https://github.com/codereport/array-language-comparisons

A comparison of array languages & libraries: APL, J, BQN, Uiua, Q, Julia, R, NumPy, Nial, Futhark, Dex, Ivy, SaC & ArrayFire.
https://github.com/codereport/array-language-comparisons

Last synced: 4 months ago
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A comparison of array languages & libraries: APL, J, BQN, Uiua, Q, Julia, R, NumPy, Nial, Futhark, Dex, Ivy, SaC & ArrayFire.

• Host: GitHub
• URL: https://github.com/codereport/array-language-comparisons
• Owner: codereport
• License: mit
• Created: 2022-08-15T17:36:51.000Z (almost 4 years ago)
• Default Branch: main
• Last Pushed: 2025-02-01T03:54:12.000Z (over 1 year ago)
• Last Synced: 2025-02-01T04:27:02.390Z (over 1 year ago)
• Language: Cuda
• Homepage:
• Size: 199 KB
• Stars: 163
• Watchers: 5
• Forks: 8
• Open Issues: 6
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# 
Array Language & Library Comparisons




    

        

    

                

    

        

    

        

    

        



![image](https://github.com/codereport/array-language-comparisons/assets/36027403/13f7164e-d9ea-4c7c-a211-bd437d51949c)

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](http://www.rosettacode.org/wiki/Rosetta_Code) |                   [BQN-Dyalog Dictionary](https://mlochbaum.github.io/BQN/doc/fromDyalog.html)                   | [ArrayFire-MATLAB-NumPy](https://github.com/arrayfire/arrayfire-api-cheat-sheet/blob/master/api_equiv_matlab_python.md) |

|    [Programming-Idioms](https://programming-idioms.org/)     |                   [BQN-Dyalog Dictionary](https://mlochbaum.github.io/BQN/doc/fromDyalog.html)                   |        [ArrayFire-Eigen](https://github.com/arrayfire/arrayfire-api-cheat-sheet/blob/master/api_equiv_eigen.md)         |

|                                                              |                       [J-Dyalog APL Rosetta](http://sigapl.org/_J-Dyalog_APL_Rosetta.html)                       |            [ArrayFire-Numpy](https://arrayfire.com/wp-content/uploads/2012/05/Matrix_WP_ArrayFire_2017.pdf)             |

|                                                              | [Q-APL Dictionary](https://github.com/codereport/The_Q_Programming_Language/blob/master/Q-Built-in-Functions.md) |                          [MatX-MATALB-NumPy](https://nvidia.github.io/MatX/matlabpython.html)                           |

### Language / Library Websites

|       |  Language  |   💲   |                                     Main Website                                     |                                 Help / Docs                                 |                             Online REPL                              |

| :---: | :--------: | :---: | :----------------------------------------------------------------------------------: | :-------------------------------------------------------------------------: | :------------------------------------------------------------------: |

|   💚   | Dyalog APL |       |                        [dyalog.com](https://www.dyalog.com/)                         |                [Dyalog Help](https://help.dyalog.com/18.2/)                 |                    [TryAPL](https://tryapl.org/)                     |

|   💛   |    Kap     |       |         [kapdemo.dhsdevelopments.com](https://kapdemo.dhsdevelopments.com/)          |        [Kap Ref](https://kapdemo.dhsdevelopments.com/reference.html)        |  [Kap Interpreter](https://kapdemo.dhsdevelopments.com/clientweb2/)  |

|   💛   |  TinyAPL   |       |               [tinyapl.rubenverg.com](https://tinyapl.rubenverg.com/)                |      [TinAPL Primitives](https://tinyapl.rubenverg.com/docs/primitive)      |       [Online REPL](https://tinyapl.rubenverg.com/run/latest/)       |

|   💚   |     J      |       |                     [jsoftware.com](https://www.jsoftware.com/)                      |              [J NuVoc](https://code.jsoftware.com/wiki/NuVoc)               | [J Playground](https://jsoftware.github.io/j-playground/bin/html2/#) |

|   💚   |    BQN     |       |             [mlochbaum.github.io/BQN](https://mlochbaum.github.io/BQN/)              |         [BQN Docs](https://mlochbaum.github.io/BQN/doc/index.html)          |             [BQNPAD](https://bqnpad.mechanize.systems/)              |

|   💚   |    Uiua    |       |                          [uiua.org](https://www.uiua.org/)                           |                   [Uiua Docs](https://www.uiua.org/docs)                    |                 [UiuaPAD](https://www.uiua.org/pad)                  |

|   💚   |     Q      |   💲   |                       [code.kx.com/q](https://code.kx.com/q/)                        |           [Q Ref](https://code.kx.com/q4m3/A_Built-in_Functions/)           |                                  ⛔                                   |

|   💙   |   Julia    |       |                       [julialang.org](https://julialang.org/)                        |               [Julia Docs](https://docs.julialang.org/en/v1/)               |          [Replit](https://julialang.org/learning/tryjulia/)          |

|   💙   |   MATLAB   |   💲   | [mathworks.com/products/matlab.html](https://www.mathworks.com/products/matlab.html) |            [MATLAB Help](https://www.mathworks.com/help/matlab/)            |                                  💲                                   |

|   💙   |   NumPy*   |       |                           [numpy.org](https://numpy.org/)                            |                 [NumPy Docs](https://numpy.org/doc/stable/)                 |            [Replit](https://replit.com/languages/python3)            |

|   💙   |     R      |       |                     [r-project.org](https://www.r-project.org/)                      |                  [R Docs](https://www.rdocumentation.org/)                  |         [JDoodle](https://www.jdoodle.com/execute-r-online/)         |

|   💜   |    Nial    |       |           [nial-array-language.org](https://www.nial-array-language.org/)            | [Nial Dictionary](https://www.nial-array-language.org/ndocs/NialDict2.html) |                     [TIO](https://tio.run/#Nial)                     |

|   💜   |  Futhark   |       |                    [futhark-lang.org](https://futhark-lang.org/)                     |             [Futhark Docs](https://futhark-lang.org/docs.html)              |                                  ⛔                                   |

|   💜   |    Dex     |       |  [github.com/google-research/dex-lang](https://github.com/google-research/dex-lang)  |       [InDex](https://google-research.github.io/dex-lang/index.html)        |                                  ⛔                                   |

|   💜   |    Ivy     |       |            [pkg.go.dev/robpike.io/ivy](https://pkg.go.dev/robpike.io/ivy)            |     [Ivy Docs](https://pkg.go.dev/robpike.io/ivy#section-documentation)     |                                  ⛔                                   |

|  💜💗   |    SaC     |       |                      [sac-home.org](https://www.sac-home.org/)                       |               [SaC Docs](https://www.sac-home.org/docs:main)                |                                  ⛔                                   |

|   💗   | ArrayFire* |       |                       [arrayfire.com](https://arrayfire.com/)                        |                [ArrayFire Docs](https://arrayfire.org/docs/)                |                                  ⛔                                   |

|   💗   |   MatX*    |       |          [nvidia.github.io/MatX](https://nvidia.github.io/MatX/index.html)           |                    [MatX API Ref](nvidia.github.io/MatX)                    |                                  ⛔                                   |

|   💗   |   ATen*    |       |                                          -                                           |               [ATen Docs](https://pytorch.org/cppdocs/#aten)                |                                  ⛔                                   |

|   💗   |   Eigen*   |       |                 [eigen.tuxfamily.org](https://eigen.tuxfamily.org/)                  |                [Eigen Dox](https://eigen.tuxfamily.org/dox/)                |                   [Godbolt](https://godbolt.org/)                    |

\* 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](https://aplwiki.com/wiki/Leading_axis_theory)

   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   |

|  TinyAPL  |   💚   |        0        |   `LA`    | `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   |

6. Length of Array (Leading Axis)

7. Shape of Array

8. Rank of Array

9. Number of Elements in Array

|           |       6        |      7       |         8         |          9           |

| :-------: | :------------: | :----------: | :---------------: | :------------------: |

|    APL    |      `≢`       |     `⍴`      |       `⍴⍴`        |        `×/⍴`         |

|    Kap    |      `≢`       |     `⍴`      |       `⍴⍴`        |        `×/⍴`         |

|  TinyAPL  |      `≢`       |     `⍴`      |        `ϼ`        |        `×⍆⍴`         |

|     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](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/matrix_identity.md)

2. [Creating an Iota Matrix](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/matrix_iota.md)

3. [Reversing a Matrix Row-wise, Column-wise and in Memory](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/matrix_reversing.md)

4. [Summing a Matrix Row-wise, Column-wise and Down to a Scalar](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/matrix_summing.md)

### Leetcode / PWC Problems

|   #   |       | Problem                                                                                                                                                              |                                                    :video_camera:                                                    |

| :---: | :---: | :------------------------------------------------------------------------------------------------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------: |

|   1   |   💛   | [P0485 - MCO (Max Consecutive Ones)](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P0485_MCO.md)                           |                                                          -                                                           |

|   2   |   💚   | [P1351 - Count Negatives](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P1351_Count_Negatives.md)                          |                           [YouTube Solution](https://www.youtube.com/watch?v=MKb4WD6mioE)                            |

|   3   |   💛   | [P1614 - Maximum Nesting Depth of the Parentheses](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P1614_Max_Paren_Depth.md) | [YouTube Solution](https://www.youtube.com/watch?v=zrOIQEN3Wkk) \| [II](https://www.youtube.com/watch?v=6-mk6OpcUdM) |

|   4   |   💚   | [P1672 - Richest Customer Wealth](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P1672_Richest_Customer_Wealth.md)          |                           [YouTube Solution](https://www.youtube.com/watch?v=MKb4WD6mioE)                            |

|   5   |   💚   | [P1822 - Sign of the Product of Array](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P1822_Sign_Product_Array.md)          |                           [YouTube Solution](https://www.youtube.com/watch?v=a7CSK7HNEWQ)                            |

|   6   |   💛   | [P2319 - Check if Matrix Is X-Matrix](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P2319_Check_Matrix.md)                 |                           [YouTube Solution](https://www.youtube.com/watch?v=8ynsN4nJxzU)                            |

|   7   |   💛   | [P0674 - LCIS (Longest Continuous Increasing Subsequence)](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P0674_LCIS.md)    |                                                          -                                                           |

|   8   |   💛   | [P00064 - Maixmum Gap](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/leetcode/P0064_Max_Gap.md)                                     |                                                          -                                                           |

|   9   |   💛   | [PWC198 P1 - Maximum Gap Count](https://github.com/codereport/array-language-comparisons/blob/main/comparisons/pwc/PWC198_P1_Max_Gap_Count.md)                       |                                                          -                                                           |

* 💚 = All solutions complete

* 💛 = Some solutions missing

#### Progress

| Language  |  1a   |  1b   |   2   |   3   |   4   |   5   |   6   |   7   |   8   |   9   |

| :-------: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |

|    APL    |   💚   |   ⛔   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|    Kap    |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|  TinyAPL  |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|     J     |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|    BQN    |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|   Uiua    |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|     Q     |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |

|   Julia   |   ⛔   |   💚   |   💚   |   ⛔   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|  MATLAB   |   🔜   |   ⛔   |   💚   |   ⛔   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|   NumPy   |   💚   |   💚   |   💚   |   ⛔   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|     R     |   🔜   |   💚   |   💚   |   🔜   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|   Nial    |   💚   |   ⛔   |   💚   |   💚   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|  Futhark  |   🔜   |   💚   |   💚   |   💚   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|    Dex    |   ⛔   |   ⛔   |   💚   |   ⛔   |   💚   |   💚   |   🔜   |   ⛔   |

|    Ivy    |   ⛔   |   ⛔   |   💚   |   💚   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|    SaC    |   🔜   |   🔜   |   💚   |   🔜   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

| ArrayFire |   🔜   |   🔜   |   💚   |   🔜   |   💚   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |

|   MatX    |   🔜   |   🔜   |   💚   |   🔜   |   💚   |   💚   |   🔜   |   🔜   |   🔜   |   🔜   |