Rank and Leading Axis Theory

Array Cast - May 27, 2022
Show Notes

[01] 00:02:00 APL logo https://aplwiki.com/wiki/APL_logo
[02] 00:02:24 APL Merch On Bonfire: https://bonfire.com/store/apl-stuff/
On Redbubble: https://redbubble.com/shop/ap/111813275
Aaron Hsu's site: https://www.bonfire.com/store/arcfide/[03] 00:03:00 BQN FFI XXXXXXXXXX
[04] 00:03:58 kx download https://kx.com/developers/download-licenses/
[05] 00:04:20 kx download request mailto:[email protected]
[06] 00:05:18 Rank https://aplwiki.com/wiki/Rank
Leading Axis Theory https://aplwiki.com/wiki/Leading_axis_theory
[07] 00:06:24 Adoption in APL https://aplwiki.com/wiki/Leading_axis_theory#Adoption_in_APL
[08] 00:08:27 APL https://aplwiki.com/wiki/Main_Page
BQN https://mlochbaum.github.io/BQN/
J https://www.jsoftware.com/#/README
[09] 00:10:19 + Rank 0 https://aplwiki.com/wiki/Add
Rank operator: https://apl.wiki/Rank_(operator)
Multidimensional arrays: https://apl.wiki/Array_model
Ravel order: https://apl.wiki/Ravel_order
[10] 00:10:53 ≡ Match Rank Infinity https://aplwiki.com/wiki/Match
APL: https://tryapl.org/?clear&q=a%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20b%E2%86%903%203%E2%8D%B4%E2%8D%B36%20%E2%8B%84%20a(%E2%89%A1%E2%8D%A41)b&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=YeKGkDPigL8z4qWKMSvihpU5IOKLhCBi4oaQM+KAvzPipYoxK+KGlTYg4ouEIGEg4omh4o6JMSBi
J: https://jsoftware.github.io/j-playground/bin/html2/#code=a%3D%3A%20i.%203%203%0Ab%3D%3A%203%203%20%24%20i.%206%0Aa%20-%3A%221%20b%0A
Function rank: https://apl.wiki/Function_rank
Raze (;): https://apl.wiki/Raze
[11] 00:12:23 Rank of verb in J https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Rank of noun in J https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
[12] 00:14:50 ". Do verb https://code.jsoftware.com/wiki/Vocabulary/quotedot
[13] 00:16:05 @ Atop https://code.jsoftware.com/wiki/Vocabulary/at
[14] 00:16:10 @: At https://code.jsoftware.com/wiki/Vocabulary/atco
[15] 00:18:53 Combinators https://mlochbaum.github.io/BQN/tutorial/combinator.html
Close composition: https://apl.wiki/Close_composition
[16] 00:19:32 The J diagram of composition patterns: https://code.jsoftware.com/wiki/File:Funcomp.png
[17] 00:20:10 Scalar APL https://aplwiki.com/wiki/Scalar
J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Atom
BQN https://mlochbaum.github.io/BQN/doc/based.html#starting-from-atoms
Scalar function: https://apl.wiki/Scalar_function
Everything else: https://apl.wiki/Mixed_function
Atom: https://apl.wiki/Simple_scalar
Leading axis agreement: https://apl.wiki/Leading_axis_agreement
Scalar agreement: https://apl.wiki/Scalar_extension
[18] 00:25:50 Numpy https://numpy.org/
Julia https://julialang.org/
[19] 00:26:58 APL: https://tryapl.org/?clear&q=1%202%203(%2B%E2%8D%A41)2%203%E2%8D%B41%202%203&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=MeKAvzLigL8zK+KOiTEgMuKAvzPipYox4oC/MuKAvzM=
J: (3 3 $ 1 2 3) +"1 (1 2 3) https://jsoftware.github.io/j-playground/bin/html2/#code=%283%203%20%24%201%202%203%29%20%2B%221%20%281%202%203%29%0A
[20] 00:27:40 Reduce https://aplwiki.com/wiki/Reduce
Scan https://aplwiki.com/wiki/scan
Reverse https://aplwiki.com/wiki/reverse
Rotate https://aplwiki.com/wiki/rotate
[21] 00:33:00 ⍪ Catenate First https://aplwiki.com/wiki/Catenate
[22] 00:37:50 Major cells https://aplwiki.com/wiki/Major_cell
Cell: https://apl.wiki/Cell
"Items": https://apl.wiki/Major_cell
Arthur Whitney: https://apl.wiki/Arthur_Whitney
[23] 00:38:48 Operators and Enclosed Arrays https://www.jsoftware.com/papers/opea.htm
[24] 00:40:17 Original Iverson Notation http://www.jsoftware.com/papers/DFSP.htm
Iverson Notation: https://apl.wiki/Iverson_notation
Roger Hui: https://apl.com/Roger_Hui
[25] 00:41:32 [] Bracket Axis https://aplwiki.com/wiki/Function_axis
[26] 00:43:32 Scan https://aplwiki.com/wiki/Scan
Scan with axis: https://tryapl.org/?clear&q=%E2%8E%95IO%E2%86%900%20%E2%8B%84%20m%E2%86%903%203%E2%8D%B41%202%203%20%E2%8B%84%20(%2B%5Cm)%20(%2B%5C%5B0%5Dm)%20(%2B%E2%8D%80m)&run
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%20%24%201%202%203%0Am%3B%28%2B%2F%5C%20m%29%0A%0A
[27] 00:48:32 A Programming Language http://www.jsoftware.com/papers/APL.htm
[28] 00:51:40 BQN to APL Translation https://mlochbaum.github.io/BQN/doc/fromDyalog.html
[29] 00:52:13 ˘ Cells https://mlochbaum.github.io/BQN/help/cells.html
Breve symbol: https://en.wikipedia.org/wiki/Breve
SHARP APL: https://apl.wiki/SHARP_APL
APL2: https://apl.wiki/APL2
[30] 00:53:34 Items J https://code.jsoftware.com/wiki/Vocabulary/Nouns#Item
[31] 00:54:59 ˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
[32] 00:56:09 Catenation https://aplwiki.com/wiki/Catenate
Concatenation reduction of a matrix:
APL: https://tryapl.org/?clear&q=%2C%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsudbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=m%3D%3A%203%203%241%2Bi.9%0A%2C%2Fm
BQN with Each: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CuKIvsKoy51t
J with each: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%241%2Bi.9%0A%2C%2Feach%20m%0A
[33] 00:57:50 k language https://aplwiki.com/wiki/K
APL\360: https://apl.wiki/APL\360
[34] 01:00:34 / Insert J https://code.jsoftware.com/wiki/Vocabulary/slash
˝ Insert BQN https://mlochbaum.github.io/BQN/help/insert.html
J NuVoc: https://code.jsoftware.com/wiki/NuVoc
⌿ Reduce First APL https://aplwiki.com/wiki/Reduce
[35] 01:03:40 J for C Programmers Declarations https://www.jsoftware.com/help/jforc/declarations.htm#_Toc191734319
J for C Programmers Verbs have rank https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm#_Toc191734331
Summing rows:
APL: https://tryapl.org/?clear&q=%2B%2F3%203%E2%8D%B4%E2%8D%B39&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5CivCtMuYbQ==
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A3%203%24%3E%3Ai.9%0A%2B%2F%221%20m%0A
Summing rows of coordinate pairs:
APL: https://tryapl.org/?clear&q=m%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN with insert: https://mlochbaum.github.io/BQN/try.html#code=K8udy5gxK+KGlTPigL8z
BQN with fold: https://mlochbaum.github.io/BQN/try.html#code=K8K0y5gxK+KGlTPigL8z
J: https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%7B%3B~%3E%3Ai.3%0A%2Beach%2F%20m%0A
[36] 01:07:00 Based Arrays https://aplwiki.com/wiki/Array_model#Based_array_theory
[37] 01:08:47 http://tryapl.com https://tryapl.org/
[38] 01:09:01 iota ⍳ https://aplwiki.com/wiki/Index_Generator
[39] 01:11:20 aplcart https://aplcart.info/
[40] 01:13:30 Einstein Summation Notation https://en.wikipedia.org/wiki/Einstein_notation
einsum: https://numpy.org/doc/stable/reference/generated/numpy.einsum.html
[41] 01:15:00 Dex programming language https://github.com/google-research/dex-lang#readme
[42] 01:18:00 ⍉ Transpose https://aplwiki.com/wiki/Transpose
Mirrors:
APL: https://tryapl.org/?clear&q=M%E2%86%903%203%E2%8D%B4%E2%8D%B39%20%E2%8B%84%20m%20(%E2%8A%96m)%20(%E2%8C%BDm)&run
BQN: https://mlochbaum.github.io/BQN/try.html#code=beKGkDPigL8z4qWKMSvihpU5IOKLhCDin6htLOKMvW0s4oy9y5ht4p+p
J:https://jsoftware.github.io/j-playground/bin/html2/#code=%0Am%3D%3A%3E%3Ai.%203%203%0A%28%5D%20%3B%20%7C.%20%3B%20%7C.%221%29%20m%0A
[43] 01:20:00 BQN ⊸ Before https://mlochbaum.github.io/BQN/help/before_bind.html
⟜ After https://mlochbaum.github.io/BQN/help/after_bind.html
Conor's number of permutations tweet: https://twitter.com/code_report/status/1528844402046685187
Combinators: https://apl.wiki/Function_composition
[44] 01:31:30 Joel Kaplan on the ArrayCast https://www.arraycast.com/episodes/episode27-joel-kaplan