Array Language & Library Comparisons

This is a collection of idioms and small programs in APL, J, BQN, Julia, R, NumPy, Nial, Futhark & SaC.

There are several sites that do these kinds of comparisons:

General	Array Language Specific	Array Library Specific
Rosetta Code	BQN-Dyalog Dictionary	ArrayFire-MATLAB-NumPy
Programming-Idioms	BQN-Dyalog Dictionary	ArrayFire-Eigen
	J-Dyalog APL Rosetta	ArrayFire-Numpy
	Q-APL Dictionary	MatX-MATALB-NumPy

Language / Library Websites

	Language	💲	Main Website	Help / Docs	Online REPL
💚	Dyalog APL		dyalog.com	Dyalog Help	TryAPL
💛	Kap		kapdemo.dhsdevelopments.com	Kap Ref	Kap Interpreter
💚	J		jsoftware.com	J NuVoc	J Playground
💚	BQN		mlochbaum.github.io/BQN	BQN Docs	BQNPAD
💚	Uiua		uiua.org	Uiua Docs	UiuaPAD
💚	Q	💲	code.kx.com/q	Q Ref	🚫
💙	Julia		julialang.org	Julia Docs	Replit
💙	MATLAB	💲	mathworks.com/products/matlab.html	MATLAB Help	💲
💙	NumPy*		numpy.org	NumPy Docs	Replit
💙	R		r-project.org	R Docs	JDoodle
💜	Nial		nial-array-language.org	Nial Dictionary	TIO
💜	Futhark		futhark-lang.org	Futhark Docs	🚫
💜	Dex		github.com/google-research/dex-lang	InDex	🚫
💜	Ivy		pkg.go.dev/robpike.io/ivy	Ivy Docs	🚫
💜💗	SaC		sac-home.org	SaC Docs	🚫
💗	ArrayFire*		arrayfire.com	ArrayFire Docs	🚫
💗	MatX*		nvidia.github.io/MatX	MatX API Ref	🚫
💗	ATen*		-	ATen Docs	🚫
💗	Eigen*		eigen.tuxfamily.org	Eigen Dox	Godbolt

* Library, not an actual language

• 💚 Main (APL-Family) Array Languages
• 💛 Fringe (APL-Family) Array Languages
• 💙 Main (Non-APL-Family) Array Languages
• 💜 Fringe / Research Array Languages
• 💗 Array Compiler Backends / Array Libraries

Comparisons

1. REPL
2. Index Base
3. Axis/Rank Model
   1. LA = Leading Axis
   2. TA = Trailing Axis
   3. AA = Axis Agnostic
4. Application Model
   1. () = Parentheses
   2. LR = Left to Right
   3. RL = Right to Left
5. Row-major or Column-Major

	1	2	3	4	5
APL	💚	1 (or ⎕IO)	LA/TA	RL	Row
Kap	💚	0	LA/TA	RL	Row
J	💚	0	LA	RL	Row
BQN	💚	0	LA	RL	Row
Uiua	💚	0	LA	RL	Row
Q	💛	0	🚫	RL	Row
Julia	💚	1	AA	()	Column
MATLAB	💚	1	LA	()	Column
NumPy	💚	0	AA	()	Row
R	💚	1	AA	()	Column
Nial	💛	1	AA	LR	Row
Futhark	💛	0	🚫	LR	Row
Dex	💛	0		()
Ivy	💛	1 (or origin)	🚫	RL	Row
SaC	🚫	0	LA	()	Row
ArrayFire	🚫	0	LA	()	Column
MatX	🚫	0	LA	()	Row

1. Length of Array (Leading Axis)
2. Shape of Array
3. Rank of Array
4. Number of Elements in Array

	6	7	8	9
APL	≢	⍴	⍴⍴	×/⍴
Kap	≢	⍴	⍴⍴	×/⍴
J	#	$	$$	*/@$
BQN	≠	≢	≢≢	×´≢
Uiua	⧻	△	⧻△	⧻♭
Q	count	🚫	🚫	count raze
Julia	size(a, 1)	size(a)	ndims(a)	length(a)
MATLAB	length(a)	size(a)	rank(a)	numel(a)
NumPy	len(a)	a.shape	np.ndim(a)	a.size
R	dim(a)[1]	dim(a)	length(dim(a))	length(a)
Nial	first shape	shape	valence	tally
Futhark	length	🚫	🚫	flatten |> length
Dex	size*	🚫	🚫
Ivy	1 take rho	rho	rho rho	rho ,
SaC	shape(a)[0]	shape(a)	shape(shape(a))	prod(shape(a))
ArrayFire	a.dims()[0]	a.dims()*	a.numdims()*	a.elements()
MatX	a.Shape()[0]	a.Shape()	a.Rank()	TotalSize(a)

💛 Means the REPL has certain limitations

• Q REPL has no HOME, END, or any arrows (CTRL or not)
• Nial REPL has no CTRL left or right arrow
• Futhark REPL has no HOME, END, or DEL
• Dex REPL as no UP, DOWN and does not work with rlwrap

If you are using Q, Nial, Futhark or other languages with REPL limitations, you can get around this by invoking with rlwrap. On Linux using the Q REPL:

sudo apt install rlwrap
rlwrap taskset -c 2 ./q

Note that even when using rlwrap, some of the limitations will remain (such as CTRL + arrows).

Other Comparisons

1. Creating an Identity Matrix
2. Creating an Iota Matrix
3. Reversing a Matrix Row-wise, Column-wise and in Memory
4. Summing a Matrix Row-wise, Column-wise and Down to a Scalar

Leetcode / PWC Problems

#		Problem	📹
1	💛	P0485 - MCO (Max Consecutive Ones)	-
2	💚	P1351 - Count Negatives	YouTube Solution
3	💛	P1614 - Maximum Nesting Depth of the Parentheses	YouTube Solution | II
4	💚	P1672 - Richest Customer Wealth	YouTube Solution
5	💚	P1822 - Sign of the Product of Array	YouTube Solution
6	💛	P2319 - Check if Matrix Is X-Matrix	YouTube Solution
7	💛	P0674 - LCIS (Longest Continuous Increasing Subsequence)	-
8	💛	P00064 - Maixmum Gap	-
9	💛	PWC198 P1 - Maximum Gap Count	-

• 💚 = All solutions complete
• 💛 = Some solutions missing

Progress

Language	1a	1b	2	3	4	5	6	7	8	9
APL	💚	🚫	💚	💚	💚	💚	💚	💚	💚	💚
Kap	💚	💚	💚	💚	💚	💚	💚	💚	💚	💚
J	💚	💚	💚	💚	💚	💚	💚	💚	💚	💚
BQN	💚	💚	💚	💚	💚	💚	💚	💚	💚	💚
Uiua	💚	💚	💚	💚	💚	💚	💚	💚	💚	💚
Q	💚	💚	💚	💚	💚	💚	💚	💚	💚	💚
Julia	🚫	💚	💚	🚫	💚	💚	💚	🔜	🔜	🔜
MATLAB	🔜	🚫	💚	🚫	💚	💚	💚	🔜	🔜	🔜
NumPy	💚	💚	💚	🚫	💚	💚	💚	🔜	🔜	🔜
R	🔜	💚	💚	🔜	💚	💚	💚	🔜	🔜	🔜
Nial	💚	🚫	💚	💚	💚	💚	💚	🔜	🔜	🔜
Futhark	🔜	💚	💚	💚	💚	💚	💚	🔜	🔜	🔜
Dex	🚫	🚫	💚	🚫	💚	💚	🔜	🚫
Ivy	🚫	🚫	💚	💚	💚	💚	💚	🔜	🔜	🔜
SaC	🔜	🔜	💚	🔜	💚	💚	💚	🔜	🔜	🔜
ArrayFire	🔜	🔜	💚	🔜	💚	💚	💚	🔜	🔜	🔜
MatX	🔜	🔜	💚	🔜	💚	💚	🔜	🔜	🔜	🔜