Various strength reductions

2 files changed, 18 insertions, 18 deletions

diff --git a/docs/bqn.js b/docs/bqn.js
index cecee5e0..bcd61924 100644
--- a/docs/bqn.js
+++ b/docs/bqn.js
@@ -244,9 +244,9 @@ let provide = [
 ];
 
 let [runtime,setPrims] = run(
-  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  ,provide.concat([0,1,2,Infinity,-Infinity,-1,32,3,8,5,4,'∾','+','-','×','÷','⋆','¬','⌊','⌈','∨','∧','≠','=','>','≥','˙','√','<','⊢','⊣','≍','↑','↓','↕','⌽','⍉','/','⊔','˜','¨','⌜','˘','`','∘','○','⌾','⍟','⊘','⊸','⟜',str("+-×÷⋆√⌊⌈|¬∧∨<>≠=≤≥≡≢⊣⊢⥊∾≍↑↓↕«»⌽⍉/⍋⍒⊏⊑⊐⊒∊⍷⊔!˙˜˘¨⌜⁼´˝`∘○⊸⟜⌾⊘◶⎉⚇⍟⎊%"),str("´: 𝕩 must be a list"),str("´: Identity not found"),str("Mapping: Equal-rank argument shapes don\'t agree"),str("Mapping: Argument shape prefixes don\'t agree"),str("⍋𝕩: 𝕩 must have rank at least 1"),str("⍋ or ⍒: Rank of 𝕨 must be at least 1"),str("⍋ or ⍒: Rank of 𝕩 must be at least cell rank of 𝕨"),str("⍋ or ⍒: 𝕨 must be sorted"),str("/: Replication argument must have rank 1"),str("/: Amounts to replicate must be natural numbers"),str("⌽𝕩: 𝕩 must have rank at least 1"),str("𝕨⌽𝕩: 𝕨 must consist of integers"),str("↑𝕩: 𝕩 must have rank at least 1"),str("↓𝕩: 𝕩 must have rank at least 1"),str("⊏𝕩: 𝕩 must have rank at least 1"),str("⊏𝕩: 𝕩 cannot have length 0"),str("𝕨⊏𝕩: 𝕨 must be an array"),str("𝕨⊏𝕩: Indices in 𝕨 must be integers"),str("𝕨⊏𝕩: Indices out of range"),str("𝕨⊑𝕩: Index out of range"),str("𝕨⊑𝕩: Indices in 𝕨 must consist of integers"),str("𝕨⊑𝕩: 𝕩 must be a list when 𝕨 is a number"),str("⌾: Incompatible result elements in structural Under"),str(">𝕩: Elements of 𝕩 must have matching shapes"),str("∾𝕩: Elements of 𝕩 must all have the same rank"),str("∾𝕩: 𝕩 element rank must be at least argument rank"),str("∾𝕩: 𝕩 element shapes must be compatible"),str("∾𝕩: 𝕩 element trailing shapes must match"),str("∾𝕩: empty 𝕩 fill rank must be at least argument rank"),str("∾𝕩: 𝕩 must be an array"),str("⊢⊣˜∘○⊸⟜⊘◶"),str("=≠≢"),str("<"),str("≍"),str("↕/»«⊔"),str("⥊↑↓⌽⍉⊏⊑"),str("𝕨"),str("𝕩: 𝕨 must "),str("have rank at most 1"),str("consist of integers"),str("↑"),str("↓"),str("« or »: 𝕩 must have rank at least 1"),str("« or »: 𝕨 must not have higher rank than 𝕩"),str("« or »: Rank of 𝕨 must be at least rank of 𝕩 minus 1"),str("« or »: 𝕨 must share 𝕩\'s major cell shape"),str("𝕨↕𝕩: 𝕨 must have rank at most 1"),str("𝕨↕𝕩: Length of 𝕨 must be at most rank of 𝕩"),str("𝕨↕𝕩: 𝕨 must consist of natural numbers"),str("𝕨↕𝕩: Window length 𝕨 must be at most axis length plus one"),str("First-axis primitive: 𝕩 must have rank at least 1"),str("Multi-axis primitive: 𝕨 must have rank at most 1"),str("Multi-axis primitive: Length of 𝕨 must be at most rank of 𝕩"),str("∊𝕩 or ⊐𝕩: 𝕩 must have rank at least 1"),str("≥: No monadic form"),str("≤: No monadic form"),str("∘⌊⌽↑"),str("𝕨⥊𝕩: 𝕨 must have rank at most 1"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers"),str("𝕨⥊𝕩: Can\'t compute axis length when rest of shape is empty"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers or ∘ ⌊ ⌽ ↑"),str("𝕨⥊𝕩: Shape must be exact when reshaping with ∘"),str("𝕨⊑𝕩: Indices in compound 𝕨 must be lists"),str("𝕨⊑𝕩: Index length in 𝕨 must match rank of 𝕩"),str("↕𝕩: 𝕩 must consist of natural numbers"),str("↕𝕩: 𝕩 must be a number or list"),str("⎉ or ⚇: 𝔽 result must have rank at most 1"),str("⎉ or ⚇: 𝔽 result must have 1 to 3 elements"),str("⎉ or ⚇: 𝔽 result must consist of integers"),str("˝: 𝕩 must have rank at least 1"),str("˝: Identity does not exist"),str("𝕨∾𝕩: Rank of 𝕨 and 𝕩 must differ by at most 1"),str("𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match"),str("𝕨/𝕩: Lengths of components of 𝕨 must match 𝕩"),str("⍟: Repetition numbers in 𝕨𝔾𝕩 must be integers"),str("⊔: Grouping argument must consist of integers"),str("⊔: Grouping argument values cannot be less than ¯1"),str("⊔𝕩: 𝕩 must be a list"),str("𝕨⊔𝕩: 𝕩 must be an array"),str("𝕨⊔𝕩: Compound 𝕨 must be a list"),str("𝕨⊔𝕩: Total rank of 𝕨 must be at most rank of 𝕩"),str("𝕨⊔𝕩: Lengths of 𝕨 must equal to 𝕩, or one more only in a rank-1 component"),str("p⊐𝕩 or 𝕨∊p: p must have rank at least 1"),str("p⊐n or n∊p: Rank of n must be at least cell rank of p"),str("⍷𝕩: Rank of 𝕨 cannot exceed rank of 𝕩"),str("𝕨⍉𝕩: 𝕨 must have rank at most 1"),str("𝕨⍉𝕩: Length of 𝕨 must not exceed rank of 𝕩"),str("𝕨⍉𝕩: 𝕨 must consist of natural numbers"),str("𝕨⍉𝕩: Skipped result axis"),str("⊒: Rank of 𝕨 must be at least 1"),str("⊒: Rank of 𝕩 must be at least cell rank of 𝕨"),str("Cannot currently invert blocks"),str("Cannot invert modifier"),str("⁼: Inverse failed"),str("⁼: Inverse does not exist"),str("⁼: Inverse not found")])
- ,[[0,1,0,190],[0,0,4152,3],[0,0,4160,3],[0,0,4164,3],[2,0,4177,6],[0,0,4204,3],[0,0,4208,3],[0,0,4212,3],[1,0,4216,5],[1,0,4224,5],[2,0,4242,6],[2,0,4257,6],[2,0,4276,6],[2,0,4298,6],[2,0,4320,6],[0,0,4352,3],[0,0,4364,3],[0,0,4373,3],[0,0,4379,3],[0,0,4396,3],[0,0,4405,3],[1,0,4414,9],[0,0,4527,4],[0,0,4603,3],[0,0,4643,5],[0,0,4718,3],[1,1,4735,2],[2,1,4766,3],[1,1,4800,2],[2,1,4817,4],[0,0,4895,3],[1,1,4902,4],[1,1,4975,3],[0,0,5053,3],[0,0,5064,4],[1,0,5134,9],[0,0,5206,5],[2,0,5290,12],[1,1,5501,3],[1,0,5525,14],[0,0,5977,4],[0,0,6031,6],[0,0,6121,3],[0,0,6146,7],[0,0,6275,4],[0,0,6336,4],[0,0,6449,3],[0,0,6517,4],[1,1,6594,2],[0,0,6627,3],[0,0,6677,4],[0,0,6819,3],[0,0,6920,4],[2,1,7021,3],[1,0,7064,5],[0,0,7102,3],[2,0,7106,11],[0,0,7237,3],[0,0,7245,6],[0,0,7272,5],[0,0,7293,6],[1,0,7320,19],[0,0,7823,3],[0,0,7850,3],[0,0,7876,3],[2,1,7915,3],[0,0,7984,4],[0,0,8081,7],[0,0,8128,14],[0,0,8362,5],[0,0,8459,3],[1,1,8499,8],[1,0,8552,6],[1,1,8660,2],[0,0,8718,5],[0,0,8880,5],[0,0,9017,7],[0,0,9186,3],[0,0,9245,4],[1,0,9312,5],[2,1,9329,4],[1,0,9372,6],[0,0,9511,3],[0,0,9538,3],[0,0,9560,3],[0,0,9582,3],[0,0,9601,9],[0,0,9766,4],[0,0,9968,3],[0,0,9986,5],[0,0,10020,3],[1,1,10117,2],[2,0,10186,10],[2,0,10245,8],[1,0,10438,7],[0,0,10505,8],[0,0,10745,5],[0,0,10835,3],[2,0,10869,10],[1,0,10944,9],[0,0,11099,4],[0,0,11218,10],[1,1,11682,4],[0,0,11736,4],[0,0,11844,3],[0,0,11920,3],[0,0,11975,4],[0,0,12108,4],[0,0,12230,4],[1,1,12341,2],[2,0,12349,6],[1,1,12364,2],[0,0,12479,3],[0,0,12487,3],[0,0,12495,3],[0,0,12516,8],[0,0,12598,3],[0,0,12606,3],[0,0,12614,3],[0,0,12622,3],[0,0,12630,3],[0,0,12638,3],[0,0,12650,3],[2,0,12675,7],[0,0,12716,6],[0,0,12940,4],[0,0,13046,3],[0,0,13089,5],[0,0,13233,3],[0,0,13280,3],[0,0,13306,3],[1,0,13397,5],[0,0,13425,3],[0,0,13461,3],[0,0,13509,3],[0,0,13563,3],[0,0,13575,3],[1,1,13655,2],[0,0,13685,4],[0,0,13722,3],[0,0,13737,3],[0,0,13766,3],[0,0,13781,3],[0,0,13799,3],[0,0,13814,3],[0,0,13824,3],[2,0,13881,6],[0,0,13909,3],[1,1,13937,2],[1,1,13941,2],[0,0,13945,3],[0,0,13957,3],[0,0,13980,3],[0,0,14001,3],[0,0,14009,3],[1,0,14017,6],[1,0,14134,11],[1,0,14355,5],[0,0,14370,3],[0,0,14384,3],[0,0,14398,7],[0,0,14475,6],[0,0,14523,3],[1,0,14568,8],[0,0,14706,4],[0,0,14733,3],[0,0,14752,8],[0,0,14919,3],[0,0,14945,3],[0,0,14955,3],[0,0,14972,9],[0,0,15155,6],[0,0,15230,3],[2,0,15238,11],[1,0,15315,5],[0,0,15346,3],[0,0,15356,3],[1,0,15366,5],[0,0,15399,4],[0,0,15410,4],[0,0,15421,3],[0,0,15429,3],[0,0,15447,3],[0,0,15455,3],[1,0,15499,7],[0,0,15525,9],[1,0,15811,5],[0,0,15827,7],[0,0,15994,11],[0,0,16236,8],[0,0,16548,3],[0,0,16576,5],[0,0,16671,8],[0,0,16930,3],[0,0,16977,3],[0,0,16997,3],[1,0,17063,6],[0,0,17216,7],[0,0,17358,5],[0,0,17438,3],[0,0,17461,3],[0,0,17472,3],[0,0,17493,3],[0,0,17504,3],[0,0,17512,9],[0,0,17656,3],[0,0,17685,3],[0,0,17717,3],[0,0,17748,3],[0,0,17786,4],[0,0,17963,3],[0,0,17981,3],[0,0,18006,3],[0,0,18028,3],[0,0,18039,3],[1,1,18053,2],[1,0,18057,5],[1,0,18068,5],[0,0,18079,3],[0,0,18118,5],[0,0,18231,3],[0,0,18283,14],[0,0,18453,3],[0,0,18476,3],[0,0,18496,3],[0,0,18511,3],[0,0,18519,8],[0,0,18590,3],[0,0,18612,5],[0,0,18641,11],[2,0,18853,6],[0,0,18892,3],[0,0,18963,3],[0,0,18995,3],[1,0,19006,5],[1,1,19017,2],[2,1,19036,3],[0,0,19058,3],[0,0,19087,4],[0,0,19110,3],[1,0,19143,5],[0,0,19169,3],[0,0,19239,3],[0,0,19253,3],[0,0,19264,5],[0,0,19400,3],[0,0,19430,3],[0,0,19450,3],[0,0,19504,3],[0,0,19539,3],[0,0,19563,3],[0,0,19578,3],[1,0,19621,5],[0,0,19632,3],[0,0,19675,3],[0,0,19696,5],[2,0,19825,6],[1,1,19840,2],[1,1,19848,2],[0,0,19856,5],[0,0,19895,3],[0,0,19934,3],[0,0,20017,3],[0,0,20051,3],[0,0,20080,3],[0,0,20098,3],[0,0,20115,6],[0,0,20195,3],[0,0,20224,4],[0,0,20285,3],[0,0,20298,4],[0,0,20330,3],[0,0,20340,3],[0,0,20358,3],[0,0,20390,3],[0,0,20417,3],[0,0,20457,3]]
+ ,[[0,1,0,192],[0,0,4196,3],[0,0,4204,3],[0,0,4208,3],[2,0,4221,6],[0,0,4248,3],[0,0,4252,3],[0,0,4256,3],[1,0,4260,5],[1,0,4268,5],[2,0,4286,6],[2,0,4301,6],[2,0,4320,6],[2,0,4342,6],[2,0,4364,6],[0,0,4396,3],[0,0,4408,3],[0,0,4417,3],[0,0,4423,3],[0,0,4440,3],[0,0,4449,3],[1,0,4458,9],[0,0,4578,4],[0,0,4654,3],[0,0,4694,5],[0,0,4769,3],[1,1,4786,2],[2,1,4817,3],[1,1,4851,2],[2,1,4868,4],[0,0,4946,3],[1,1,4953,4],[1,1,5026,3],[0,0,5104,3],[0,0,5115,4],[1,0,5185,9],[0,0,5257,5],[2,0,5341,12],[1,1,5552,2],[1,1,5585,3],[1,0,5609,14],[0,0,6061,4],[0,0,6115,6],[0,0,6205,3],[0,0,6230,7],[0,0,6359,4],[0,0,6420,4],[0,0,6533,3],[0,0,6601,4],[0,0,6678,3],[0,0,6728,4],[0,0,6870,3],[0,0,6971,4],[2,1,7072,3],[0,0,7115,3],[2,0,7119,11],[0,0,7250,3],[0,0,7258,6],[0,0,7285,5],[0,0,7306,6],[1,0,7333,19],[0,0,7836,3],[0,0,7863,3],[0,0,7889,3],[1,0,7928,5],[2,1,7966,3],[0,0,8035,4],[0,0,8123,7],[0,0,8170,14],[0,0,8404,5],[0,0,8501,3],[1,1,8541,8],[1,0,8594,6],[1,1,8702,2],[0,0,8760,5],[0,0,8922,5],[0,0,9059,7],[0,0,9228,3],[0,0,9287,4],[1,0,9354,5],[2,1,9371,4],[1,0,9414,6],[0,0,9553,3],[0,0,9580,3],[0,0,9602,3],[0,0,9624,3],[0,0,9643,9],[0,0,9808,4],[0,0,10010,3],[0,0,10028,5],[0,0,10062,3],[1,1,10159,2],[2,0,10228,10],[2,0,10287,8],[1,0,10480,7],[0,0,10547,8],[0,0,10787,5],[0,0,10877,3],[2,0,10911,10],[1,0,10986,9],[0,0,11141,4],[0,0,11260,10],[1,1,11724,4],[0,0,11778,4],[0,0,11886,3],[0,0,11962,3],[0,0,12017,4],[0,0,12150,4],[0,0,12272,4],[1,1,12383,2],[2,0,12391,6],[1,1,12406,2],[0,0,12521,3],[0,0,12529,3],[0,0,12537,3],[0,0,12558,8],[0,0,12640,3],[0,0,12648,3],[0,0,12656,3],[0,0,12664,3],[0,0,12672,3],[0,0,12680,3],[0,0,12692,3],[2,0,12717,7],[0,0,12758,6],[0,0,12982,4],[0,0,13088,3],[0,0,13131,5],[0,0,13275,3],[0,0,13322,3],[0,0,13348,3],[1,0,13439,5],[0,0,13467,3],[0,0,13503,3],[0,0,13551,3],[0,0,13605,3],[0,0,13617,3],[1,1,13697,2],[0,0,13727,4],[0,0,13764,3],[0,0,13779,3],[0,0,13808,3],[0,0,13823,3],[0,0,13841,3],[0,0,13856,3],[0,0,13866,3],[2,0,13923,6],[0,0,13951,3],[1,1,13979,2],[1,1,13983,2],[0,0,13987,3],[0,0,13999,3],[0,0,14022,3],[0,0,14037,3],[0,0,14045,3],[1,0,14053,6],[1,0,14170,11],[1,0,14391,5],[0,0,14406,3],[0,0,14420,3],[0,0,14434,7],[0,0,14511,6],[0,0,14559,3],[1,0,14604,8],[0,0,14742,4],[0,0,14769,3],[0,0,14788,8],[0,0,14955,3],[0,0,14981,3],[0,0,14991,3],[0,0,15008,9],[0,0,15179,6],[0,0,15254,3],[2,0,15262,11],[1,0,15339,5],[0,0,15370,3],[0,0,15380,3],[1,0,15390,5],[0,0,15423,4],[0,0,15434,4],[0,0,15445,3],[0,0,15453,3],[0,0,15470,3],[0,0,15478,3],[1,0,15522,7],[0,0,15548,9],[1,0,15834,5],[0,0,15850,7],[0,0,16017,11],[0,0,16259,8],[0,0,16571,3],[0,0,16599,5],[0,0,16694,8],[0,0,16953,3],[0,0,17000,3],[0,0,17020,3],[1,0,17086,6],[0,0,17239,7],[0,0,17381,5],[0,0,17461,3],[0,0,17484,3],[0,0,17495,3],[0,0,17516,3],[0,0,17527,3],[0,0,17535,9],[0,0,17679,3],[0,0,17708,3],[0,0,17740,3],[0,0,17771,3],[0,0,17809,4],[0,0,17986,3],[0,0,18004,3],[0,0,18029,3],[0,0,18051,3],[0,0,18062,3],[1,1,18076,2],[1,0,18080,5],[1,0,18091,5],[0,0,18102,3],[0,0,18141,5],[0,0,18254,3],[0,0,18306,14],[0,0,18476,3],[0,0,18499,3],[0,0,18519,3],[0,0,18534,3],[0,0,18542,8],[0,0,18616,3],[0,0,18638,5],[0,0,18667,11],[2,0,18879,6],[0,0,18927,3],[0,0,18998,3],[0,0,19030,3],[1,0,19041,5],[1,1,19052,2],[2,1,19071,3],[0,0,19093,3],[0,0,19122,4],[0,0,19145,3],[1,0,19178,5],[0,0,19204,3],[0,0,19274,3],[0,0,19288,3],[0,0,19299,5],[0,0,19435,3],[0,0,19465,3],[0,0,19485,3],[0,0,19539,3],[0,0,19574,3],[0,0,19598,3],[0,0,19613,3],[1,0,19656,5],[0,0,19667,3],[0,0,19710,3],[0,0,19731,5],[2,0,19860,6],[1,1,19875,2],[1,1,19883,2],[0,0,19891,5],[0,0,19930,3],[0,0,19969,3],[0,0,20052,3],[0,0,20086,3],[0,0,20115,3],[0,0,20133,3],[0,0,20150,6],[0,0,20230,3],[0,0,20259,4],[0,0,20320,3],[0,0,20333,4],[0,0,20365,3],[0,0,20375,3],[0,0,20393,3],[0,0,20425,3],[0,0,20452,3],[0,0,20492,3]]
 );
 
 let rtAssert = runtime[42] = assertFn("!");
diff --git a/src/r.bqn b/src/r.bqn
index b89f5161..690df8e1 100644
--- a/src/r.bqn
+++ b/src/r.bqn
@@ -38,7 +38,7 @@ _fold←{
   "´: 𝕩 must be a list" ! 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↩𝕩 F r}(l-1)⊸-⊑𝕩˙)⌜↕l
   r
 }
 ´ ← _fold
@@ -158,6 +158,7 @@ _grade_←{
     }´(2⋆ni-1+⊢)⌜↕ni←⌈2 Log l+l=0
   }⟩𝕩
 }
+_sort ← {(𝕗⊑⟨Cmp,Cmp˜⟩)_grade_𝕗 ⊸ ⊏}
 _binSearch ← {
   B ← 𝔽
   {
@@ -225,8 +226,6 @@ Suffixes←{
   l⊸⊑⊸Fill {𝕩⊸+⌜↕l-𝕩}⊸⊏⟜𝕩⌜ ↕1+l
 }
 
-_sort ← {(𝕗⊑⟨Cmp,Cmp˜⟩)_grade_𝕗 ⊸ ⊏}
-
 FirstCell←{
   "⊏𝕩: 𝕩 must have rank at least 1" ! 1≤=𝕩
   "⊏𝕩: 𝕩 cannot have length 0" ! 0<≠𝕩
@@ -239,7 +238,7 @@ SelSub←{
   "𝕨⊏𝕩: Indices out of range" ! 1×´⥊ ((-l)⊸≤×l⊸>)⌜ 𝕨
   𝕨 (⊢+l×0>⊢)⌜⊸⊏ 𝕩
 }
-First ← (0<≠)◶⟨Fill,0⊸⊑⟩ Deshape
+First ← IsArray◶⟨⊢, (0<≠)◶⟨Fill,0⊸⊑⟩⥊⟩
 
 eRange←"𝕨⊑𝕩: Index out of range"
 ChkInd←"𝕨⊑𝕩: Indices in 𝕨 must consist of integers" ! Int
@@ -254,8 +253,6 @@ _fillByPure_←{
   𝕘 (3≤Type∘⊣)◶⟨{𝕨Fill𝕏},{(𝕨HomFil𝕩)_fillBy_𝕨}⍟(IsPure⊣)⟩ 𝕗
 }
 
-¨ ← {𝕨𝔽⌜⊘(𝔽_eachd)_fillByPure_𝔽○ToArray𝕩}
-
 StructErr←{𝕩}
 IsStructErr ← (3=Type)◶⟨0,StructErr˙⊸=⟩
 _under_←{
@@ -263,12 +260,12 @@ _under_←{
   # Traverse indices 𝕩 and values 𝕨.
   # Return a list of index‿value pairs, or structErr if 𝕨 doesn't capture 𝕩.
   GetInserts←{
-    conform ← {𝕨◶0‿𝕩}´⟨IsArray⊢, =○=, 1×´=¨○≢⟩
+    conform ← {𝕨◶0‿𝕩}´⟨IsArray⊢, =○=, MatchShape○≢⟩
     Fail←{𝕊‿0}
     # 𝕎 is parent traversal; 𝕩 is current components of ind and val
     Trav←(IsArray 0⊑⊢)◶⟨Pair, Conform´∘⊢◶Fail‿{
-      Parent←𝕎 ⋄ n←≠0⊑a←⥊¨𝕩 ⋄ j←¯1
-      Child←Trav⟜(⊑¨⟜a)
+      Parent←𝕎 ⋄ n←≠0⊑a←⥊⌜𝕩 ⋄ j←¯1
+      Child←Trav⟜(< ⊑_eachd a˙)
       { j+↩1 ⋄ f←n⊸≤◶⟨𝕊˙⊸Child,Parent˙⟩j ⋄ F 0 }
     }⟩
     count←0⋄{IsArray◶⟨{𝕩⋄count+↩1},𝕊⌜⟩𝕩}𝕩
@@ -291,7 +288,7 @@ _under_←{
         }⍟(e=⊢)P j↩1+j}0⋄r
       }⟩⌜↕l
     }
-    _at_ ← {(↕≠𝕩) 𝔽⍟((𝔾𝕩)=⊣)¨ 𝕩}
+    _at_ ← {𝔽⍟((𝔾𝕩)=⊣)⟜(⊑⟜𝕩)⌜ ↕≠𝕩}
     Set ← 0⊸{ (𝕨≥≠root)◶⟨≢⥊(1+𝕨)⊸𝕊_at_(𝕨⊑root˙)∘⥊, Set1⟩ 𝕩 }
     IsArray∘root◶⟨1⊑0⊑𝕨˙, Set⟩ 𝕩
   } _fillBy_ ⊢
@@ -336,31 +333,34 @@ _structural←{
   StructFn ← (0⊸⊑ 0⊸≤◶⟨3,2⊸≤◶⊢‿2⟩∘⊣◶⟨
     SE · StructPrim 1⊑⊢      #  0 primitive
     E˙                       #  1 block
-    Recompose⟜{StructFn¨1↓𝕩} #    other operation
+    Recompose⟜{StructFn⌜1↓𝕩} #    other operation
     SE 1⊑⊢                   # ¯1 constant
   ⟩ ⊢) Decompose
   IsStruct◶⟨0‿StructErr,1‿3⊏Decompose⟩ {𝕎𝕩}´ ⟨StructFn 𝕗, ¯1 _s_ 0⟩
 }
 
+MatchS ← 1×´=_eachd
+MatchShape ← =○≠◶0‿MatchS
 match←{(0⊑𝕨)◶(1⊑𝕨)‿𝕩}´⟨
   ⟨=○IsArray, 0⟩
   ⟨IsArray∘⊢, =⟩
   ⟨=○=      , 0⟩
-  ⟨1×´=¨○≢  , 0⟩
-  {1×´⥊𝕨Match¨𝕩}
+  ⟨MatchS○≢ , 0⟩
+  {1×´⥊𝕨 Match _eachd 𝕩}
 ⟩
 Depth←IsArray◶0‿{1+0(⊣-≤×-)´Depth⌜⥊𝕩}
 
 ≡ ← Depth          ⊘ Match
 ≢ ↩ IsArray◶⟨⟩‿≢   ⊘ (1-Match)
+¨ ← {𝕨𝔽⌜⊘(𝔽_eachd)_fillByPure_𝔽○ToArray𝕩}
 
 IF ← ⊢⊣!∘≡  # Intersect fill
 IEF← (0<≠)◶⟨⊢_fillBy_ Fill, ⊢_fillBy_ IF´⟩∘⥊
 _fillMerge_ ← {(0<≠∘⥊)◶⟨(𝔾○≢⥊⟨⟩˙)_fillBy_⊢⟜Fill, 𝔽 ⊣_fillBy_⊢ IEF⟩}
 Merge←{
   c←≢0⊑⥊𝕩
-  ">𝕩: Elements of 𝕩 must have matching shapes" ! 1×´(c≡≢)⌜⥊𝕩
-  𝕩⊑⟜Deshape˜⌜c⥊↕1×´c
+  (">𝕩: Elements of 𝕩 must have matching shapes" ! c MatchShape ≢)⌜⥊𝕩
+  (Deshape⌜𝕩)⊑˜⌜c⥊↕1×´c
 }_fillMerge_∾⍟IsArray
 
 Join1←{
@@ -608,7 +608,7 @@ JoinTo←∨○(1<=)◶(∾○⥊)‿{
   a←1⌈´k←≠⌜s
   "𝕨∾𝕩: Rank of 𝕨 and 𝕩 must differ by at most 1" ! 1∧´1≥a-k
   c←(k¬a)+⟜(↕a-1)⊸⊏¨s
-  "𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match" ! ≡´c
+  "𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match" ! MatchS´c
   l←0+´(a=k)⊣◶1‿(0⊑⊢)¨s
   (⟨l⟩∾0⊑c)⥊𝕨∾○⥊𝕩
 } _fillBy_ IF