much
 # faster and supports inverses better.
 
-impl ← "◶ ← {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}     # LIMITED to number left operand result
-⊘ ← {𝕨((1{𝔽}𝕨)-0)◶𝔽‿𝔾 𝕩}
-#⊢ ← {𝕩}  # Prevents dyadic negative ⍟
-⊣ ← {𝕩}⊘{𝕨}
-˜ ← {𝕩𝔽𝕨⊣𝕩}
-∘ ← {𝔽𝕨𝔾𝕩}
-○ ← {(𝔾𝕨)𝔽𝔾𝕩}
-⊸ ← {(𝔽𝕨⊣𝕩)𝔾𝕩}
-⟜ ← {(𝕨⊣𝕩)𝔽𝔾𝕩}
-⍟ ← {𝕨((𝕨𝔾𝕩)⊑⊢‿𝕗){𝔽}𝕩}   # LIMITED to boolean right operand result
-
-# LIMITED to numeric arguments for scalar cases
-√ ← ⋆⟜(÷2)   ⊘ (⋆⟜÷˜)
-∧ ←            ×
-∨ ←            (+-×)
-¬ ← 1+-
-< ← {⟨⟩⥊⟨𝕩⟩} ⊘ (¬≤˜)
-> ←            (¬≤)
-≥ ← !∘0      ⊘ (≤˜)
-≢ ↩ IsArray◶⟨⟩‿≢  # LIMITED to monadic case
-Length ← (0<0⊑≢)◶⟨1⋄0⊑⊢⟩∘≢
-≠ ← Length   ⊘ (¬∘=)
-× ↩ 0⊸(<->)  ⊘ ×
-| ← ×⟜×      ⊘ {𝕩-𝕨×⌊𝕩÷𝕨}
-
-_fold←{
-  ! 1==𝕩
-  l←≠v←𝕩 ⋄ F←𝔽
-  r←𝕨 (0<l)◶{𝕩⋄Identity f}‿{l↩l-1⋄l⊑𝕩}⊘⊣ 𝕩
-  {r↩(𝕩⊑v)F r}⌜(l-1)⊸-⌜↕l
-  r
-}
-´ ← _fold
-
-
-#⌜
-# LAYER 2: Pervasion
-# After defining _perv, we apply it to all scalar functions,
-# making them pervasive. I'm not going to write that out.
-
-ToArray ← <⍟(¬IsArray)
-
-∾ ← {k←≠𝕨⋄k⊸≤◶⟨⊑⟜𝕨⋄-⟜k⊑𝕩˜⟩⌜↕k+≠𝕩}  # LIMITED to two vector arguments
-
-_eachd←{
-  _e←{ # 𝕨 has smaller or equal rank
-    k←≠p←≢𝕨 ⋄ q←≢𝕩
-    ! ∧´(⊑⟜p=⊑⟜q)⌜↕k
-    l←×´(q⊑˜k⊸+)⌜↕q≠⊸-k
-    a←⥊𝕨 ⋄ b←⥊𝕩
-    q⥊⥊(≠a) (⊑⟜a𝔽l⊸×⊸+⊑b˜)⌜○↕ l
-  }
-  (>○=)◶⟨𝔽_e⋄𝔽˜_e˜⟩
-}
-
-¨ ↩ {(𝔽⌜)⊘(𝔽_eachd○ToArray)}
-
-_perv←{ # Pervasion
-  (⊢⊘∨○IsArray)◶⟨𝔽⋄𝔽{𝕨𝔽_perv𝕩}¨⟩
-}
-⌊ ↩ ⌊        ⊘ ({(𝕨>𝕩)⊑𝕨‿𝕩} _perv)
-⌈ ← -∘⌊∘-    ⊘ ({(𝕨<𝕩)⊑𝕨‿𝕩} _perv)
-
-identity ← {(0⊑𝕨){𝕗=𝕩}◶𝕩‿(1⊑𝕨)}´ ⟨+‿0,-‿0,×‿1,÷‿1,⋆‿1,√‿1,∧‿1,∨‿0,|‿0,⌊‿∞,⌈‿¯∞,<‿0,≤‿1,=‿1,≥‿1,>‿0,≠‿0,⊑⟨!∘0⟩⟩
-
-
-#⌜
-# LAYER 3: Remove other limits
-# Now all implementations are full except ∾ and ⊑; ↕ is monadic only
-
-Int←IsArray◶⟨⌊⊸=,0⟩
-Nat←IsArray◶⟨0⊸≤∧⌊⊸=,0⟩
-
-Deshape←IsArray◶{⟨𝕩⟩}‿⥊
-Reshape←{
-  ! 1≥=𝕨
-  𝕨↩⥊𝕨
-  ! ∧´Nat¨𝕨
-  l←×´𝕨
-  n←×´≢𝕩
-  𝕨⥊{
-    𝕩(0<n)◶⟨Type⊸(⊣⌜)⋄⥊⊸{⊑⟜𝕨¨n|𝕩}⟩↕l
-  }⍟(l≠n)𝕩
-}⟜ToArray
-⥊ ↩ Deshape        ⊘ Reshape
-
-Range←{
-  I←{!Nat𝕩⋄↕𝕩}
-  M←{!1==𝕩⋄(<⟨⟩)⥊⊸∾⌜´I¨𝕩}
-  IsArray◶I‿M 𝕩
-}
-
-match←{¬∘(0⊑𝕨)◶(1⊑𝕨)‿𝕩}´⟨
-  ⟨≠○IsArray , 0⟩
-  ⟨¬IsArray∘⊢, =⟩
-  ⟨≠○=       , 0⟩
-  ⟨∨´≠○≢     , 0⟩
-  {∧´⥊𝕨Match¨𝕩}
-⟩
-
-Depth←IsArray◶0‿{1+0⌈´Depth¨⥊𝕩}
-
-↕ ↩ Range
-
-≡ ← Depth          ⊘ Match
-≢ ↩ ≢              ⊘ (¬Match)
-
-
-#⌜
-# LAYER 4: Operators
-
-
-DropV← {⊑⟜𝕩¨𝕨+↕𝕨-˜≠𝕩}
-Cell ← DropV⟜≢
-Pair ← {⟨𝕩⟩} ⊘ {⟨𝕨,𝕩⟩}
-
-Merge←{
-  c←≢⊑𝕩
-  ! ∧´⥊(c≡≢)¨𝕩
-  𝕩⊑⟜⥊˜⌜c⥊↕×´c
-}⍟(0<≠∘⥊)
-> ↩ Merge          ⊘ >
-≍ ← >∘Pair
-_ranks ← {⟨2⟩⊘⟨1,0⟩((⊣-1+|)˜⟜≠⊑¨<∘⊢)⥊∘𝔽}
-_depthOp_←{
-  neg←0>n←𝕨𝔾_ranks𝕩 ⋄ F←𝔽
-  _d←{
-    R←(𝕗+neg)_d
-    𝕨(2⥊(neg∧𝕗≥0)∨(0⌈𝕗)≥Pair○≡)◶(⟨R¨⋄R⟜𝕩¨∘⊣⟩≍⟨(𝕨R⊢)¨∘⊢⋄F⟩)𝕩
-  }
-  𝕨 n _d 𝕩
-}
-⚇ ← _depthOp_
-_rankOp_←{
-  k←𝕨(Pair○= (0≤⊢)◶⟨⌊⟜-,0⌈-⟩¨ 𝔾_ranks)𝕩
-  Enc←{
-    f←⊑⟜(≢𝕩)¨↕𝕨
-    c←×´s←𝕨Cell𝕩
-    f⥊⊑⟜(⥊𝕩)¨∘((s⥊↕c)+c×⊢)¨↕×´f
-  }
-  Enc↩(>⟜0+≥⟜=)◶⟨<⊢,Enc,<¨⊢⟩
-  > ((0⊑k)Enc𝕨) 𝔽¨ ((1-˜≠)⊸⊑k)Enc𝕩
-}
-_scan←{
-  ! IsArray 𝕩
-  ! 1≤=𝕩
-  F←𝔽
-  {
-    r←⥊𝕩 ⋄ l←≠𝕩 ⋄ c←×´1 Cell 𝕩
-    {r↩r𝕩_amend˜𝕨F○(⊑⟜r)𝕩}⟜(c⊸+)¨↕c-˜≠r
-    (≢𝕩)⥊r
-  }⍟(0<≠∘⥊)𝕩
-}
-
-` ← _scan
-⎉ ← _rankOp_
-˘ ← ⎉¯1
-_insert←{
-  ! 1≤=𝕩
-  𝕨 𝔽´ <˘𝕩
-}
-˝ ← _insert
-
-
-#⌜
-# LAYER 5: Structural functions
-
-_onAxes_←{
-  F←𝔽
-  (𝔾<≡)∘⊣◶{ # One axis
-    ! 1≤=𝕩
-    𝕨F𝕩
-  }‿{ # Multiple axes
-    ! 1≥=𝕨
-    ! 𝕨≤○≠≢𝕩
-    R←{(0⊑⥊𝕨)F(1 DropV 𝕨)⊸R˘𝕩}⍟{0<≠𝕨}
-    𝕨R𝕩
-  }
-}
-
-SelSub←{
-  ! IsArray 𝕨
-  ! ∧´⥊Int¨ 𝕨
-  ! ∧´⥊ 𝕨 (≥⟜-∧<) ≠𝕩
-  𝕨↩𝕨+(≠𝕩)×𝕨<0
-  𝕨(1≠=∘⊢)◶{
-    ⊑⟜𝕩¨𝕨
-  }‿{
-    c←×´s←1 Cell 𝕩
-    ⊑⟜(⥊𝕩)¨(c×𝕨)+⌜s⥊↕c
-  }𝕩
-}
-Select←ToArray⊸(SelSub _onAxes_ 1)
-⊏ ← 0⊸Select       ⊘ Select
-
-JoinTo←{
-  s←𝕨Pair○≢𝕩
-  a←1⌈´k←≠¨s
-  ! ∧´1≥a-k
-  c←(k¬a)+⟜(↕a-1)⊸⊏¨s
-  ! ≡´c
-  l←+´(a=k)⊣◶1‿(0⊑⊢)¨s
-  (⟨l⟩∾0⊑c)⥊𝕨∾○⥊𝕩
-}
-
-Take←{
-  T←{
-    ! Int 𝕨
-    l←≠𝕩
-    i←(l+1)|¯1⌈l⌊((𝕨<0)×𝕨+l)+↕|𝕨
-    i⊏JoinTo⟜(1⊸Cell⥊Type)⍟(∨´l=i)𝕩
-  }
-  𝕨 T _onAxes_ 0 (⟨1⟩⥊˜0⌈𝕨-○≠⊢)⊸∾∘≢⊸⥊𝕩
-}
-Prefixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Take¨<𝕩}
-↑ ← Prefixes       ⊘ Take
-Drop←{
-  s←(≠𝕨)(⊣↑⊢∾˜1⥊˜0⌈-⟜≠)≢𝕩
-  ((sׯ1⋆𝕨>0)+(-s)⌈s⌊𝕨)↑𝕩
-}
-Suffixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Drop¨<𝕩}
-↓ ← Suffixes       ⊘ Drop
-
-Windows←{
-  ! IsArray 𝕩
-  ! 1≥=𝕨
-  ! 𝕨≤○≠≢𝕩
-  ! ∧´Nat¨⥊𝕨
-  s←(≠𝕨)↑≢𝕩
-  ! ∧´𝕨≤1+s
-  𝕨{(∾⟜(𝕨≠⊸↓≢𝕩)∘≢⥊>)<¨⊸⊏⟜𝕩¨s(¬+⌜○↕⊢)⥊𝕨}⍟(0<≠𝕨)𝕩
-}
-
-Reverse ← {!1≤=𝕩 ⋄ (-↕⊸¬≠𝕩)⊏𝕩}
-Rotate ← {!Int𝕨 ⋄ l←≠𝕩⋄(l|𝕨+↕l)⊏𝕩} _onAxes_ 0
-
-Indices←{
-  ! 1==𝕩
-  ! ∧´Nat¨𝕩
-  ⟨⟩∾´𝕩⥊¨↕≠𝕩
-}
-Rep ← Indices⊸⊏
-Replicate ← {0<=𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep𝕩} _onAxes_ (1-0=≠)
-
-↕ ↩ ↕              ⊘ Windows
-⌽ ← Reverse        ⊘ Rotate
-/ ← Indices        ⊘ Replicate
-
-
-#⌜
-# LAYER 6: Everything else
-
-Join←{
-  C←(<⟨⟩)⥊⊸∾⌜´⊢  # Cartesian array product
-  ! IsArray 𝕩
-  s←≢¨𝕩
-  d←≠0⊑⥊s
-  ! ∧´⥊d=≠¨s
-  ! d≥=𝕩
-  l←(≢𝕩){(𝕩⊑⟜≢a⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=a←𝕩
-  ! (r↑¨s)≡C l
-  i←C{p←+´¨↑𝕩⋄(↕0⊑⌽p)-𝕩/¯1↓p}¨l
-  >i<¨⊸⊏¨l/𝕩
-}⍟(0<≠∘⥊)
-
-Group←{
-  ! IsArray 𝕩
-  Chk←{!1==𝕩⋄!∧´Int¨𝕩⋄!∧´¯1≤𝕩⋄≠𝕩}
-  l←(1<≡)◶Chk‿{!1==𝕩⋄Chk¨𝕩}𝕨
-  ! l≤○≠≢𝕩
-  ! ∧´l=l≠⊸↑≢𝕩
-  (𝕨⊸=/𝕩˜)¨↕1+¯1⌈´⚇1𝕨
-}
-
-∾ ↩ Join           ⊘ JoinTo
-⊔ ← Group⟜(↕≠⚇1)   ⊘ Group
-
-Pick1←{
-  ! 1==𝕨
-  ! 𝕨=○≠s←≢𝕩
-  ! ∧´Int¨𝕨
-  ! ∧´𝕨(≥⟜-∧<)s
-  𝕨↩𝕨+s×𝕨<0
-  (⥊𝕩)⊑˜0(⊑⟜𝕨+⊑⟜s×⊢)´-↕⊸¬≠𝕨
-}
-Pickd←(∨´∘⥊IsArray¨∘⊣)◶Pick1‿{Pickd⟜𝕩¨𝕨}
-Pick←IsArray◶⥊‿⊢⊸Pickd
-⊑ ↩ (0¨∘≢)⊸Pick    ⊘ Pick
-◶ ↩ {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}  # Same definition, new Pick
-
-# Searching
-IndexOf←{
-  c←1-˜=𝕨
-  ! 0≤c
-  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,(+˝∧`)≢⎉c⎉c‿∞⟩ 𝕩
-}
-UniqueMask←{
-  ! 1≤=𝕩
-  u←0↑𝕩
-  {(≠u)>⊑u IndexOf 𝕩}◶{u↩u∾𝕩⋄1}‿0˘𝕩
-}
-Find←{
-  r←=𝕨
-  ! r≤=𝕩
-  𝕨 ≡⎉r (≢𝕨) ↕⎉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
-_cmpLen ← {
-  e←𝕨-˜○(∨´0⊸=)𝕩
-  c←𝕗
-  𝕨(e=0)◶⟨0,e⟩‿{
-    c←×c+𝕨-○≠𝕩
-    r←𝕨⌊○≠𝕩
-    l←𝕨{
-      i←+´∧`𝕨=𝕩
-      m←×´⊑⟜𝕨¨↕i
-      {c↩×-´𝕩⋄m↩m×⌊´𝕩}∘(⊑¨⟜𝕨‿𝕩)⍟(r⊸>)i
-      m
-    }○(((-1+↕r)+≠)⊸{⊑⟜𝕩¨𝕨})𝕩
-    ⟨l,c⟩
-  }𝕩
-}
-_getCellCmp ← {
-  Ci←𝔽⋄l←𝕨⋄c←𝕩
-  {
-    a←𝕨⋄b←𝕩
-    S←(l⊸=)◶{S∘(1+𝕩)⍟(0⊸=)a Ci○(𝕩⊸+)b}‿c
-    S 0
-  }
-}
-Cmp ← ∨○IsArray◶{ # No arrays
-  𝕨(>-<)𝕩 # Assume they're numbers
-}‿{ # At least one array
-  lc←𝕨(𝕨-○IsArray𝕩)_cmpLen○≢𝕩
-  cc ← (⊑⟜(⥊𝕨))⊸Cmp⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
-  Cc˜0
-}
-
-_binSearch ← {
-  B ← 𝔽
-  {
-    R←{𝕨{a←B m←𝕩+h←⌊𝕨÷2⋄(h+a×2|𝕨)R a⊑𝕩‿m}⍟(>⟜1)𝕩}
-    1+(𝕩+1)R ¯1
-  }⍟(0⊸<)
-}
-_grade←{
-  ! 1≤=𝕩
-  m←×´1 Cell 𝕩 ⋄ Ci←𝔽○(⊑⟜(⥊𝕩))
-  cc←m Ci _getCellCmp 0
-  Ins←{𝕨⊸(≤+<)◶⟨⊑⟜𝕩,i,-⟜1⊑𝕩˜⟩¨↕1+i←≠𝕩}
-  ⟨⟩ {𝕩Ins˜(𝕨(Cc≤0˜)˜m×⊑⟜𝕩)_binSearch≠𝕩}´ m×(↕-˜-⟜1)≠𝕩
-}
-_bins←{
-  c←1-˜=𝕨
-  ! 0≤c
-  ! c≤=𝕩
-  lw←×´sw←1 Cell 𝕨
-  cw←lw 𝔽○(⊑⟜(⥊𝕨)) _getCellCmp 0
-  ! 0⊸<◶⟨1,∧´0≤˜·cw¨⟜(lw⊸+)lw×↕∘-⟜1⟩≠𝕨
-  cx←c-˜=𝕩
-  sx←cx Cell 𝕩 ⋄ lc←sw 0 _cmpLen sx
-  cc ← (⊑⟜(⥊𝕨))⊸𝔽⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
-  B←(×´sw)⊸×⊸Cc≤0˜
-  (≠𝕨) {B⟜𝕩 _binSearch 𝕨}¨ (×´sx) × ⥊⟜(↕×´)⊑⟜(≢𝕩)¨↕cx
-}
-
-OccurrenceCount ← ⊐˜(⊢-⊏)⍋∘⍋
-ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩}
-
-⍋ ←   Cmp _grade   ⊘ (  Cmp _bins)
-⍒ ← -∘Cmp _grade   ⊘ (-∘Cmp _bins)
-∧ ↩ ⍋⊸⊏            ⊘ ∧
-∨ ↩ ⍒⊸⊏            ⊘ ∨
-⊒ ← OccurrenceCount⊘ ProgressiveIndexOf
-
-_repeat_←{
-  n←𝕨𝔾𝕩
-  f←0⊑𝕨⟨𝔽⟩⊘⟨𝕨𝔽⊢⟩𝕩
-  l←u←0
-  {!Int𝕩⋄l↩l⌊𝕩⋄u↩u⌈𝕩}⚇0 n
-  a←𝕩⋄_p←{𝔽∘⊣`(1+𝕩)⥊<a}
-  pos←F _p u ⋄ neg←F⁼_p-l
-  (|⊑<⟜0⊑pos‿neg˜)⚇0 n
-}
-⍟ ↩ _repeat_
-"
+impl ← •LNS "impl.bqn"
 
 X←Raw←{≤4}
 {
@@ -464,7 +60,7 @@ X←Raw←{≤4}
   }
 
   lf ← •UCS 10
-  pre ← E_isdef◶E_proc‿E_redef¨ lf((⊢-˜¬×+`)∘=⊔⊢)impl
+  pre ← E_isdef◶E_proc‿E_redef¨ impl
   Raw↩⍎
   ExecFile←{Raw ∾ ∾⟜lf¨ E_proc¨ •LNS 𝕩}
   X↩Raw∘E_proc
diff --git a/impl.bqn b/impl.bqn
new file mode 100644
index 00000000..454c1c99
--- /dev/null
+++ b/impl.bqn
@@ -0,0 +1,404 @@
+◶ ← {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}     # LIMITED to number left operand result
+⊘ ← {𝕨((1{𝔽}𝕨)-0)◶𝔽‿𝔾 𝕩}
+#⊢ ← {𝕩}  # Prevents dyadic negative ⍟
+⊣ ← {𝕩}⊘{𝕨}
+˜ ← {𝕩𝔽𝕨⊣𝕩}
+∘ ← {𝔽𝕨𝔾𝕩}
+○ ← {(𝔾𝕨)𝔽𝔾𝕩}
+⊸ ← {(𝔽𝕨⊣𝕩)𝔾𝕩}
+⟜ ← {(𝕨⊣𝕩)𝔽𝔾𝕩}
+⍟ ← {𝕨((𝕨𝔾𝕩)⊑⊢‿𝕗){𝔽}𝕩}   # LIMITED to boolean right operand result
+
+# LIMITED to numeric arguments for scalar cases
+√ ← ⋆⟜(÷2)   ⊘ (⋆⟜÷˜)
+∧ ←            ×
+∨ ←            (+-×)
+¬ ← 1+-
+< ← {⟨⟩⥊⟨𝕩⟩} ⊘ (¬≤˜)
+> ←            (¬≤)
+≥ ← !∘0      ⊘ (≤˜)
+≢ ↩ IsArray◶⟨⟩‿≢  # LIMITED to monadic case
+Length ← (0<0⊑≢)◶⟨1⋄0⊑⊢⟩∘≢
+≠ ← Length   ⊘ (¬∘=)
+× ↩ 0⊸(<->)  ⊘ ×
+| ← ×⟜×      ⊘ {𝕩-𝕨×⌊𝕩÷𝕨}
+
+_fold←{
+  ! 1==𝕩
+  l←≠v←𝕩 ⋄ F←𝔽
+  r←𝕨 (0<l)◶{𝕩⋄Identity f}‿{l↩l-1⋄l⊑𝕩}⊘⊣ 𝕩
+  {r↩(𝕩⊑v)F r}⌜(l-1)⊸-⌜↕l
+  r
+}
+´ ← _fold
+
+
+#⌜
+# LAYER 2: Pervasion
+# After defining _perv, we apply it to all scalar functions,
+# making them pervasive. I'm not going to write that out.
+
+ToArray ← <⍟(¬IsArray)
+
+∾ ← {k←≠𝕨⋄k⊸≤◶⟨⊑⟜𝕨⋄-⟜k⊑𝕩˜⟩⌜↕k+≠𝕩}  # LIMITED to two vector arguments
+
+_eachd←{
+  _e←{ # 𝕨 has smaller or equal rank
+    k←≠p←≢𝕨 ⋄ q←≢𝕩
+    ! ∧´(⊑⟜p=⊑⟜q)⌜↕k
+    l←×´(q⊑˜k⊸+)⌜↕q≠⊸-k
+    a←⥊𝕨 ⋄ b←⥊𝕩
+    q⥊⥊(≠a) (⊑⟜a𝔽l⊸×⊸+⊑b˜)⌜○↕ l
+  }
+  (>○=)◶⟨𝔽_e⋄𝔽˜_e˜⟩
+}
+
+¨ ↩ {(𝔽⌜)⊘(𝔽_eachd○ToArray)}
+
+_perv←{ # Pervasion
+  (⊢⊘∨○IsArray)◶⟨𝔽⋄𝔽{𝕨𝔽_perv𝕩}¨⟩
+}
+⌊ ↩ ⌊        ⊘ ({(𝕨>𝕩)⊑𝕨‿𝕩} _perv)
+⌈ ← -∘⌊∘-    ⊘ ({(𝕨<𝕩)⊑𝕨‿𝕩} _perv)
+
+identity ← {(0⊑𝕨){𝕗=𝕩}◶𝕩‿(1⊑𝕨)}´ ⟨+‿0,-‿0,×‿1,÷‿1,⋆‿1,√‿1,∧‿1,∨‿0,|‿0,⌊‿∞,⌈‿¯∞,<‿0,≤‿1,=‿1,≥‿1,>‿0,≠‿0,⊑⟨!∘0⟩⟩
+
+
+#⌜
+# LAYER 3: Remove other limits
+# Now all implementations are full except ∾ and ⊑; ↕ is monadic only
+
+Int←IsArray◶⟨⌊⊸=,0⟩
+Nat←IsArray◶⟨0⊸≤∧⌊⊸=,0⟩
+
+Deshape←IsArray◶{⟨𝕩⟩}‿⥊
+Reshape←{
+  ! 1≥=𝕨
+  𝕨↩⥊𝕨
+  ! ∧´Nat¨𝕨
+  l←×´𝕨
+  n←×´≢𝕩
+  𝕨⥊{
+    𝕩(0<n)◶⟨Type⊸(⊣⌜)⋄⥊⊸{⊑⟜𝕨¨n|𝕩}⟩↕l
+  }⍟(l≠n)𝕩
+}⟜ToArray
+⥊ ↩ Deshape        ⊘ Reshape
+
+Range←{
+  I←{!Nat𝕩⋄↕𝕩}
+  M←{!1==𝕩⋄(<⟨⟩)⥊⊸∾⌜´I¨𝕩}
+  IsArray◶I‿M 𝕩
+}
+
+match←{¬∘(0⊑𝕨)◶(1⊑𝕨)‿𝕩}´⟨
+  ⟨≠○IsArray , 0⟩
+  ⟨¬IsArray∘⊢, =⟩
+  ⟨≠○=       , 0⟩
+  ⟨∨´≠○≢     , 0⟩
+  {∧´⥊𝕨Match¨𝕩}
+⟩
+
+Depth←IsArray◶0‿{1+0⌈´Depth¨⥊𝕩}
+
+↕ ↩ Range
+
+≡ ← Depth          ⊘ Match
+≢ ↩ ≢              ⊘ (¬Match)
+
+
+#⌜
+# LAYER 4: Operators
+
+
+DropV← {⊑⟜𝕩¨𝕨+↕𝕨-˜≠𝕩}
+Cell ← DropV⟜≢
+Pair ← {⟨𝕩⟩} ⊘ {⟨𝕨,𝕩⟩}
+
+Merge←{
+  c←≢⊑𝕩
+  ! ∧´⥊(c≡≢)¨𝕩
+  𝕩⊑⟜⥊˜⌜c⥊↕×´c
+}⍟(0<≠∘⥊)
+> ↩ Merge          ⊘ >
+≍ ← >∘Pair
+_ranks ← {⟨2⟩⊘⟨1,0⟩((⊣-1+|)˜⟜≠⊑¨<∘⊢)⥊∘𝔽}
+_depthOp_←{
+  neg←0>n←𝕨𝔾_ranks𝕩 ⋄ F←𝔽
+  _d←{
+    R←(𝕗+neg)_d
+    𝕨(2⥊(neg∧𝕗≥0)∨(0⌈𝕗)≥Pair○≡)◶(⟨R¨⋄R⟜𝕩¨∘⊣⟩≍⟨(𝕨R⊢)¨∘⊢⋄F⟩)𝕩
+  }
+  𝕨 n _d 𝕩
+}
+⚇ ← _depthOp_
+_rankOp_←{
+  k←𝕨(Pair○= (0≤⊢)◶⟨⌊⟜-,0⌈-⟩¨ 𝔾_ranks)𝕩
+  Enc←{
+    f←⊑⟜(≢𝕩)¨↕𝕨
+    c←×´s←𝕨Cell𝕩
+    f⥊⊑⟜(⥊𝕩)¨∘((s⥊↕c)+c×⊢)¨↕×´f
+  }
+  Enc↩(>⟜0+≥⟜=)◶⟨<⊢,Enc,<¨⊢⟩
+  > ((0⊑k)Enc𝕨) 𝔽¨ ((1-˜≠)⊸⊑k)Enc𝕩
+}
+_scan←{
+  ! IsArray 𝕩
+  ! 1≤=𝕩
+  F←𝔽
+  {
+    r←⥊𝕩 ⋄ l←≠𝕩 ⋄ c←×´1 Cell 𝕩
+    {r↩r𝕩_amend˜𝕨F○(⊑⟜r)𝕩}⟜(c⊸+)¨↕c-˜≠r
+    (≢𝕩)⥊r
+  }⍟(0<≠∘⥊)𝕩
+}
+
+` ← _scan
+⎉ ← _rankOp_
+˘ ← ⎉¯1
+_insert←{
+  ! 1≤=𝕩
+  𝕨 𝔽´ <˘𝕩
+}
+˝ ← _insert
+
+
+#⌜
+# LAYER 5: Structural functions
+
+_onAxes_←{
+  F←𝔽
+  (𝔾<≡)∘⊣◶{ # One axis
+    ! 1≤=𝕩
+    𝕨F𝕩
+  }‿{ # Multiple axes
+    ! 1≥=𝕨
+    ! 𝕨≤○≠≢𝕩
+    R←{(0⊑⥊𝕨)F(1 DropV 𝕨)⊸R˘𝕩}⍟{0<≠𝕨}
+    𝕨R𝕩
+  }
+}
+
+SelSub←{
+  ! IsArray 𝕨
+  ! ∧´⥊Int¨ 𝕨
+  ! ∧´⥊ 𝕨 (≥⟜-∧<) ≠𝕩
+  𝕨↩𝕨+(≠𝕩)×𝕨<0
+  𝕨(1≠=∘⊢)◶{
+    ⊑⟜𝕩¨𝕨
+  }‿{
+    c←×´s←1 Cell 𝕩
+    ⊑⟜(⥊𝕩)¨(c×𝕨)+⌜s⥊↕c
+  }𝕩
+}
+Select←ToArray⊸(SelSub _onAxes_ 1)
+⊏ ← 0⊸Select       ⊘ Select
+
+JoinTo←{
+  s←𝕨Pair○≢𝕩
+  a←1⌈´k←≠¨s
+  ! ∧´1≥a-k
+  c←(k¬a)+⟜(↕a-1)⊸⊏¨s
+  ! ≡´c
+  l←+´(a=k)⊣◶1‿(0⊑⊢)¨s
+  (⟨l⟩∾0⊑c)⥊𝕨∾○⥊𝕩
+}
+
+Take←{
+  T←{
+    ! Int 𝕨
+    l←≠𝕩
+    i←(l+1)|¯1⌈l⌊((𝕨<0)×𝕨+l)+↕|𝕨
+    i⊏JoinTo⟜(1⊸Cell⥊Type)⍟(∨´l=i)𝕩
+  }
+  𝕨 T _onAxes_ 0 (⟨1⟩⥊˜0⌈𝕨-○≠⊢)⊸∾∘≢⊸⥊𝕩
+}
+Prefixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Take¨<𝕩}
+↑ ← Prefixes       ⊘ Take
+Drop←{
+  s←(≠𝕨)(⊣↑⊢∾˜1⥊˜0⌈-⟜≠)≢𝕩
+  ((sׯ1⋆𝕨>0)+(-s)⌈s⌊𝕨)↑𝕩
+}
+Suffixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Drop¨<𝕩}
+↓ ← Suffixes       ⊘ Drop
+
+Windows←{
+  ! IsArray 𝕩
+  ! 1≥=𝕨
+  ! 𝕨≤○≠≢𝕩
+  ! ∧´Nat¨⥊𝕨
+  s←(≠𝕨)↑≢𝕩
+  ! ∧´𝕨≤1+s
+  𝕨{(∾⟜(𝕨≠⊸↓≢𝕩)∘≢⥊>)<¨⊸⊏⟜𝕩¨s(¬+⌜○↕⊢)⥊𝕨}⍟(0<≠𝕨)𝕩
+}
+
+Reverse ← {!1≤=𝕩 ⋄ (-↕⊸¬≠𝕩)⊏𝕩}
+Rotate ← {!Int𝕨 ⋄ l←≠𝕩⋄(l|𝕨+↕l)⊏𝕩} _onAxes_ 0
+
+Indices←{
+  ! 1==𝕩
+  ! ∧´Nat¨𝕩
+  ⟨⟩∾´𝕩⥊¨↕≠𝕩
+}
+Rep ← Indices⊸⊏
+Replicate ← {0<=𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep𝕩} _onAxes_ (1-0=≠)
+
+↕ ↩ ↕              ⊘ Windows
+⌽ ← Reverse        ⊘ Rotate
+/ ← Indices        ⊘ Replicate
+
+
+#⌜
+# LAYER 6: Everything else
+
+Join←{
+  C←(<⟨⟩)⥊⊸∾⌜´⊢  # Cartesian array product
+  ! IsArray 𝕩
+  s←≢¨𝕩
+  d←≠0⊑⥊s
+  ! ∧´⥊d=≠¨s
+  ! d≥=𝕩
+  l←(≢𝕩){(𝕩⊑⟜≢a⊑˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=a←𝕩
+  ! (r↑¨s)≡C l
+  i←C{p←+´¨↑𝕩⋄(↕0⊑⌽p)-𝕩/¯1↓p}¨l
+  >i<¨⊸⊏¨l/𝕩
+}⍟(0<≠∘⥊)
+
+Group←{
+  ! IsArray 𝕩
+  Chk←{!1==𝕩⋄!∧´Int¨𝕩⋄!∧´¯1≤𝕩⋄≠𝕩}
+  l←(1<≡)◶Chk‿{!1==𝕩⋄Chk¨𝕩}𝕨
+  ! l≤○≠≢𝕩
+  ! ∧´l=l≠⊸↑≢𝕩
+  (𝕨⊸=/𝕩˜)¨↕1+¯1⌈´⚇1𝕨
+}
+
+∾ ↩ Join           ⊘ JoinTo
+⊔ ← Group⟜(↕≠⚇1)   ⊘ Group
+
+Pick1←{
+  ! 1==𝕨
+  ! 𝕨=○≠s←≢𝕩
+  ! ∧´Int¨𝕨
+  ! ∧´𝕨(≥⟜-∧<)s
+  𝕨↩𝕨+s×𝕨<0
+  (⥊𝕩)⊑˜0(⊑⟜𝕨+⊑⟜s×⊢)´-↕⊸¬≠𝕨
+}
+Pickd←(∨´∘⥊IsArray¨∘⊣)◶Pick1‿{Pickd⟜𝕩¨𝕨}
+Pick←IsArray◶⥊‿⊢⊸Pickd
+⊑ ↩ (0¨∘≢)⊸Pick    ⊘ Pick
+◶ ↩ {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}  # Same definition, new Pick
+
+# Searching
+IndexOf←{
+  c←1-˜=𝕨
+  ! 0≤c
+  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,(+˝∧`)≢⎉c⎉c‿∞⟩ 𝕩
+}
+UniqueMask←{
+  ! 1≤=𝕩
+  u←0↑𝕩
+  {(≠u)>⊑u IndexOf 𝕩}◶{u↩u∾𝕩⋄1}‿0˘𝕩
+}
+Find←{
+  r←=𝕨
+  ! r≤=𝕩
+  𝕨 ≡⎉r (≢𝕨) ↕⎉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
+_cmpLen ← {
+  e←𝕨-˜○(∨´0⊸=)𝕩
+  c←𝕗
+  𝕨(e=0)◶⟨0,e⟩‿{
+    c←×c+𝕨-○≠𝕩
+    r←𝕨⌊○≠𝕩
+    l←𝕨{
+      i←+´∧`𝕨=𝕩
+      m←×´⊑⟜𝕨¨↕i
+      {c↩×-´𝕩⋄m↩m×⌊´𝕩}∘(⊑¨⟜𝕨‿𝕩)⍟(r⊸>)i
+      m
+    }○(((-1+↕r)+≠)⊸{⊑⟜𝕩¨𝕨})𝕩
+    ⟨l,c⟩
+  }𝕩
+}
+_getCellCmp ← {
+  Ci←𝔽⋄l←𝕨⋄c←𝕩
+  {
+    a←𝕨⋄b←𝕩
+    S←(l⊸=)◶{S∘(1+𝕩)⍟(0⊸=)a Ci○(𝕩⊸+)b}‿c
+    S 0
+  }
+}
+Cmp ← ∨○IsArray◶{ # No arrays
+  𝕨(>-<)𝕩 # Assume they're numbers
+}‿{ # At least one array
+  lc←𝕨(𝕨-○IsArray𝕩)_cmpLen○≢𝕩
+  cc ← (⊑⟜(⥊𝕨))⊸Cmp⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
+  Cc˜0
+}
+
+_binSearch ← {
+  B ← 𝔽
+  {
+    R←{𝕨{a←B m←𝕩+h←⌊𝕨÷2⋄(h+a×2|𝕨)R a⊑𝕩‿m}⍟(>⟜1)𝕩}
+    1+(𝕩+1)R ¯1
+  }⍟(0⊸<)
+}
+_grade←{
+  ! 1≤=𝕩
+  m←×´1 Cell 𝕩 ⋄ Ci←𝔽○(⊑⟜(⥊𝕩))
+  cc←m Ci _getCellCmp 0
+  Ins←{𝕨⊸(≤+<)◶⟨⊑⟜𝕩,i,-⟜1⊑𝕩˜⟩¨↕1+i←≠𝕩}
+  ⟨⟩ {𝕩Ins˜(𝕨(Cc≤0˜)˜m×⊑⟜𝕩)_binSearch≠𝕩}´ m×(↕-˜-⟜1)≠𝕩
+}
+_bins←{
+  c←1-˜=𝕨
+  ! 0≤c
+  ! c≤=𝕩
+  lw←×´sw←1 Cell 𝕨
+  cw←lw 𝔽○(⊑⟜(⥊𝕨)) _getCellCmp 0
+  ! 0⊸<◶⟨1,∧´0≤˜·cw¨⟜(lw⊸+)lw×↕∘-⟜1⟩≠𝕨
+  cx←c-˜=𝕩
+  sx←cx Cell 𝕩 ⋄ lc←sw 0 _cmpLen sx
+  cc ← (⊑⟜(⥊𝕨))⊸𝔽⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
+  B←(×´sw)⊸×⊸Cc≤0˜
+  (≠𝕨) {B⟜𝕩 _binSearch 𝕨}¨ (×´sx) × ⥊⟜(↕×´)⊑⟜(≢𝕩)¨↕cx
+}
+
+OccurrenceCount ← ⊐˜(⊢-⊏)⍋∘⍋
+ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩}
+
+⍋ ←   Cmp _grade   ⊘ (  Cmp _bins)
+⍒ ← -∘Cmp _grade   ⊘ (-∘Cmp _bins)
+∧ ↩ ⍋⊸⊏            ⊘ ∧
+∨ ↩ ⍒⊸⊏            ⊘ ∨
+⊒ ← OccurrenceCount⊘ ProgressiveIndexOf
+
+_repeat_←{
+  n←𝕨𝔾𝕩
+  f←0⊑𝕨⟨𝔽⟩⊘⟨𝕨𝔽⊢⟩𝕩
+  l←u←0
+  {!Int𝕩⋄l↩l⌊𝕩⋄u↩u⌈𝕩}⚇0 n
+  a←𝕩⋄_p←{𝔽∘⊣`(1+𝕩)⥊<a}
+  pos←F _p u ⋄ neg←F⁼_p-l
+  (|⊑<⟜0⊑pos‿neg˜)⚇0 n
+}
+⍟ ↩ _repeat_