├── .github
└── workflows
│ └── deploy.yaml
├── .gitignore
├── .nojeklyll
├── 01_APL.ipynb
├── 02_functions.ipynb
├── 03_operators.ipynb
├── 04_competition.ipynb
├── 05_the_rest.ipynb
├── LICENSE
├── MANIFEST.in
├── README.md
├── _quarto.yml
├── aplstudy
├── __init__.py
└── _modidx.py
├── index.ipynb
├── nbdev.yml
├── python.ipynb
├── settings.ini
├── setup.py
├── sidebar.yml
├── styles.css
└── www
├── SAX2.ttf
└── SAX2.woff2
/.github/workflows/deploy.yaml:
--------------------------------------------------------------------------------
1 | name: Deploy to GitHub Pages
2 | on:
3 | push:
4 | branches: [master]
5 | workflow_dispatch:
6 | jobs:
7 | deploy:
8 | runs-on: ubuntu-latest
9 | steps:
10 | - uses: fastai/workflows/quarto-ghp@master
11 | with: {pre: 1}
12 |
--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
1 | _proc/
2 | _docs/
3 | .DS_Store
4 | *.bak
5 | .gitattributes
6 | .last_checked
7 | .gitconfig
8 | *.bak
9 | *.log
10 | *~
11 | ~*
12 | _tmp*
13 | tmp*
14 | tags
15 | *.pkg
16 |
17 | # Byte-compiled / optimized / DLL files
18 | __pycache__/
19 | *.py[cod]
20 | *$py.class
21 |
22 | # C extensions
23 | *.so
24 |
25 | # Distribution / packaging
26 | .Python
27 | env/
28 | build/
29 | develop-eggs/
30 | dist/
31 | downloads/
32 | eggs/
33 | .eggs/
34 | lib/
35 | lib64/
36 | parts/
37 | sdist/
38 | var/
39 | wheels/
40 | *.egg-info/
41 | .installed.cfg
42 | *.egg
43 |
44 | # PyInstaller
45 | # Usually these files are written by a python script from a template
46 | # before PyInstaller builds the exe, so as to inject date/other infos into it.
47 | *.manifest
48 | *.spec
49 |
50 | # Installer logs
51 | pip-log.txt
52 | pip-delete-this-directory.txt
53 |
54 | # Unit test / coverage reports
55 | htmlcov/
56 | .tox/
57 | .coverage
58 | .coverage.*
59 | .cache
60 | nosetests.xml
61 | coverage.xml
62 | *.cover
63 | .hypothesis/
64 |
65 | # Translations
66 | *.mo
67 | *.pot
68 |
69 | # Django stuff:
70 | *.log
71 | local_settings.py
72 |
73 | # Flask stuff:
74 | instance/
75 | .webassets-cache
76 |
77 | # Scrapy stuff:
78 | .scrapy
79 |
80 | # Sphinx documentation
81 | docs/_build/
82 |
83 | # PyBuilder
84 | target/
85 |
86 | # Jupyter Notebook
87 | .ipynb_checkpoints
88 |
89 | # pyenv
90 | .python-version
91 |
92 | # celery beat schedule file
93 | celerybeat-schedule
94 |
95 | # SageMath parsed files
96 | *.sage.py
97 |
98 | # dotenv
99 | .env
100 |
101 | # virtualenv
102 | .venv
103 | venv/
104 | ENV/
105 |
106 | # Spyder project settings
107 | .spyderproject
108 | .spyproject
109 |
110 | # Rope project settings
111 | .ropeproject
112 |
113 | # mkdocs documentation
114 | /site
115 |
116 | # mypy
117 | .mypy_cache/
118 |
119 | .vscode
120 | *.swp
121 |
122 | # osx generated files
123 | .DS_Store
124 | .DS_Store?
125 | .Trashes
126 | ehthumbs.db
127 | Thumbs.db
128 | .idea
129 |
130 | # pytest
131 | .pytest_cache
132 |
133 | # tools/trust-doc-nbs
134 | docs_src/.last_checked
135 |
136 | # symlinks to fastai
137 | docs_src/fastai
138 | tools/fastai
139 |
140 | # link checker
141 | checklink/cookies.txt
142 |
143 | # .gitconfig is now autogenerated
144 | .gitconfig
145 |
146 |
147 | /.quarto/
148 |
--------------------------------------------------------------------------------
/.nojeklyll:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/fastai/apl-study/115c5b1468823884889b3eb966ceaf2acfc68266/.nojeklyll
--------------------------------------------------------------------------------
/02_functions.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "raw",
5 | "id": "2990f581",
6 | "metadata": {},
7 | "source": [
8 | "---\n",
9 | "title: \"First functions\"\n",
10 | "author: \"Jeremy Howard\"\n",
11 | "date: \"2022-07-05\"\n",
12 | "categories: [Dyalog, APL, Glyphs]\n",
13 | "---"
14 | ]
15 | },
16 | {
17 | "cell_type": "code",
18 | "execution_count": null,
19 | "id": "84e8fa35",
20 | "metadata": {},
21 | "outputs": [
22 | {
23 | "data": {
24 | "text/html": [
25 | "┌→─────────────────────────────────────┐\n",
26 | "│Was ON -style=max -trains=tree -fns=on│\n",
27 | "└──────────────────────────────────────┘\n",
28 | "
"
29 | ]
30 | },
31 | "execution_count": null,
32 | "metadata": {},
33 | "output_type": "execute_result"
34 | }
35 | ],
36 | "source": [
37 | "]box on -style=max -trains=tree -fns=on"
38 | ]
39 | },
40 | {
41 | "cell_type": "markdown",
42 | "id": "2dbbce67",
43 | "metadata": {},
44 | "source": [
45 | "## Boolean"
46 | ]
47 | },
48 | {
49 | "cell_type": "markdown",
50 | "id": "71f403e7",
51 | "metadata": {},
52 | "source": [
53 | "### `=` (Equal sign)"
54 | ]
55 | },
56 | {
57 | "cell_type": "markdown",
58 | "id": "2df02fe7",
59 | "metadata": {},
60 | "source": [
61 | "#### dyadic `=` (Equal to)"
62 | ]
63 | },
64 | {
65 | "cell_type": "markdown",
66 | "id": "22de5339-feeb-4050-8fd2-c49604d38546",
67 | "metadata": {},
68 | "source": [
69 | "`=` is equal and returns a boolean (true/false). 1 means true, 0 means false."
70 | ]
71 | },
72 | {
73 | "cell_type": "code",
74 | "execution_count": null,
75 | "id": "f9a1f4c0",
76 | "metadata": {},
77 | "outputs": [
78 | {
79 | "data": {
80 | "text/html": [
81 | " \n",
82 | "1\n",
83 | " \n",
84 | "
"
85 | ]
86 | },
87 | "execution_count": null,
88 | "metadata": {},
89 | "output_type": "execute_result"
90 | }
91 | ],
92 | "source": [
93 | "1 = 1"
94 | ]
95 | },
96 | {
97 | "cell_type": "markdown",
98 | "id": "2dbd9b1e-f7dd-43ef-9198-42210c33f7f6",
99 | "metadata": {},
100 | "source": [
101 | "`=` works elementwise and will broadcast as needed."
102 | ]
103 | },
104 | {
105 | "cell_type": "code",
106 | "execution_count": null,
107 | "id": "e494be50",
108 | "metadata": {},
109 | "outputs": [
110 | {
111 | "data": {
112 | "text/html": [
113 | "┌→──┐\n",
114 | "│1 0│\n",
115 | "└~──┘\n",
116 | "
"
117 | ]
118 | },
119 | "execution_count": null,
120 | "metadata": {},
121 | "output_type": "execute_result"
122 | }
123 | ],
124 | "source": [
125 | "1 = 1 2"
126 | ]
127 | },
128 | {
129 | "cell_type": "code",
130 | "execution_count": null,
131 | "id": "d31b5778",
132 | "metadata": {},
133 | "outputs": [
134 | {
135 | "data": {
136 | "text/html": [
137 | "┌→──┐\n",
138 | "│1 1│\n",
139 | "└~──┘\n",
140 | "
"
141 | ]
142 | },
143 | "execution_count": null,
144 | "metadata": {},
145 | "output_type": "execute_result"
146 | }
147 | ],
148 | "source": [
149 | "1 = 1 1"
150 | ]
151 | },
152 | {
153 | "cell_type": "markdown",
154 | "id": "2fbb3372-ec47-45a7-9c0f-0c5264207eaf",
155 | "metadata": {},
156 | "source": [
157 | "We can also compare characters"
158 | ]
159 | },
160 | {
161 | "cell_type": "code",
162 | "execution_count": null,
163 | "id": "8d9ff9d7",
164 | "metadata": {},
165 | "outputs": [
166 | {
167 | "data": {
168 | "text/html": [
169 | "┌→──────────┐\n",
170 | "│0 1 0 1 0 1│\n",
171 | "└~──────────┘\n",
172 | "
"
173 | ]
174 | },
175 | "execution_count": null,
176 | "metadata": {},
177 | "output_type": "execute_result"
178 | }
179 | ],
180 | "source": [
181 | "'Banana' = 'aaaaaa'"
182 | ]
183 | },
184 | {
185 | "cell_type": "code",
186 | "execution_count": null,
187 | "id": "0077e614",
188 | "metadata": {},
189 | "outputs": [
190 | {
191 | "data": {
192 | "text/html": [
193 | "┌→──────────┐\n",
194 | "│0 1 0 1 0 1│\n",
195 | "└~──────────┘\n",
196 | "
"
197 | ]
198 | },
199 | "execution_count": null,
200 | "metadata": {},
201 | "output_type": "execute_result"
202 | }
203 | ],
204 | "source": [
205 | "'Banana' = 'a'"
206 | ]
207 | },
208 | {
209 | "cell_type": "code",
210 | "execution_count": null,
211 | "id": "aa551f28",
212 | "metadata": {},
213 | "outputs": [
214 | {
215 | "data": {
216 | "text/html": [
217 | "┌→──────────────────────────────────────┐\n",
218 | "│ ┌→──────────┐ ┌→────────┐ ┌→────────┐ │\n",
219 | "│ │0 1 0 1 0 1│ │0 0 0 0 0│ │0 1 0 0 0│ │\n",
220 | "│ └~──────────┘ └~────────┘ └~────────┘ │\n",
221 | "└∊──────────────────────────────────────┘\n",
222 | "
"
223 | ]
224 | },
225 | "execution_count": null,
226 | "metadata": {},
227 | "output_type": "execute_result"
228 | }
229 | ],
230 | "source": [
231 | "'Banana' 'Apple' 'Candy' = 'a'"
232 | ]
233 | },
234 | {
235 | "cell_type": "markdown",
236 | "id": "12b33beb",
237 | "metadata": {},
238 | "source": [
239 | "### `≠` (Not equal)"
240 | ]
241 | },
242 | {
243 | "cell_type": "markdown",
244 | "id": "3b0b6323",
245 | "metadata": {},
246 | "source": [
247 | "#### monadic `≠` (Unique Mask)"
248 | ]
249 | },
250 | {
251 | "cell_type": "markdown",
252 | "id": "5a19caf7-f061-44da-99c0-7495223a1812",
253 | "metadata": {},
254 | "source": [
255 | "Monadic `≠` returns 1 on the first occurrence of an item in an array."
256 | ]
257 | },
258 | {
259 | "cell_type": "code",
260 | "execution_count": null,
261 | "id": "0d283400",
262 | "metadata": {},
263 | "outputs": [
264 | {
265 | "data": {
266 | "text/html": [
267 | "┌→──────────────┐\n",
268 | "│1 1 0 0 1 0 1 0│\n",
269 | "└~──────────────┘\n",
270 | "
"
271 | ]
272 | },
273 | "execution_count": null,
274 | "metadata": {},
275 | "output_type": "execute_result"
276 | }
277 | ],
278 | "source": [
279 | "≠22 10 22 22 21 10 5 10"
280 | ]
281 | },
282 | {
283 | "cell_type": "code",
284 | "execution_count": null,
285 | "id": "1b52166b",
286 | "metadata": {},
287 | "outputs": [
288 | {
289 | "data": {
290 | "text/html": [
291 | "┌→──────────┐\n",
292 | "│1 1 1 0 0 0│\n",
293 | "└~──────────┘\n",
294 | "
"
295 | ]
296 | },
297 | "execution_count": null,
298 | "metadata": {},
299 | "output_type": "execute_result"
300 | }
301 | ],
302 | "source": [
303 | "≠ 'Banana'"
304 | ]
305 | },
306 | {
307 | "cell_type": "code",
308 | "execution_count": null,
309 | "id": "84ed720d",
310 | "metadata": {},
311 | "outputs": [
312 | {
313 | "data": {
314 | "text/html": [
315 | "┌→────────────────────┐\n",
316 | "│1 1 1 0 0 0 0 0 1 0 0│\n",
317 | "└~────────────────────┘\n",
318 | "
"
319 | ]
320 | },
321 | "execution_count": null,
322 | "metadata": {},
323 | "output_type": "execute_result"
324 | }
325 | ],
326 | "source": [
327 | "≠ 'Mississippi'"
328 | ]
329 | },
330 | {
331 | "cell_type": "markdown",
332 | "id": "ec2830de",
333 | "metadata": {},
334 | "source": [
335 | "#### dyadic `≠` (Not Equal To)"
336 | ]
337 | },
338 | {
339 | "cell_type": "markdown",
340 | "id": "a062070b-2923-4a0b-b964-df59052f23ed",
341 | "metadata": {},
342 | "source": [
343 | "Dyadic `≠` returns true (1) if elements are not equal, and false (0) if elements are equal. "
344 | ]
345 | },
346 | {
347 | "cell_type": "code",
348 | "execution_count": null,
349 | "id": "21b37853",
350 | "metadata": {},
351 | "outputs": [
352 | {
353 | "data": {
354 | "text/html": [
355 | "┌→────┐\n",
356 | "│1 0 1│\n",
357 | "└~────┘\n",
358 | "
"
359 | ]
360 | },
361 | "execution_count": null,
362 | "metadata": {},
363 | "output_type": "execute_result"
364 | }
365 | ],
366 | "source": [
367 | "1 2 3 ≠ 4 2 ¯1"
368 | ]
369 | },
370 | {
371 | "cell_type": "markdown",
372 | "id": "5e01edbc-b54f-458b-a3ac-2b6ad344ae54",
373 | "metadata": {},
374 | "source": [
375 | "The number 7 and the character 7 are not equal."
376 | ]
377 | },
378 | {
379 | "cell_type": "code",
380 | "execution_count": null,
381 | "id": "7b1f2164",
382 | "metadata": {},
383 | "outputs": [
384 | {
385 | "data": {
386 | "text/html": [
387 | " \n",
388 | "1\n",
389 | " \n",
390 | "
"
391 | ]
392 | },
393 | "execution_count": null,
394 | "metadata": {},
395 | "output_type": "execute_result"
396 | }
397 | ],
398 | "source": [
399 | "7 ≠ '7'"
400 | ]
401 | },
402 | {
403 | "cell_type": "markdown",
404 | "id": "2d5dfcd5",
405 | "metadata": {},
406 | "source": [
407 | "### `<` (Less than sign)"
408 | ]
409 | },
410 | {
411 | "cell_type": "markdown",
412 | "id": "4277bc63",
413 | "metadata": {},
414 | "source": [
415 | "#### dyadic `<` (Less than)"
416 | ]
417 | },
418 | {
419 | "cell_type": "code",
420 | "execution_count": null,
421 | "id": "b3c6be5e",
422 | "metadata": {},
423 | "outputs": [
424 | {
425 | "data": {
426 | "text/html": [
427 | "┌→────┐\n",
428 | "│1 0 0│\n",
429 | "└~────┘\n",
430 | "
"
431 | ]
432 | },
433 | "execution_count": null,
434 | "metadata": {},
435 | "output_type": "execute_result"
436 | }
437 | ],
438 | "source": [
439 | "1 2 3 < 4 2 ¯1"
440 | ]
441 | },
442 | {
443 | "cell_type": "code",
444 | "execution_count": null,
445 | "id": "61f6c499",
446 | "metadata": {},
447 | "outputs": [
448 | {
449 | "data": {
450 | "text/html": [
451 | "┌→────┐\n",
452 | "│1 0 0│\n",
453 | "└~────┘\n",
454 | "
"
455 | ]
456 | },
457 | "execution_count": null,
458 | "metadata": {},
459 | "output_type": "execute_result"
460 | }
461 | ],
462 | "source": [
463 | "1 2 3 < 2"
464 | ]
465 | },
466 | {
467 | "cell_type": "markdown",
468 | "id": "3bd3a0ea",
469 | "metadata": {},
470 | "source": [
471 | "### `>` (Greater than sign)"
472 | ]
473 | },
474 | {
475 | "cell_type": "markdown",
476 | "id": "b487022a",
477 | "metadata": {},
478 | "source": [
479 | "#### dyadic `>` (Greater than)"
480 | ]
481 | },
482 | {
483 | "cell_type": "code",
484 | "execution_count": null,
485 | "id": "ed7bc01e",
486 | "metadata": {},
487 | "outputs": [
488 | {
489 | "data": {
490 | "text/html": [
491 | "┌→────┐\n",
492 | "│0 0 1│\n",
493 | "└~────┘\n",
494 | "
"
495 | ]
496 | },
497 | "execution_count": null,
498 | "metadata": {},
499 | "output_type": "execute_result"
500 | }
501 | ],
502 | "source": [
503 | "1 2 3 > 4 2 ¯1"
504 | ]
505 | },
506 | {
507 | "cell_type": "code",
508 | "execution_count": null,
509 | "id": "b68ae705",
510 | "metadata": {},
511 | "outputs": [
512 | {
513 | "data": {
514 | "text/html": [
515 | "┌→────┐\n",
516 | "│0 0 1│\n",
517 | "└~────┘\n",
518 | "
"
519 | ]
520 | },
521 | "execution_count": null,
522 | "metadata": {},
523 | "output_type": "execute_result"
524 | }
525 | ],
526 | "source": [
527 | "1 2 3 > 2"
528 | ]
529 | },
530 | {
531 | "cell_type": "markdown",
532 | "id": "903c506f",
533 | "metadata": {},
534 | "source": [
535 | "### `≤` (Less than or equal to sign)"
536 | ]
537 | },
538 | {
539 | "cell_type": "markdown",
540 | "id": "21b33cbf",
541 | "metadata": {},
542 | "source": [
543 | "#### dyadic `≤` (Less than or equal to)"
544 | ]
545 | },
546 | {
547 | "cell_type": "code",
548 | "execution_count": null,
549 | "id": "985c9324",
550 | "metadata": {},
551 | "outputs": [
552 | {
553 | "data": {
554 | "text/html": [
555 | "┌→────┐\n",
556 | "│1 1 0│\n",
557 | "└~────┘\n",
558 | "
"
559 | ]
560 | },
561 | "execution_count": null,
562 | "metadata": {},
563 | "output_type": "execute_result"
564 | }
565 | ],
566 | "source": [
567 | "1 2 3 ≤ 4 2 ¯1"
568 | ]
569 | },
570 | {
571 | "cell_type": "code",
572 | "execution_count": null,
573 | "id": "ebb03a6a",
574 | "metadata": {},
575 | "outputs": [
576 | {
577 | "data": {
578 | "text/html": [
579 | "┌→────┐\n",
580 | "│1 1 0│\n",
581 | "└~────┘\n",
582 | "
"
583 | ]
584 | },
585 | "execution_count": null,
586 | "metadata": {},
587 | "output_type": "execute_result"
588 | }
589 | ],
590 | "source": [
591 | "1 2 3 ≤ 2"
592 | ]
593 | },
594 | {
595 | "cell_type": "markdown",
596 | "id": "b9409575",
597 | "metadata": {},
598 | "source": [
599 | "### `≥` (Greater than or equal to sign)"
600 | ]
601 | },
602 | {
603 | "cell_type": "markdown",
604 | "id": "8dbc6595",
605 | "metadata": {},
606 | "source": [
607 | "#### dyadic `≥` (Greater than or equal to)"
608 | ]
609 | },
610 | {
611 | "cell_type": "code",
612 | "execution_count": null,
613 | "id": "c2db65ca",
614 | "metadata": {},
615 | "outputs": [
616 | {
617 | "data": {
618 | "text/html": [
619 | "┌→────┐\n",
620 | "│0 1 1│\n",
621 | "└~────┘\n",
622 | "
"
623 | ]
624 | },
625 | "execution_count": null,
626 | "metadata": {},
627 | "output_type": "execute_result"
628 | }
629 | ],
630 | "source": [
631 | "1 2 3 ≥ 4 2 ¯1"
632 | ]
633 | },
634 | {
635 | "cell_type": "code",
636 | "execution_count": null,
637 | "id": "3c4673b1",
638 | "metadata": {},
639 | "outputs": [
640 | {
641 | "data": {
642 | "text/html": [
643 | "┌→────┐\n",
644 | "│0 1 1│\n",
645 | "└~────┘\n",
646 | "
"
647 | ]
648 | },
649 | "execution_count": null,
650 | "metadata": {},
651 | "output_type": "execute_result"
652 | }
653 | ],
654 | "source": [
655 | "1 2 3 ≥ 2"
656 | ]
657 | },
658 | {
659 | "cell_type": "markdown",
660 | "id": "af629c33",
661 | "metadata": {},
662 | "source": [
663 | "### `≡` (Equal underbar)"
664 | ]
665 | },
666 | {
667 | "cell_type": "markdown",
668 | "id": "04409fab",
669 | "metadata": {},
670 | "source": [
671 | "#### monadic `≡` (Depth)"
672 | ]
673 | },
674 | {
675 | "cell_type": "markdown",
676 | "id": "9d6a0db6-2820-4e30-a53e-65e6010d8324",
677 | "metadata": {},
678 | "source": [
679 | "Depth shows how nested an array is. A simple scalar is an array with no nesting."
680 | ]
681 | },
682 | {
683 | "cell_type": "code",
684 | "execution_count": null,
685 | "id": "fcb156fe",
686 | "metadata": {},
687 | "outputs": [
688 | {
689 | "data": {
690 | "text/html": [
691 | " \n",
692 | "0\n",
693 | " \n",
694 | "
"
695 | ]
696 | },
697 | "execution_count": null,
698 | "metadata": {},
699 | "output_type": "execute_result"
700 | }
701 | ],
702 | "source": [
703 | "≡ 7"
704 | ]
705 | },
706 | {
707 | "cell_type": "markdown",
708 | "id": "3b3f7079-1edd-4d36-8142-f2fad11bf1db",
709 | "metadata": {},
710 | "source": [
711 | "An array of simple scalars has depth 1."
712 | ]
713 | },
714 | {
715 | "cell_type": "code",
716 | "execution_count": null,
717 | "id": "53200fb6",
718 | "metadata": {},
719 | "outputs": [
720 | {
721 | "data": {
722 | "text/html": [
723 | " \n",
724 | "1\n",
725 | " \n",
726 | "
"
727 | ]
728 | },
729 | "execution_count": null,
730 | "metadata": {},
731 | "output_type": "execute_result"
732 | }
733 | ],
734 | "source": [
735 | "≡ 'abc'"
736 | ]
737 | },
738 | {
739 | "cell_type": "markdown",
740 | "id": "a9b106d5-a182-44fc-b3d9-c660344bc186",
741 | "metadata": {},
742 | "source": [
743 | "An array that is an array of simple arrays has depth 2."
744 | ]
745 | },
746 | {
747 | "cell_type": "code",
748 | "execution_count": null,
749 | "id": "35407dd6",
750 | "metadata": {},
751 | "outputs": [
752 | {
753 | "data": {
754 | "text/html": [
755 | "┌→────────────┐\n",
756 | "│ ┌→──┐ ┌→──┐ │\n",
757 | "│ │1 2│ │3 4│ │\n",
758 | "│ └~──┘ └~──┘ │\n",
759 | "└∊────────────┘\n",
760 | "
"
761 | ]
762 | },
763 | "execution_count": null,
764 | "metadata": {},
765 | "output_type": "execute_result"
766 | }
767 | ],
768 | "source": [
769 | "(1 2)(3 4)"
770 | ]
771 | },
772 | {
773 | "cell_type": "code",
774 | "execution_count": null,
775 | "id": "f64d2e8e",
776 | "metadata": {},
777 | "outputs": [
778 | {
779 | "data": {
780 | "text/html": [
781 | " \n",
782 | "2\n",
783 | " \n",
784 | "
"
785 | ]
786 | },
787 | "execution_count": null,
788 | "metadata": {},
789 | "output_type": "execute_result"
790 | }
791 | ],
792 | "source": [
793 | "≡ (1 2)(3 4)"
794 | ]
795 | },
796 | {
797 | "cell_type": "markdown",
798 | "id": "36ec6b8f-882d-483f-a42b-1b2c6f35b559",
799 | "metadata": {},
800 | "source": [
801 | "If the depth is not consistent, then it returns the max depth as a negative number."
802 | ]
803 | },
804 | {
805 | "cell_type": "code",
806 | "execution_count": null,
807 | "id": "0650e6e6",
808 | "metadata": {},
809 | "outputs": [
810 | {
811 | "data": {
812 | "text/html": [
813 | "┌→────────────────────────┐\n",
814 | "│ ┌→──┐ ┌→──┐ ┌→────────┐ │\n",
815 | "│ │1 2│ │3 4│ │ ┌→──┐ │ │\n",
816 | "│ └~──┘ └~──┘ │ 5 │6 7│ │ │\n",
817 | "│ │ └~──┘ │ │\n",
818 | "│ └∊────────┘ │\n",
819 | "└∊────────────────────────┘\n",
820 | "
"
821 | ]
822 | },
823 | "execution_count": null,
824 | "metadata": {},
825 | "output_type": "execute_result"
826 | }
827 | ],
828 | "source": [
829 | "(1 2)(3 4) (5 (6 7))"
830 | ]
831 | },
832 | {
833 | "cell_type": "code",
834 | "execution_count": null,
835 | "id": "ede6ebf7",
836 | "metadata": {},
837 | "outputs": [
838 | {
839 | "data": {
840 | "text/html": [
841 | " \n",
842 | "¯3\n",
843 | " \n",
844 | "
"
845 | ]
846 | },
847 | "execution_count": null,
848 | "metadata": {},
849 | "output_type": "execute_result"
850 | }
851 | ],
852 | "source": [
853 | "≡ (1 2)(3 4) (5 (6 7))"
854 | ]
855 | },
856 | {
857 | "cell_type": "markdown",
858 | "id": "d5e95d1d",
859 | "metadata": {},
860 | "source": [
861 | "#### dyadic `≡` (Match)"
862 | ]
863 | },
864 | {
865 | "cell_type": "markdown",
866 | "id": "0819ac30-7d8f-446a-b4b9-e6113514cf1e",
867 | "metadata": {},
868 | "source": [
869 | "Match does a comparison to see if 2 objects are equal. It is similar to `=`, but it works on entire objects rather than elementwise. In other words it is equal with a wider scope."
870 | ]
871 | },
872 | {
873 | "cell_type": "code",
874 | "execution_count": null,
875 | "id": "8f55c331",
876 | "metadata": {},
877 | "outputs": [
878 | {
879 | "data": {
880 | "text/html": [
881 | " \n",
882 | "1\n",
883 | " \n",
884 | "
"
885 | ]
886 | },
887 | "execution_count": null,
888 | "metadata": {},
889 | "output_type": "execute_result"
890 | }
891 | ],
892 | "source": [
893 | "1 ≡ 1"
894 | ]
895 | },
896 | {
897 | "cell_type": "code",
898 | "execution_count": null,
899 | "id": "ee929e76",
900 | "metadata": {},
901 | "outputs": [
902 | {
903 | "data": {
904 | "text/html": [
905 | " \n",
906 | "0\n",
907 | " \n",
908 | "
"
909 | ]
910 | },
911 | "execution_count": null,
912 | "metadata": {},
913 | "output_type": "execute_result"
914 | }
915 | ],
916 | "source": [
917 | "1 ≡ 0"
918 | ]
919 | },
920 | {
921 | "cell_type": "markdown",
922 | "id": "1f48a33b-e717-47d3-a6f8-3395c759759e",
923 | "metadata": {},
924 | "source": [
925 | "`≡` works on whole objects and **not** elementwise with broadcasting."
926 | ]
927 | },
928 | {
929 | "cell_type": "code",
930 | "execution_count": null,
931 | "id": "1419197c",
932 | "metadata": {},
933 | "outputs": [
934 | {
935 | "data": {
936 | "text/html": [
937 | " \n",
938 | "0\n",
939 | " \n",
940 | "
"
941 | ]
942 | },
943 | "execution_count": null,
944 | "metadata": {},
945 | "output_type": "execute_result"
946 | }
947 | ],
948 | "source": [
949 | "1 ≡ 1 1"
950 | ]
951 | },
952 | {
953 | "cell_type": "markdown",
954 | "id": "284ae899",
955 | "metadata": {},
956 | "source": [
957 | "### `≢` (Equal Underbar Slash)"
958 | ]
959 | },
960 | {
961 | "cell_type": "markdown",
962 | "id": "f6f859db",
963 | "metadata": {},
964 | "source": [
965 | "#### monadic `≢` (Tally)"
966 | ]
967 | },
968 | {
969 | "cell_type": "markdown",
970 | "id": "026eab0b-68de-46c8-874e-f07035768242",
971 | "metadata": {},
972 | "source": [
973 | "Tally counts the major cells in an array. This means it gives the length of the leading axis. For a vector, or rank 1 array, this is the same as it's shape but as a scalar."
974 | ]
975 | },
976 | {
977 | "cell_type": "code",
978 | "execution_count": null,
979 | "id": "10011239",
980 | "metadata": {},
981 | "outputs": [
982 | {
983 | "data": {
984 | "text/html": [
985 | " \n",
986 | "3\n",
987 | " \n",
988 | "
"
989 | ]
990 | },
991 | "execution_count": null,
992 | "metadata": {},
993 | "output_type": "execute_result"
994 | }
995 | ],
996 | "source": [
997 | "≢ 1 2 3"
998 | ]
999 | },
1000 | {
1001 | "cell_type": "code",
1002 | "execution_count": null,
1003 | "id": "6f6449ea",
1004 | "metadata": {},
1005 | "outputs": [
1006 | {
1007 | "data": {
1008 | "text/html": [
1009 | "┌→┐\n",
1010 | "│3│\n",
1011 | "└~┘\n",
1012 | "
"
1013 | ]
1014 | },
1015 | "execution_count": null,
1016 | "metadata": {},
1017 | "output_type": "execute_result"
1018 | }
1019 | ],
1020 | "source": [
1021 | "⍴ 1 2 3"
1022 | ]
1023 | },
1024 | {
1025 | "cell_type": "markdown",
1026 | "id": "9adbc6a0-e791-46df-83ef-dcf6787d0ed4",
1027 | "metadata": {},
1028 | "source": [
1029 | "If there are multiple dimensions, Tally returns the number of major cells, which is the size of the first dimension"
1030 | ]
1031 | },
1032 | {
1033 | "cell_type": "code",
1034 | "execution_count": null,
1035 | "id": "7d2d2315",
1036 | "metadata": {},
1037 | "outputs": [
1038 | {
1039 | "data": {
1040 | "text/html": [
1041 | " \n",
1042 | "2\n",
1043 | " \n",
1044 | "
"
1045 | ]
1046 | },
1047 | "execution_count": null,
1048 | "metadata": {},
1049 | "output_type": "execute_result"
1050 | }
1051 | ],
1052 | "source": [
1053 | "≢ 2 3 ⍴ ⍳6"
1054 | ]
1055 | },
1056 | {
1057 | "cell_type": "code",
1058 | "execution_count": null,
1059 | "id": "b5c6f177-ce42-4718-8c3d-710febac94c2",
1060 | "metadata": {},
1061 | "outputs": [
1062 | {
1063 | "data": {
1064 | "text/html": [
1065 | " \n",
1066 | "3\n",
1067 | " \n",
1068 | "
"
1069 | ]
1070 | },
1071 | "execution_count": null,
1072 | "metadata": {},
1073 | "output_type": "execute_result"
1074 | }
1075 | ],
1076 | "source": [
1077 | "≢ 3 2 ⍴ ⍳6"
1078 | ]
1079 | },
1080 | {
1081 | "cell_type": "markdown",
1082 | "id": "63bf5a7c",
1083 | "metadata": {},
1084 | "source": [
1085 | "#### dyadic `≢` (Not match)"
1086 | ]
1087 | },
1088 | {
1089 | "cell_type": "markdown",
1090 | "id": "b22c9e10-a63b-48c0-b811-96f416e76289",
1091 | "metadata": {},
1092 | "source": [
1093 | "Not match does a comparison to see if 2 objects are not equal. It is similar to `≠`, but it works on entire objects rather than elementwise. In other words, it is equal with a wider scope."
1094 | ]
1095 | },
1096 | {
1097 | "cell_type": "code",
1098 | "execution_count": null,
1099 | "id": "762603e0",
1100 | "metadata": {},
1101 | "outputs": [
1102 | {
1103 | "data": {
1104 | "text/html": [
1105 | " \n",
1106 | "0\n",
1107 | " \n",
1108 | "
"
1109 | ]
1110 | },
1111 | "execution_count": null,
1112 | "metadata": {},
1113 | "output_type": "execute_result"
1114 | }
1115 | ],
1116 | "source": [
1117 | "1 ≢ 1"
1118 | ]
1119 | },
1120 | {
1121 | "cell_type": "code",
1122 | "execution_count": null,
1123 | "id": "87ebb14d",
1124 | "metadata": {},
1125 | "outputs": [
1126 | {
1127 | "data": {
1128 | "text/html": [
1129 | " \n",
1130 | "1\n",
1131 | " \n",
1132 | "
"
1133 | ]
1134 | },
1135 | "execution_count": null,
1136 | "metadata": {},
1137 | "output_type": "execute_result"
1138 | }
1139 | ],
1140 | "source": [
1141 | "1 ≢ 0"
1142 | ]
1143 | },
1144 | {
1145 | "cell_type": "markdown",
1146 | "id": "0846d742-8ba9-4a7e-b141-bc8cad0171c6",
1147 | "metadata": {},
1148 | "source": [
1149 | "``≢`` works on whole objects and **not** elementwise with broadcasting."
1150 | ]
1151 | },
1152 | {
1153 | "cell_type": "code",
1154 | "execution_count": null,
1155 | "id": "9f3fb7c0",
1156 | "metadata": {},
1157 | "outputs": [
1158 | {
1159 | "data": {
1160 | "text/html": [
1161 | " \n",
1162 | "1\n",
1163 | " \n",
1164 | "
"
1165 | ]
1166 | },
1167 | "execution_count": null,
1168 | "metadata": {},
1169 | "output_type": "execute_result"
1170 | }
1171 | ],
1172 | "source": [
1173 | "1 ≢ 1 1"
1174 | ]
1175 | },
1176 | {
1177 | "cell_type": "markdown",
1178 | "id": "fa5c0d84",
1179 | "metadata": {},
1180 | "source": [
1181 | "### `∨` (Logical or)"
1182 | ]
1183 | },
1184 | {
1185 | "cell_type": "markdown",
1186 | "id": "42407b65",
1187 | "metadata": {},
1188 | "source": [
1189 | "#### dyadic `∨` (Greatest Common Divisor (Or))"
1190 | ]
1191 | },
1192 | {
1193 | "cell_type": "markdown",
1194 | "id": "37035211-ea5a-424d-8e3f-cd1735dab5a8",
1195 | "metadata": {},
1196 | "source": [
1197 | "Standard `or` operator when applied to booleans."
1198 | ]
1199 | },
1200 | {
1201 | "cell_type": "code",
1202 | "execution_count": null,
1203 | "id": "439d7541",
1204 | "metadata": {},
1205 | "outputs": [
1206 | {
1207 | "data": {
1208 | "text/html": [
1209 | "┌→──────┐\n",
1210 | "│0 1 1 1│\n",
1211 | "└~──────┘\n",
1212 | "
"
1213 | ]
1214 | },
1215 | "execution_count": null,
1216 | "metadata": {},
1217 | "output_type": "execute_result"
1218 | }
1219 | ],
1220 | "source": [
1221 | "0 1 0 1 ∨ 0 0 1 1 ⍝ Truth table for *or*"
1222 | ]
1223 | },
1224 | {
1225 | "cell_type": "markdown",
1226 | "id": "ceae61c8-16d3-4c50-83f6-655f20aaeaad",
1227 | "metadata": {},
1228 | "source": [
1229 | "5 is the largest number that divides 15 and 35 cleanly (meaning no remainder). Therefore, 5 is the greatest common divisor of 15 and 35."
1230 | ]
1231 | },
1232 | {
1233 | "cell_type": "code",
1234 | "execution_count": null,
1235 | "id": "47abd9d1",
1236 | "metadata": {},
1237 | "outputs": [
1238 | {
1239 | "data": {
1240 | "text/html": [
1241 | "┌→──────┐\n",
1242 | "│5 1 2 7│\n",
1243 | "└~──────┘\n",
1244 | "
"
1245 | ]
1246 | },
1247 | "execution_count": null,
1248 | "metadata": {},
1249 | "output_type": "execute_result"
1250 | }
1251 | ],
1252 | "source": [
1253 | "15 1 2 7 ∨ 35 1 4 0 ⍝ GCD"
1254 | ]
1255 | },
1256 | {
1257 | "cell_type": "markdown",
1258 | "id": "fc3e5b03",
1259 | "metadata": {},
1260 | "source": [
1261 | "### `⍱` (Logical NOR)"
1262 | ]
1263 | },
1264 | {
1265 | "cell_type": "markdown",
1266 | "id": "47ff8cd5",
1267 | "metadata": {},
1268 | "source": [
1269 | "#### dyadic `⍱` (Nor)"
1270 | ]
1271 | },
1272 | {
1273 | "cell_type": "markdown",
1274 | "id": "f067a891-a383-4794-9e2e-731f6d750c69",
1275 | "metadata": {},
1276 | "source": [
1277 | "For more details on logical nor, [see this page](https://en.wikipedia.org/wiki/Logical_NOR#Truth_table)"
1278 | ]
1279 | },
1280 | {
1281 | "cell_type": "code",
1282 | "execution_count": null,
1283 | "id": "dc80c88d",
1284 | "metadata": {},
1285 | "outputs": [
1286 | {
1287 | "data": {
1288 | "text/html": [
1289 | "┌→──────┐\n",
1290 | "│1 0 0 0│\n",
1291 | "└~──────┘\n",
1292 | "
"
1293 | ]
1294 | },
1295 | "execution_count": null,
1296 | "metadata": {},
1297 | "output_type": "execute_result"
1298 | }
1299 | ],
1300 | "source": [
1301 | " 0 1 0 1 ⍱ 0 0 1 1 ⍝ Truth table for *nor*"
1302 | ]
1303 | },
1304 | {
1305 | "cell_type": "markdown",
1306 | "id": "27932e1b",
1307 | "metadata": {},
1308 | "source": [
1309 | "### `∧` (Logical AND)"
1310 | ]
1311 | },
1312 | {
1313 | "cell_type": "markdown",
1314 | "id": "31a3b8b5",
1315 | "metadata": {},
1316 | "source": [
1317 | "#### dyadic `∧` (Lowest Common Multiple (And))"
1318 | ]
1319 | },
1320 | {
1321 | "cell_type": "markdown",
1322 | "id": "65f4a4d0-59ed-4e72-914e-c2ef482d8291",
1323 | "metadata": {},
1324 | "source": [
1325 | "Standard `and` operator when applied to booleans."
1326 | ]
1327 | },
1328 | {
1329 | "cell_type": "code",
1330 | "execution_count": null,
1331 | "id": "ac4309ef",
1332 | "metadata": {},
1333 | "outputs": [
1334 | {
1335 | "data": {
1336 | "text/html": [
1337 | "┌→──────┐\n",
1338 | "│0 0 0 1│\n",
1339 | "└~──────┘\n",
1340 | "
"
1341 | ]
1342 | },
1343 | "execution_count": null,
1344 | "metadata": {},
1345 | "output_type": "execute_result"
1346 | }
1347 | ],
1348 | "source": [
1349 | "0 1 0 1 ∧ 0 0 1 1 ⍝ Truth table for *and*"
1350 | ]
1351 | },
1352 | {
1353 | "cell_type": "markdown",
1354 | "id": "71b974e9-6f78-4e29-937f-ffb31a62af74",
1355 | "metadata": {},
1356 | "source": [
1357 | "105 is the smallest multiple of both 15 and 35, therefore 105 is the lowest common multiple of 15 and 35."
1358 | ]
1359 | },
1360 | {
1361 | "cell_type": "code",
1362 | "execution_count": null,
1363 | "id": "fbfaebf4",
1364 | "metadata": {},
1365 | "outputs": [
1366 | {
1367 | "data": {
1368 | "text/html": [
1369 | "┌→────────┐\n",
1370 | "│105 1 4 0│\n",
1371 | "└~────────┘\n",
1372 | "
"
1373 | ]
1374 | },
1375 | "execution_count": null,
1376 | "metadata": {},
1377 | "output_type": "execute_result"
1378 | }
1379 | ],
1380 | "source": [
1381 | "15 1 2 7 ∧ 35 1 4 0 ⍝ LCM"
1382 | ]
1383 | },
1384 | {
1385 | "cell_type": "markdown",
1386 | "id": "04987504-6a54-4e01-b38f-3e69b99c1abe",
1387 | "metadata": {},
1388 | "source": [
1389 | "### `~` (Logical NOT)"
1390 | ]
1391 | },
1392 | {
1393 | "cell_type": "markdown",
1394 | "id": "09ab7565-f35c-4072-ab77-3e1cd58e17ee",
1395 | "metadata": {},
1396 | "source": [
1397 | "#### monadic `~` (Not)"
1398 | ]
1399 | },
1400 | {
1401 | "cell_type": "code",
1402 | "execution_count": null,
1403 | "id": "b0abb3ae",
1404 | "metadata": {},
1405 | "outputs": [
1406 | {
1407 | "data": {
1408 | "text/html": [
1409 | "┌→──┐\n",
1410 | "│1 0│\n",
1411 | "└~──┘\n",
1412 | "
"
1413 | ]
1414 | },
1415 | "execution_count": null,
1416 | "metadata": {},
1417 | "output_type": "execute_result"
1418 | }
1419 | ],
1420 | "source": [
1421 | "~ 0 1 ⍝ Truth table for *not*"
1422 | ]
1423 | },
1424 | {
1425 | "cell_type": "markdown",
1426 | "id": "190b5d68-57b5-4f04-a21e-3864fe8d8122",
1427 | "metadata": {},
1428 | "source": [
1429 | "#### dyadic `~` (Without;Excluding)"
1430 | ]
1431 | },
1432 | {
1433 | "cell_type": "markdown",
1434 | "id": "d41d8180-bfaa-46f2-808e-d451673f4e5f",
1435 | "metadata": {},
1436 | "source": [
1437 | "Gives the elements from the left argument that are not in the right."
1438 | ]
1439 | },
1440 | {
1441 | "cell_type": "code",
1442 | "execution_count": null,
1443 | "id": "f6b788cd",
1444 | "metadata": {},
1445 | "outputs": [
1446 | {
1447 | "data": {
1448 | "text/html": [
1449 | "┌→──┐\n",
1450 | "│3 4│\n",
1451 | "└~──┘\n",
1452 | "
"
1453 | ]
1454 | },
1455 | "execution_count": null,
1456 | "metadata": {},
1457 | "output_type": "execute_result"
1458 | }
1459 | ],
1460 | "source": [
1461 | "3 1 4 1 5 ~ 5 1"
1462 | ]
1463 | },
1464 | {
1465 | "cell_type": "markdown",
1466 | "id": "82641989-2b43-4e01-a3d1-0489c417cae5",
1467 | "metadata": {},
1468 | "source": [
1469 | "Also works on the character vectors"
1470 | ]
1471 | },
1472 | {
1473 | "cell_type": "code",
1474 | "execution_count": null,
1475 | "id": "bfdf7e89",
1476 | "metadata": {},
1477 | "outputs": [
1478 | {
1479 | "data": {
1480 | "text/html": [
1481 | "┌→──────────┐\n",
1482 | "│ ┌→─┐ ┌→─┐ │\n",
1483 | "│ │aa│ │cc│ │\n",
1484 | "│ └──┘ └──┘ │\n",
1485 | "└∊──────────┘\n",
1486 | "
"
1487 | ]
1488 | },
1489 | "execution_count": null,
1490 | "metadata": {},
1491 | "output_type": "execute_result"
1492 | }
1493 | ],
1494 | "source": [
1495 | "'aa' 'bb' 'cc' 'bb' ~ 'bb' 'xx'"
1496 | ]
1497 | },
1498 | {
1499 | "cell_type": "markdown",
1500 | "id": "51a97128-c2ee-499a-a5e7-2f2e84897496",
1501 | "metadata": {},
1502 | "source": [
1503 | "Also works on nested arrays"
1504 | ]
1505 | },
1506 | {
1507 | "cell_type": "code",
1508 | "execution_count": null,
1509 | "id": "9085478e",
1510 | "metadata": {},
1511 | "outputs": [
1512 | {
1513 | "data": {
1514 | "text/html": [
1515 | "┌→┐\n",
1516 | "│3│\n",
1517 | "└~┘\n",
1518 | "
"
1519 | ]
1520 | },
1521 | "execution_count": null,
1522 | "metadata": {},
1523 | "output_type": "execute_result"
1524 | }
1525 | ],
1526 | "source": [
1527 | "(1 2) 3 ~ ⊂1 2"
1528 | ]
1529 | },
1530 | {
1531 | "cell_type": "markdown",
1532 | "id": "5f8cab64",
1533 | "metadata": {},
1534 | "source": [
1535 | "### `⍲` (Logical NAND)"
1536 | ]
1537 | },
1538 | {
1539 | "cell_type": "markdown",
1540 | "id": "8b59feac",
1541 | "metadata": {},
1542 | "source": [
1543 | "#### dyadic `⍲` (Nand)"
1544 | ]
1545 | },
1546 | {
1547 | "cell_type": "markdown",
1548 | "id": "abf07f68-d2d1-4784-b9f3-2fce4665a498",
1549 | "metadata": {},
1550 | "source": [
1551 | "Nand is \"Not and\""
1552 | ]
1553 | },
1554 | {
1555 | "cell_type": "code",
1556 | "execution_count": null,
1557 | "id": "0ee272ec",
1558 | "metadata": {},
1559 | "outputs": [
1560 | {
1561 | "data": {
1562 | "text/html": [
1563 | "┌→──────┐\n",
1564 | "│1 1 1 0│\n",
1565 | "└~──────┘\n",
1566 | "
"
1567 | ]
1568 | },
1569 | "execution_count": null,
1570 | "metadata": {},
1571 | "output_type": "execute_result"
1572 | }
1573 | ],
1574 | "source": [
1575 | " 0 1 0 1 ⍲ 0 0 1 1 ⍝ Truth table for *nand*"
1576 | ]
1577 | },
1578 | {
1579 | "cell_type": "markdown",
1580 | "id": "327836f3-8acd-474d-a594-2fa525763bc6",
1581 | "metadata": {},
1582 | "source": [
1583 | "We could use and (`^`) apply not (`~`) afterward to get the same result. As you can see it truly is \"Not and\""
1584 | ]
1585 | },
1586 | {
1587 | "cell_type": "code",
1588 | "execution_count": null,
1589 | "id": "113f86fa-9645-4c8e-b559-6b5cf7c822f8",
1590 | "metadata": {},
1591 | "outputs": [
1592 | {
1593 | "data": {
1594 | "text/html": [
1595 | "┌→──────┐\n",
1596 | "│1 1 1 0│\n",
1597 | "└~──────┘\n",
1598 | "
"
1599 | ]
1600 | },
1601 | "execution_count": null,
1602 | "metadata": {},
1603 | "output_type": "execute_result"
1604 | }
1605 | ],
1606 | "source": [
1607 | "~ 0 1 0 1 ∧ 0 0 1 1 ⍝ Truth table for *nand*"
1608 | ]
1609 | },
1610 | {
1611 | "cell_type": "markdown",
1612 | "id": "ebf0e3e4",
1613 | "metadata": {},
1614 | "source": [
1615 | "### `/` (Slash)"
1616 | ]
1617 | },
1618 | {
1619 | "cell_type": "markdown",
1620 | "id": "81223d6f",
1621 | "metadata": {},
1622 | "source": [
1623 | "#### monadic `/` (Replicate)"
1624 | ]
1625 | },
1626 | {
1627 | "cell_type": "code",
1628 | "execution_count": null,
1629 | "id": "1e6ccb42",
1630 | "metadata": {},
1631 | "outputs": [
1632 | {
1633 | "data": {
1634 | "text/html": [
1635 | "┌→──────────────┐\n",
1636 | "│1 1 0 0 1 0 1 0│\n",
1637 | "└~──────────────┘\n",
1638 | "
"
1639 | ]
1640 | },
1641 | "execution_count": null,
1642 | "metadata": {},
1643 | "output_type": "execute_result"
1644 | }
1645 | ],
1646 | "source": [
1647 | "v←22 10 22 22 21 10 5 10\n",
1648 | "≠v"
1649 | ]
1650 | },
1651 | {
1652 | "cell_type": "code",
1653 | "execution_count": null,
1654 | "id": "ed0370b6",
1655 | "metadata": {},
1656 | "outputs": [
1657 | {
1658 | "data": {
1659 | "text/html": [
1660 | "┌→─────────┐\n",
1661 | "│22 10 21 5│\n",
1662 | "└~─────────┘\n",
1663 | "
"
1664 | ]
1665 | },
1666 | "execution_count": null,
1667 | "metadata": {},
1668 | "output_type": "execute_result"
1669 | }
1670 | ],
1671 | "source": [
1672 | "(≠v)/v"
1673 | ]
1674 | },
1675 | {
1676 | "cell_type": "code",
1677 | "execution_count": null,
1678 | "id": "4a7aa794",
1679 | "metadata": {},
1680 | "outputs": [
1681 | {
1682 | "data": {
1683 | "text/html": [
1684 | "┌→───────────┐\n",
1685 | "│BBBannnannna│\n",
1686 | "└────────────┘\n",
1687 | "
"
1688 | ]
1689 | },
1690 | "execution_count": null,
1691 | "metadata": {},
1692 | "output_type": "execute_result"
1693 | }
1694 | ],
1695 | "source": [
1696 | "3 1 3 1 3 1 / 'Banana'"
1697 | ]
1698 | },
1699 | {
1700 | "cell_type": "markdown",
1701 | "id": "95f0d135",
1702 | "metadata": {},
1703 | "source": [
1704 | "## Min, max, index, concat"
1705 | ]
1706 | },
1707 | {
1708 | "cell_type": "markdown",
1709 | "id": "c184a076",
1710 | "metadata": {},
1711 | "source": [
1712 | "### `⍳` (iota)"
1713 | ]
1714 | },
1715 | {
1716 | "cell_type": "markdown",
1717 | "id": "8485edff",
1718 | "metadata": {},
1719 | "source": [
1720 | "#### monadic `⍳` (index generator)"
1721 | ]
1722 | },
1723 | {
1724 | "cell_type": "markdown",
1725 | "id": "6581d1bf-551f-42b5-a027-b080d72d4629",
1726 | "metadata": {},
1727 | "source": [
1728 | "Creates index locations for array with specified shape."
1729 | ]
1730 | },
1731 | {
1732 | "cell_type": "code",
1733 | "execution_count": null,
1734 | "id": "69cc99e0",
1735 | "metadata": {},
1736 | "outputs": [
1737 | {
1738 | "data": {
1739 | "text/html": [
1740 | "┌→──────┐\n",
1741 | "│1 2 3 4│\n",
1742 | "└~──────┘\n",
1743 | "
"
1744 | ]
1745 | },
1746 | "execution_count": null,
1747 | "metadata": {},
1748 | "output_type": "execute_result"
1749 | }
1750 | ],
1751 | "source": [
1752 | "⍳4"
1753 | ]
1754 | },
1755 | {
1756 | "cell_type": "code",
1757 | "execution_count": null,
1758 | "id": "155302ac",
1759 | "metadata": {},
1760 | "outputs": [
1761 | {
1762 | "data": {
1763 | "text/html": [
1764 | "┌→──────────────────┐\n",
1765 | "↓ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
1766 | "│ │1 1│ │1 2│ │1 3│ │\n",
1767 | "│ └~──┘ └~──┘ └~──┘ │\n",
1768 | "│ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
1769 | "│ │2 1│ │2 2│ │2 3│ │\n",
1770 | "│ └~──┘ └~──┘ └~──┘ │\n",
1771 | "└∊──────────────────┘\n",
1772 | "
"
1773 | ]
1774 | },
1775 | "execution_count": null,
1776 | "metadata": {},
1777 | "output_type": "execute_result"
1778 | }
1779 | ],
1780 | "source": [
1781 | "⍳2 3"
1782 | ]
1783 | },
1784 | {
1785 | "cell_type": "markdown",
1786 | "id": "841c9175-1100-41ed-8a7c-ec4bb7783504",
1787 | "metadata": {},
1788 | "source": [
1789 | "`⍳` is often used with `⍴` to create arrays "
1790 | ]
1791 | },
1792 | {
1793 | "cell_type": "code",
1794 | "execution_count": null,
1795 | "id": "73e93a04",
1796 | "metadata": {},
1797 | "outputs": [
1798 | {
1799 | "data": {
1800 | "text/html": [
1801 | "┌→────┐\n",
1802 | "↓1 2 3│\n",
1803 | "│4 5 6│\n",
1804 | "└~────┘\n",
1805 | "
"
1806 | ]
1807 | },
1808 | "execution_count": null,
1809 | "metadata": {},
1810 | "output_type": "execute_result"
1811 | }
1812 | ],
1813 | "source": [
1814 | "2 3 ⍴ ⍳6"
1815 | ]
1816 | },
1817 | {
1818 | "cell_type": "markdown",
1819 | "id": "22e8cdfd-5251-432f-b0a6-716bd803085d",
1820 | "metadata": {},
1821 | "source": [
1822 | "To generate an array with various patterns you can combine with other functions."
1823 | ]
1824 | },
1825 | {
1826 | "cell_type": "code",
1827 | "execution_count": null,
1828 | "id": "1744f807",
1829 | "metadata": {},
1830 | "outputs": [
1831 | {
1832 | "data": {
1833 | "text/html": [
1834 | "┌→────────────┐\n",
1835 | "│3 5 7 9 11 13│\n",
1836 | "└~────────────┘\n",
1837 | "
"
1838 | ]
1839 | },
1840 | "execution_count": null,
1841 | "metadata": {},
1842 | "output_type": "execute_result"
1843 | }
1844 | ],
1845 | "source": [
1846 | "1+2×⍳6"
1847 | ]
1848 | },
1849 | {
1850 | "cell_type": "markdown",
1851 | "id": "f92ecb85-02b0-46fe-9812-d4ed90ed9498",
1852 | "metadata": {},
1853 | "source": [
1854 | "Array of shape 0 is nan empty vector and the index locations of a shape 0 array is and empty vector."
1855 | ]
1856 | },
1857 | {
1858 | "cell_type": "code",
1859 | "execution_count": null,
1860 | "id": "3fd77f85",
1861 | "metadata": {},
1862 | "outputs": [
1863 | {
1864 | "data": {
1865 | "text/html": [
1866 | "┌⊖┐\n",
1867 | "│0│\n",
1868 | "└~┘\n",
1869 | "
"
1870 | ]
1871 | },
1872 | "execution_count": null,
1873 | "metadata": {},
1874 | "output_type": "execute_result"
1875 | }
1876 | ],
1877 | "source": [
1878 | "⍳0"
1879 | ]
1880 | },
1881 | {
1882 | "cell_type": "markdown",
1883 | "id": "51f01e92",
1884 | "metadata": {},
1885 | "source": [
1886 | "#### dyadic `⍳` (index of)"
1887 | ]
1888 | },
1889 | {
1890 | "cell_type": "markdown",
1891 | "id": "24713038-4260-48c3-aa7a-e79815cec6e8",
1892 | "metadata": {},
1893 | "source": [
1894 | "Provides the index locations for where `⍵` (right argument) is in `⍺` (left argument)"
1895 | ]
1896 | },
1897 | {
1898 | "cell_type": "code",
1899 | "execution_count": null,
1900 | "id": "db34fc0c",
1901 | "metadata": {},
1902 | "outputs": [
1903 | {
1904 | "data": {
1905 | "text/html": [
1906 | " \n",
1907 | "2\n",
1908 | " \n",
1909 | "
"
1910 | ]
1911 | },
1912 | "execution_count": null,
1913 | "metadata": {},
1914 | "output_type": "execute_result"
1915 | }
1916 | ],
1917 | "source": [
1918 | "1 3 6 5 4 ⍳ 3"
1919 | ]
1920 | },
1921 | {
1922 | "cell_type": "code",
1923 | "execution_count": null,
1924 | "id": "1604dc20",
1925 | "metadata": {},
1926 | "outputs": [
1927 | {
1928 | "data": {
1929 | "text/html": [
1930 | "┌→────────┐\n",
1931 | "│1 3 10 11│\n",
1932 | "└~────────┘\n",
1933 | "
"
1934 | ]
1935 | },
1936 | "execution_count": null,
1937 | "metadata": {},
1938 | "output_type": "execute_result"
1939 | }
1940 | ],
1941 | "source": [
1942 | "'ABCDABCDEF' ⍳ 'ACFG'"
1943 | ]
1944 | },
1945 | {
1946 | "cell_type": "code",
1947 | "execution_count": null,
1948 | "id": "e6a697da",
1949 | "metadata": {},
1950 | "outputs": [
1951 | {
1952 | "data": {
1953 | "text/html": [
1954 | "┌→──┐\n",
1955 | "↓1 2│\n",
1956 | "│3 4│\n",
1957 | "│5 6│\n",
1958 | "└~──┘\n",
1959 | "
"
1960 | ]
1961 | },
1962 | "execution_count": null,
1963 | "metadata": {},
1964 | "output_type": "execute_result"
1965 | }
1966 | ],
1967 | "source": [
1968 | "⎕←mat←3 2 ⍴ ⍳6"
1969 | ]
1970 | },
1971 | {
1972 | "cell_type": "markdown",
1973 | "id": "4a0af1fb-7e47-4b68-8639-2d5e34d75dc2",
1974 | "metadata": {},
1975 | "source": [
1976 | "`⍳` works on major cells, or along the first dimension. The third major cell of mat is `5 6`."
1977 | ]
1978 | },
1979 | {
1980 | "cell_type": "code",
1981 | "execution_count": null,
1982 | "id": "e7e56d92",
1983 | "metadata": {},
1984 | "outputs": [
1985 | {
1986 | "data": {
1987 | "text/html": [
1988 | " \n",
1989 | "3\n",
1990 | " \n",
1991 | "
"
1992 | ]
1993 | },
1994 | "execution_count": null,
1995 | "metadata": {},
1996 | "output_type": "execute_result"
1997 | }
1998 | ],
1999 | "source": [
2000 | "mat←3 2 ⍴ ⍳6\n",
2001 | "mat ⍳ 5 6"
2002 | ]
2003 | },
2004 | {
2005 | "cell_type": "markdown",
2006 | "id": "8dbfe270",
2007 | "metadata": {},
2008 | "source": [
2009 | "### `⍸` (iota underbar)"
2010 | ]
2011 | },
2012 | {
2013 | "cell_type": "markdown",
2014 | "id": "c623312c",
2015 | "metadata": {},
2016 | "source": [
2017 | "#### monadic `⍸` (Where)"
2018 | ]
2019 | },
2020 | {
2021 | "cell_type": "markdown",
2022 | "id": "6eb50df5-420e-456b-aebc-df8bcc377870",
2023 | "metadata": {},
2024 | "source": [
2025 | "When applied to a boolean/binary array, where gives index locations of the true values."
2026 | ]
2027 | },
2028 | {
2029 | "cell_type": "code",
2030 | "execution_count": null,
2031 | "id": "cd826c58",
2032 | "metadata": {},
2033 | "outputs": [
2034 | {
2035 | "data": {
2036 | "text/html": [
2037 | "┌→────┐\n",
2038 | "│1 4 5│\n",
2039 | "└~────┘\n",
2040 | "
"
2041 | ]
2042 | },
2043 | "execution_count": null,
2044 | "metadata": {},
2045 | "output_type": "execute_result"
2046 | }
2047 | ],
2048 | "source": [
2049 | "⍸ 1 0 0 1 1"
2050 | ]
2051 | },
2052 | {
2053 | "cell_type": "markdown",
2054 | "id": "80929a44-9b23-491a-98ef-d530ba1f3490",
2055 | "metadata": {},
2056 | "source": [
2057 | "When applied to a natural number, where repeats the index locations if the number is greater than 1. For example `⍸1 2 3` would give `1 2 2 3 3 3`"
2058 | ]
2059 | },
2060 | {
2061 | "cell_type": "code",
2062 | "execution_count": null,
2063 | "id": "1b6a928b-705a-48bc-89b9-0f48158568cc",
2064 | "metadata": {},
2065 | "outputs": [
2066 | {
2067 | "data": {
2068 | "text/html": [
2069 | "┌→──────────┐\n",
2070 | "│1 2 2 3 3 3│\n",
2071 | "└~──────────┘\n",
2072 | "
"
2073 | ]
2074 | },
2075 | "execution_count": null,
2076 | "metadata": {},
2077 | "output_type": "execute_result"
2078 | }
2079 | ],
2080 | "source": [
2081 | "⍸1 2 3"
2082 | ]
2083 | },
2084 | {
2085 | "cell_type": "code",
2086 | "execution_count": null,
2087 | "id": "f6dd11af",
2088 | "metadata": {},
2089 | "outputs": [
2090 | {
2091 | "data": {
2092 | "text/html": [
2093 | "┌→────────┐\n",
2094 | "│1 1 4 4 5│\n",
2095 | "└~────────┘\n",
2096 | "
"
2097 | ]
2098 | },
2099 | "execution_count": null,
2100 | "metadata": {},
2101 | "output_type": "execute_result"
2102 | }
2103 | ],
2104 | "source": [
2105 | "⍸ 2 0 0 2 1"
2106 | ]
2107 | },
2108 | {
2109 | "cell_type": "markdown",
2110 | "id": "7be22017-4047-404f-a9fa-34c0a589c6ed",
2111 | "metadata": {},
2112 | "source": [
2113 | "When applied to a higher rank array it still provides the index locations of the elements, but index locations have multiple values (in this case row and column)."
2114 | ]
2115 | },
2116 | {
2117 | "cell_type": "code",
2118 | "execution_count": null,
2119 | "id": "a8a4bf88",
2120 | "metadata": {},
2121 | "outputs": [
2122 | {
2123 | "data": {
2124 | "text/html": [
2125 | "┌→────┐\n",
2126 | "↓0 1 0│\n",
2127 | "│1 0 1│\n",
2128 | "└~────┘\n",
2129 | "
"
2130 | ]
2131 | },
2132 | "execution_count": null,
2133 | "metadata": {},
2134 | "output_type": "execute_result"
2135 | },
2136 | {
2137 | "data": {
2138 | "text/html": [
2139 | "┌→──────────────────┐\n",
2140 | "│ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
2141 | "│ │1 2│ │2 1│ │2 3│ │\n",
2142 | "│ └~──┘ └~──┘ └~──┘ │\n",
2143 | "└∊──────────────────┘\n",
2144 | "
"
2145 | ]
2146 | },
2147 | "execution_count": null,
2148 | "metadata": {},
2149 | "output_type": "execute_result"
2150 | }
2151 | ],
2152 | "source": [
2153 | "⎕←bmat ← 2 3 ⍴ 0 1 0 1 0 1\n",
2154 | "⍸ bmat"
2155 | ]
2156 | },
2157 | {
2158 | "cell_type": "code",
2159 | "execution_count": null,
2160 | "id": "b3c0b9fa-98a8-4914-973e-57e01081c83b",
2161 | "metadata": {},
2162 | "outputs": [
2163 | {
2164 | "data": {
2165 | "text/html": [
2166 | "┌→────┐\n",
2167 | "↓0 2 0│\n",
2168 | "│2 0 2│\n",
2169 | "└~────┘\n",
2170 | "
"
2171 | ]
2172 | },
2173 | "execution_count": null,
2174 | "metadata": {},
2175 | "output_type": "execute_result"
2176 | },
2177 | {
2178 | "data": {
2179 | "text/html": [
2180 | "┌→────────────────────────────────────┐\n",
2181 | "│ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
2182 | "│ │1 2│ │1 2│ │2 1│ │2 1│ │2 3│ │2 3│ │\n",
2183 | "│ └~──┘ └~──┘ └~──┘ └~──┘ └~──┘ └~──┘ │\n",
2184 | "└∊────────────────────────────────────┘\n",
2185 | "
"
2186 | ]
2187 | },
2188 | "execution_count": null,
2189 | "metadata": {},
2190 | "output_type": "execute_result"
2191 | }
2192 | ],
2193 | "source": [
2194 | "⎕←bmat ← 2 3 ⍴ 0 2 0 2 0 2\n",
2195 | "⍸ bmat"
2196 | ]
2197 | },
2198 | {
2199 | "cell_type": "markdown",
2200 | "id": "1c86ab76",
2201 | "metadata": {},
2202 | "source": [
2203 | "#### dyadic `⍸` (Interval Index)"
2204 | ]
2205 | },
2206 | {
2207 | "cell_type": "markdown",
2208 | "id": "057b305f-dd6e-4658-9c53-55576cef9585",
2209 | "metadata": {},
2210 | "source": [
2211 | "Interval index creates intervals and returns an array that tells you which interval a value falls in.\n",
2212 | "\n",
2213 | "If the following example, `⍵` is `2 4 6`. Therefore the following intervals (sometimes called bins) are created.\n",
2214 | "\n",
2215 | "+ **0th interval:** Less than 2\n",
2216 | "+ **1st interval:** 2-4 (excluding 4)\n",
2217 | "+ **2nd interval:** 4-6 (excluding 6)\n",
2218 | "+ **3rd interval:** Greater than or equal to 6\n",
2219 | "\n",
2220 | "`⍺` (right argument) is `1 2 3 4 5 6 7` so let's put those into intervals, which the first interval starting at 0.\n",
2221 | "\n",
2222 | "+ The first value of `⍺` is 1. 1 is Less than 2. Therefore it is in the 0th interval and interval index returns 0.\n",
2223 | "+ The second value of `⍺` is 2. 2 is in the 2-4 range. Therefore it is in the 1st interval and interval index returns 1.\n",
2224 | "+ The third value of `⍺` is 3. 3 is in the 2-4 range. Therefore it is in the 1st interval and interval index returns 1.\n",
2225 | "+ The fourth value of `⍺` is 4. 4 is in the 4-6 range. Therefore it is in the 2nd interval and interval index returns 2.\n",
2226 | "\n",
2227 | "And so on and so forth."
2228 | ]
2229 | },
2230 | {
2231 | "cell_type": "code",
2232 | "execution_count": null,
2233 | "id": "c402ce31",
2234 | "metadata": {},
2235 | "outputs": [
2236 | {
2237 | "data": {
2238 | "text/html": [
2239 | "┌→────────────┐\n",
2240 | "│0 1 1 2 2 3 3│\n",
2241 | "└~────────────┘\n",
2242 | "
"
2243 | ]
2244 | },
2245 | "execution_count": null,
2246 | "metadata": {},
2247 | "output_type": "execute_result"
2248 | }
2249 | ],
2250 | "source": [
2251 | "2 4 6 ⍸ 1 2 3 4 5 6 7"
2252 | ]
2253 | },
2254 | {
2255 | "cell_type": "markdown",
2256 | "id": "46aea64b-c2d1-4ce9-ab66-de44e7cf5f52",
2257 | "metadata": {},
2258 | "source": [
2259 | "Interval index works the same way with character vectors.\n",
2260 | "\n",
2261 | "+ `D` is in the first interval because it is between `A` and `E`.\n",
2262 | "+ `Y` is in the last interval (fifth) because it is larger than all values\n",
2263 | "+ `A` is in the first interval because it is between `A` and `E`.\n",
2264 | "+ `L` is in the third interval because it is between `I` and `O`.\n",
2265 | "\n",
2266 | "etc."
2267 | ]
2268 | },
2269 | {
2270 | "cell_type": "code",
2271 | "execution_count": null,
2272 | "id": "f66c7d8a",
2273 | "metadata": {},
2274 | "outputs": [
2275 | {
2276 | "data": {
2277 | "text/html": [
2278 | "┌→──────────┐\n",
2279 | "│1 5 1 3 4 2│\n",
2280 | "└~──────────┘\n",
2281 | "
"
2282 | ]
2283 | },
2284 | "execution_count": null,
2285 | "metadata": {},
2286 | "output_type": "execute_result"
2287 | }
2288 | ],
2289 | "source": [
2290 | "'AEIOU' ⍸ 'DYALOG'"
2291 | ]
2292 | },
2293 | {
2294 | "cell_type": "markdown",
2295 | "id": "88e6e4a7-6538-4372-b752-48c2cfc9dfb1",
2296 | "metadata": {},
2297 | "source": [
2298 | "Interval index works across major cells."
2299 | ]
2300 | },
2301 | {
2302 | "cell_type": "code",
2303 | "execution_count": null,
2304 | "id": "9c607eb4",
2305 | "metadata": {},
2306 | "outputs": [
2307 | {
2308 | "data": {
2309 | "text/html": [
2310 | "┌→──┐\n",
2311 | "↓1 2│\n",
2312 | "│3 4│\n",
2313 | "│5 6│\n",
2314 | "└~──┘\n",
2315 | "
"
2316 | ]
2317 | },
2318 | "execution_count": null,
2319 | "metadata": {},
2320 | "output_type": "execute_result"
2321 | }
2322 | ],
2323 | "source": [
2324 | "⎕←mat←3 2⍴⍳6"
2325 | ]
2326 | },
2327 | {
2328 | "cell_type": "code",
2329 | "execution_count": null,
2330 | "id": "d4e1c0b4",
2331 | "metadata": {},
2332 | "outputs": [
2333 | {
2334 | "data": {
2335 | "text/html": [
2336 | " \n",
2337 | "1\n",
2338 | " \n",
2339 | "
"
2340 | ]
2341 | },
2342 | "execution_count": null,
2343 | "metadata": {},
2344 | "output_type": "execute_result"
2345 | }
2346 | ],
2347 | "source": [
2348 | "mat ⍸ 3 3"
2349 | ]
2350 | },
2351 | {
2352 | "cell_type": "code",
2353 | "execution_count": null,
2354 | "id": "5af2f8d1",
2355 | "metadata": {},
2356 | "outputs": [
2357 | {
2358 | "data": {
2359 | "text/html": [
2360 | " \n",
2361 | "2\n",
2362 | " \n",
2363 | "
"
2364 | ]
2365 | },
2366 | "execution_count": null,
2367 | "metadata": {},
2368 | "output_type": "execute_result"
2369 | }
2370 | ],
2371 | "source": [
2372 | "mat ⍸ 3 5"
2373 | ]
2374 | },
2375 | {
2376 | "cell_type": "code",
2377 | "execution_count": null,
2378 | "id": "fc9be234",
2379 | "metadata": {},
2380 | "outputs": [
2381 | {
2382 | "data": {
2383 | "text/html": [
2384 | "┌→──┐\n",
2385 | "│1 2│\n",
2386 | "└~──┘\n",
2387 | "
"
2388 | ]
2389 | },
2390 | "execution_count": null,
2391 | "metadata": {},
2392 | "output_type": "execute_result"
2393 | }
2394 | ],
2395 | "source": [
2396 | "mat ⍸ 2 2 ⍴ 3 3 3 5"
2397 | ]
2398 | },
2399 | {
2400 | "cell_type": "markdown",
2401 | "id": "ad28d0b2",
2402 | "metadata": {},
2403 | "source": [
2404 | "### `⌈` (Upstile)"
2405 | ]
2406 | },
2407 | {
2408 | "cell_type": "markdown",
2409 | "id": "3db6d6cb",
2410 | "metadata": {},
2411 | "source": [
2412 | "#### monadic `⌈` (Ceiling)"
2413 | ]
2414 | },
2415 | {
2416 | "cell_type": "markdown",
2417 | "id": "f162a21e-b887-4a58-bb02-9c70e67100fa",
2418 | "metadata": {},
2419 | "source": [
2420 | "Rounds up to nearest whole number."
2421 | ]
2422 | },
2423 | {
2424 | "cell_type": "code",
2425 | "execution_count": null,
2426 | "id": "7223b897",
2427 | "metadata": {},
2428 | "outputs": [
2429 | {
2430 | "data": {
2431 | "text/html": [
2432 | "┌→───────┐\n",
2433 | "│4 ¯3 3 0│\n",
2434 | "└~───────┘\n",
2435 | "
"
2436 | ]
2437 | },
2438 | "execution_count": null,
2439 | "metadata": {},
2440 | "output_type": "execute_result"
2441 | }
2442 | ],
2443 | "source": [
2444 | "⌈ 3.4 ¯3.4 3 0"
2445 | ]
2446 | },
2447 | {
2448 | "cell_type": "markdown",
2449 | "id": "0717d224",
2450 | "metadata": {},
2451 | "source": [
2452 | "#### dyadic `⌈` (Maximum)"
2453 | ]
2454 | },
2455 | {
2456 | "cell_type": "markdown",
2457 | "id": "e97c8bc5-420c-44a4-850d-1f900c0f48e8",
2458 | "metadata": {},
2459 | "source": [
2460 | "Takes maximum of 2 values"
2461 | ]
2462 | },
2463 | {
2464 | "cell_type": "code",
2465 | "execution_count": null,
2466 | "id": "785a5a38",
2467 | "metadata": {},
2468 | "outputs": [
2469 | {
2470 | "data": {
2471 | "text/html": [
2472 | " \n",
2473 | "3\n",
2474 | " \n",
2475 | "
"
2476 | ]
2477 | },
2478 | "execution_count": null,
2479 | "metadata": {},
2480 | "output_type": "execute_result"
2481 | }
2482 | ],
2483 | "source": [
2484 | "3⌈2"
2485 | ]
2486 | },
2487 | {
2488 | "cell_type": "code",
2489 | "execution_count": null,
2490 | "id": "7a410ee3",
2491 | "metadata": {},
2492 | "outputs": [
2493 | {
2494 | "data": {
2495 | "text/html": [
2496 | "┌→──┐\n",
2497 | "│3 3│\n",
2498 | "└~──┘\n",
2499 | "
"
2500 | ]
2501 | },
2502 | "execution_count": null,
2503 | "metadata": {},
2504 | "output_type": "execute_result"
2505 | }
2506 | ],
2507 | "source": [
2508 | "3 2⌈2 3"
2509 | ]
2510 | },
2511 | {
2512 | "cell_type": "code",
2513 | "execution_count": null,
2514 | "id": "f9f78ce3",
2515 | "metadata": {},
2516 | "outputs": [
2517 | {
2518 | "data": {
2519 | "text/html": [
2520 | " \n",
2521 | "6\n",
2522 | " \n",
2523 | "
"
2524 | ]
2525 | },
2526 | "execution_count": null,
2527 | "metadata": {},
2528 | "output_type": "execute_result"
2529 | }
2530 | ],
2531 | "source": [
2532 | "4 ⌈ 6 ⌈ 2"
2533 | ]
2534 | },
2535 | {
2536 | "cell_type": "code",
2537 | "execution_count": null,
2538 | "id": "04ed6871",
2539 | "metadata": {},
2540 | "outputs": [
2541 | {
2542 | "data": {
2543 | "text/html": [
2544 | "┌→────┐\n",
2545 | "│0 6 2│\n",
2546 | "└~────┘\n",
2547 | "
"
2548 | ]
2549 | },
2550 | "execution_count": null,
2551 | "metadata": {},
2552 | "output_type": "execute_result"
2553 | }
2554 | ],
2555 | "source": [
2556 | "a ← ¯4 6 2\n",
2557 | "0 ⌈ a"
2558 | ]
2559 | },
2560 | {
2561 | "cell_type": "markdown",
2562 | "id": "c9a8d1b5",
2563 | "metadata": {},
2564 | "source": [
2565 | "### `⌊` (Downstile)"
2566 | ]
2567 | },
2568 | {
2569 | "cell_type": "markdown",
2570 | "id": "c054a3e9",
2571 | "metadata": {},
2572 | "source": [
2573 | "#### monadic `⌊` (Floor)"
2574 | ]
2575 | },
2576 | {
2577 | "cell_type": "markdown",
2578 | "id": "8feeafed-2657-4651-b817-95a4e09075a6",
2579 | "metadata": {},
2580 | "source": [
2581 | "Rounds down to nearest whole number"
2582 | ]
2583 | },
2584 | {
2585 | "cell_type": "code",
2586 | "execution_count": null,
2587 | "id": "aa41f28e",
2588 | "metadata": {},
2589 | "outputs": [
2590 | {
2591 | "data": {
2592 | "text/html": [
2593 | "┌→───────┐\n",
2594 | "│3 ¯4 3 0│\n",
2595 | "└~───────┘\n",
2596 | "
"
2597 | ]
2598 | },
2599 | "execution_count": null,
2600 | "metadata": {},
2601 | "output_type": "execute_result"
2602 | }
2603 | ],
2604 | "source": [
2605 | "⌊ 3.4 ¯3.4 3 0"
2606 | ]
2607 | },
2608 | {
2609 | "cell_type": "markdown",
2610 | "id": "a40dd397",
2611 | "metadata": {},
2612 | "source": [
2613 | "#### dyadic `⌊` (Minimum)"
2614 | ]
2615 | },
2616 | {
2617 | "cell_type": "markdown",
2618 | "id": "524a4b1b-3f65-4a2c-850a-37dd0deed965",
2619 | "metadata": {},
2620 | "source": [
2621 | "Takes minimum of 2 values"
2622 | ]
2623 | },
2624 | {
2625 | "cell_type": "code",
2626 | "execution_count": null,
2627 | "id": "d9a0b9a6",
2628 | "metadata": {},
2629 | "outputs": [
2630 | {
2631 | "data": {
2632 | "text/html": [
2633 | " \n",
2634 | "2.5\n",
2635 | " \n",
2636 | "
"
2637 | ]
2638 | },
2639 | "execution_count": null,
2640 | "metadata": {},
2641 | "output_type": "execute_result"
2642 | }
2643 | ],
2644 | "source": [
2645 | "4 ⌊ 6 ⌊ 2.5"
2646 | ]
2647 | }
2648 | ],
2649 | "metadata": {
2650 | "kernelspec": {
2651 | "display_name": "Dyalog APL",
2652 | "language": "apl",
2653 | "name": "dyalog-kernel"
2654 | }
2655 | },
2656 | "nbformat": 4,
2657 | "nbformat_minor": 5
2658 | }
2659 |
--------------------------------------------------------------------------------
/05_the_rest.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "raw",
5 | "id": "2990f581",
6 | "metadata": {},
7 | "source": [
8 | "---\n",
9 | "title: \"The rest of the glyphs\"\n",
10 | "author: \"Jeremy Howard\"\n",
11 | "date: \"2022-07-05\"\n",
12 | "categories: [Dyalog, APL, Glyphs]\n",
13 | "---"
14 | ]
15 | },
16 | {
17 | "cell_type": "code",
18 | "execution_count": null,
19 | "id": "84e8fa35",
20 | "metadata": {},
21 | "outputs": [
22 | {
23 | "data": {
24 | "text/html": [
25 | "┌→─────────────────────────────────────┐\n",
26 | "│Was ON -style=max -trains=tree -fns=on│\n",
27 | "└──────────────────────────────────────┘\n",
28 | "
"
29 | ]
30 | },
31 | "execution_count": null,
32 | "metadata": {},
33 | "output_type": "execute_result"
34 | }
35 | ],
36 | "source": [
37 | "]box on -style=max -trains=tree -fns=on"
38 | ]
39 | },
40 | {
41 | "cell_type": "markdown",
42 | "id": "da2674b7",
43 | "metadata": {},
44 | "source": [
45 | "## Sets and stuff"
46 | ]
47 | },
48 | {
49 | "cell_type": "markdown",
50 | "id": "84f5b849",
51 | "metadata": {},
52 | "source": [
53 | "### `∊` (Epsilon)"
54 | ]
55 | },
56 | {
57 | "cell_type": "markdown",
58 | "id": "1407b15c",
59 | "metadata": {},
60 | "source": [
61 | "#### monadic `∊` (Enlist)"
62 | ]
63 | },
64 | {
65 | "cell_type": "code",
66 | "execution_count": null,
67 | "id": "90a3cbab",
68 | "metadata": {},
69 | "outputs": [
70 | {
71 | "data": {
72 | "text/html": [
73 | "┌→────┐\n",
74 | "↓1 2 3│\n",
75 | "│4 5 6│\n",
76 | "└~────┘\n",
77 | "
"
78 | ]
79 | },
80 | "execution_count": null,
81 | "metadata": {},
82 | "output_type": "execute_result"
83 | }
84 | ],
85 | "source": [
86 | "⎕←mat←2 3⍴⍳6"
87 | ]
88 | },
89 | {
90 | "cell_type": "code",
91 | "execution_count": null,
92 | "id": "3c31775c",
93 | "metadata": {},
94 | "outputs": [
95 | {
96 | "data": {
97 | "text/html": [
98 | "┌→─────────────────────┐\n",
99 | "│0 1 2 3 4 5 6 7 8 nine│\n",
100 | "└+─────────────────────┘\n",
101 | "
"
102 | ]
103 | },
104 | "execution_count": null,
105 | "metadata": {},
106 | "output_type": "execute_result"
107 | }
108 | ],
109 | "source": [
110 | "∊ 0 mat (7 8) 'nine'"
111 | ]
112 | },
113 | {
114 | "cell_type": "markdown",
115 | "id": "36fb24f6",
116 | "metadata": {},
117 | "source": [
118 | "#### dyadic `∊` (Member of)"
119 | ]
120 | },
121 | {
122 | "cell_type": "code",
123 | "execution_count": null,
124 | "id": "8f66b6f4",
125 | "metadata": {},
126 | "outputs": [
127 | {
128 | "data": {
129 | "text/html": [
130 | "┌→──┐\n",
131 | "│0 1│\n",
132 | "└~──┘\n",
133 | "
"
134 | ]
135 | },
136 | "execution_count": null,
137 | "metadata": {},
138 | "output_type": "execute_result"
139 | }
140 | ],
141 | "source": [
142 | "'abc' 4 ∊ 4 'ab' 'abcd'"
143 | ]
144 | },
145 | {
146 | "cell_type": "code",
147 | "execution_count": null,
148 | "id": "42c03182",
149 | "metadata": {},
150 | "outputs": [
151 | {
152 | "data": {
153 | "text/html": [
154 | "┌→────┐\n",
155 | "↓0 1 0│\n",
156 | "│1 0 1│\n",
157 | "└~────┘\n",
158 | "
"
159 | ]
160 | },
161 | "execution_count": null,
162 | "metadata": {},
163 | "output_type": "execute_result"
164 | }
165 | ],
166 | "source": [
167 | "mat←2 3⍴⍳6\n",
168 | "mat ∊ 6 2 7 4"
169 | ]
170 | },
171 | {
172 | "cell_type": "markdown",
173 | "id": "567c7021",
174 | "metadata": {},
175 | "source": [
176 | "### `⍷` (Epsilon Underbar)"
177 | ]
178 | },
179 | {
180 | "cell_type": "markdown",
181 | "id": "05507611",
182 | "metadata": {},
183 | "source": [
184 | "#### dyadic `⍷` (Find)"
185 | ]
186 | },
187 | {
188 | "cell_type": "code",
189 | "execution_count": null,
190 | "id": "60eeabd6",
191 | "metadata": {},
192 | "outputs": [
193 | {
194 | "data": {
195 | "text/html": [
196 | "┌→────────────┐\n",
197 | "│0 1 0 1 0 0 0│\n",
198 | "└~────────────┘\n",
199 | "
"
200 | ]
201 | },
202 | "execution_count": null,
203 | "metadata": {},
204 | "output_type": "execute_result"
205 | }
206 | ],
207 | "source": [
208 | "1 ⍷ 3 1 4 1 5 9 2"
209 | ]
210 | },
211 | {
212 | "cell_type": "code",
213 | "execution_count": null,
214 | "id": "4ad69e8d",
215 | "metadata": {},
216 | "outputs": [
217 | {
218 | "data": {
219 | "text/html": [
220 | "┌→────────────┐\n",
221 | "│0 1 0 0 0 0 0│\n",
222 | "└~────────────┘\n",
223 | "
"
224 | ]
225 | },
226 | "execution_count": null,
227 | "metadata": {},
228 | "output_type": "execute_result"
229 | }
230 | ],
231 | "source": [
232 | "1 4 ⍷ 3 1 4 1 5 9 2"
233 | ]
234 | },
235 | {
236 | "cell_type": "code",
237 | "execution_count": null,
238 | "id": "210249f5",
239 | "metadata": {},
240 | "outputs": [
241 | {
242 | "data": {
243 | "text/html": [
244 | "┌→──────────┐\n",
245 | "│0 1 0 1 0 0│\n",
246 | "└~──────────┘\n",
247 | "
"
248 | ]
249 | },
250 | "execution_count": null,
251 | "metadata": {},
252 | "output_type": "execute_result"
253 | }
254 | ],
255 | "source": [
256 | "'ana' ⍷ 'Banana'"
257 | ]
258 | },
259 | {
260 | "cell_type": "code",
261 | "execution_count": null,
262 | "id": "965336e9",
263 | "metadata": {},
264 | "outputs": [
265 | {
266 | "data": {
267 | "text/html": [
268 | "┌→────────────────┐\n",
269 | "│ ┌→──┐ ┌→──────┐ │\n",
270 | "│ ↓0 1│ ↓0 1 0 0│ │\n",
271 | "│ │1 0│ │1 0 0 1│ │\n",
272 | "│ └~──┘ │0 0 1 0│ │\n",
273 | "│ │0 1 0 0│ │\n",
274 | "│ └~──────┘ │\n",
275 | "└∊────────────────┘\n",
276 | "
"
277 | ]
278 | },
279 | "execution_count": null,
280 | "metadata": {},
281 | "output_type": "execute_result"
282 | }
283 | ],
284 | "source": [
285 | "X ← 2 2 ⍴ 0 1 1 0\n",
286 | "Y ← 4 4 ⍴ 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0\n",
287 | "X Y"
288 | ]
289 | },
290 | {
291 | "cell_type": "code",
292 | "execution_count": null,
293 | "id": "14467662",
294 | "metadata": {},
295 | "outputs": [
296 | {
297 | "data": {
298 | "text/html": [
299 | "┌→──────┐\n",
300 | "↓1 0 0 0│\n",
301 | "│0 0 1 0│\n",
302 | "│0 1 0 0│\n",
303 | "│0 0 0 0│\n",
304 | "└~──────┘\n",
305 | "
"
306 | ]
307 | },
308 | "execution_count": null,
309 | "metadata": {},
310 | "output_type": "execute_result"
311 | }
312 | ],
313 | "source": [
314 | "X ⍷ Y"
315 | ]
316 | },
317 | {
318 | "cell_type": "markdown",
319 | "id": "426ab86a",
320 | "metadata": {},
321 | "source": [
322 | "### `∩` (Up shoe)"
323 | ]
324 | },
325 | {
326 | "cell_type": "markdown",
327 | "id": "01db0c25",
328 | "metadata": {},
329 | "source": [
330 | "#### dyadic `∩` (Intersection)"
331 | ]
332 | },
333 | {
334 | "cell_type": "code",
335 | "execution_count": null,
336 | "id": "7e4acc70",
337 | "metadata": {},
338 | "outputs": [
339 | {
340 | "data": {
341 | "text/html": [
342 | "┌→──┐\n",
343 | "│ARA│\n",
344 | "└───┘\n",
345 | "
"
346 | ]
347 | },
348 | "execution_count": null,
349 | "metadata": {},
350 | "output_type": "execute_result"
351 | }
352 | ],
353 | "source": [
354 | "'ABRA'∩'CAR'"
355 | ]
356 | },
357 | {
358 | "cell_type": "code",
359 | "execution_count": null,
360 | "id": "dc6d81d2",
361 | "metadata": {},
362 | "outputs": [
363 | {
364 | "data": {
365 | "text/html": [
366 | "┌→────────┐\n",
367 | "│ ┌→─┐ │\n",
368 | "│ 22 │ab│ │\n",
369 | "│ └──┘ │\n",
370 | "└∊────────┘\n",
371 | "
"
372 | ]
373 | },
374 | "execution_count": null,
375 | "metadata": {},
376 | "output_type": "execute_result"
377 | }
378 | ],
379 | "source": [
380 | "22 'ab' 'fg' ∩ 'a' 'ab' 22"
381 | ]
382 | },
383 | {
384 | "cell_type": "markdown",
385 | "id": "fb7757a4",
386 | "metadata": {},
387 | "source": [
388 | "### `∪` (Down shoe)"
389 | ]
390 | },
391 | {
392 | "cell_type": "markdown",
393 | "id": "b5515721",
394 | "metadata": {},
395 | "source": [
396 | "#### monadic `∪` (Unique)"
397 | ]
398 | },
399 | {
400 | "cell_type": "code",
401 | "execution_count": null,
402 | "id": "b87f55b6",
403 | "metadata": {},
404 | "outputs": [],
405 | "source": [
406 | "a ← 2 3 4 2 3 4 5"
407 | ]
408 | },
409 | {
410 | "cell_type": "code",
411 | "execution_count": null,
412 | "id": "c4d34ad5",
413 | "metadata": {},
414 | "outputs": [
415 | {
416 | "data": {
417 | "text/html": [
418 | "┌→──────┐\n",
419 | "│2 3 4 5│\n",
420 | "└~──────┘\n",
421 | "
"
422 | ]
423 | },
424 | "execution_count": null,
425 | "metadata": {},
426 | "output_type": "execute_result"
427 | }
428 | ],
429 | "source": [
430 | "∪a"
431 | ]
432 | },
433 | {
434 | "cell_type": "code",
435 | "execution_count": null,
436 | "id": "8e0bc0e8",
437 | "metadata": {},
438 | "outputs": [
439 | {
440 | "data": {
441 | "text/html": [
442 | "┌→──────┐\n",
443 | "│2 3 4 5│\n",
444 | "└~──────┘\n",
445 | "
"
446 | ]
447 | },
448 | "execution_count": null,
449 | "metadata": {},
450 | "output_type": "execute_result"
451 | }
452 | ],
453 | "source": [
454 | "(≠a)/a "
455 | ]
456 | },
457 | {
458 | "cell_type": "code",
459 | "execution_count": null,
460 | "id": "dfbbec06",
461 | "metadata": {},
462 | "outputs": [
463 | {
464 | "data": {
465 | "text/html": [
466 | "┌→──────────────┐\n",
467 | "│ ┌→─┐ ┌→─┐ │\n",
468 | "│ │ab│ │ba│ 1 2 │\n",
469 | "│ └──┘ └──┘ │\n",
470 | "└∊──────────────┘\n",
471 | "
"
472 | ]
473 | },
474 | "execution_count": null,
475 | "metadata": {},
476 | "output_type": "execute_result"
477 | }
478 | ],
479 | "source": [
480 | "∪ 'ab' 'ba' 'ab' 1 1 2"
481 | ]
482 | },
483 | {
484 | "cell_type": "markdown",
485 | "id": "5e5b8871",
486 | "metadata": {},
487 | "source": [
488 | "#### dyadic `∪` (Union)"
489 | ]
490 | },
491 | {
492 | "cell_type": "code",
493 | "execution_count": null,
494 | "id": "7fcc51fa",
495 | "metadata": {},
496 | "outputs": [
497 | {
498 | "data": {
499 | "text/html": [
500 | "┌→────┐\n",
501 | "│ABRAC│\n",
502 | "└─────┘\n",
503 | "
"
504 | ]
505 | },
506 | "execution_count": null,
507 | "metadata": {},
508 | "output_type": "execute_result"
509 | }
510 | ],
511 | "source": [
512 | "'ABRA'∪'CAR'"
513 | ]
514 | },
515 | {
516 | "cell_type": "code",
517 | "execution_count": null,
518 | "id": "1d1e7955",
519 | "metadata": {},
520 | "outputs": [
521 | {
522 | "data": {
523 | "text/html": [
524 | "┌→───────────────┐\n",
525 | "│ ┌→─┐ ┌→─┐ │\n",
526 | "│ 22 │ab│ │fg│ a │\n",
527 | "│ └──┘ └──┘ - │\n",
528 | "└∊───────────────┘\n",
529 | "
"
530 | ]
531 | },
532 | "execution_count": null,
533 | "metadata": {},
534 | "output_type": "execute_result"
535 | }
536 | ],
537 | "source": [
538 | "22 'ab' 'fg' ∪ 'a' 'ab' 22"
539 | ]
540 | },
541 | {
542 | "cell_type": "markdown",
543 | "id": "f8056248",
544 | "metadata": {},
545 | "source": [
546 | "## Sort / index"
547 | ]
548 | },
549 | {
550 | "cell_type": "markdown",
551 | "id": "77e272c6",
552 | "metadata": {},
553 | "source": [
554 | "### `⌷` (Squad)"
555 | ]
556 | },
557 | {
558 | "cell_type": "markdown",
559 | "id": "0c816033",
560 | "metadata": {},
561 | "source": [
562 | "#### monadic `⌷` (Materialise)"
563 | ]
564 | },
565 | {
566 | "cell_type": "markdown",
567 | "id": "5ba60006",
568 | "metadata": {},
569 | "source": [
570 | "For `⌷ ⍵`: If ⍵ is an array, returns ⍵. For a class/COM/.Net object, it materialises the items."
571 | ]
572 | },
573 | {
574 | "cell_type": "markdown",
575 | "id": "d8e72637",
576 | "metadata": {},
577 | "source": [
578 | "#### dyadic `⌷` (Index)"
579 | ]
580 | },
581 | {
582 | "cell_type": "code",
583 | "execution_count": null,
584 | "id": "72801c8e",
585 | "metadata": {},
586 | "outputs": [
587 | {
588 | "data": {
589 | "text/html": [
590 | " \n",
591 | "6\n",
592 | " \n",
593 | "
"
594 | ]
595 | },
596 | "execution_count": null,
597 | "metadata": {},
598 | "output_type": "execute_result"
599 | }
600 | ],
601 | "source": [
602 | "v ← 2×⍳12\n",
603 | "3⌷v"
604 | ]
605 | },
606 | {
607 | "cell_type": "code",
608 | "execution_count": null,
609 | "id": "b9a792d4",
610 | "metadata": {},
611 | "outputs": [
612 | {
613 | "data": {
614 | "text/html": [
615 | "┌→───┐\n",
616 | "│6 10│\n",
617 | "└~───┘\n",
618 | "
"
619 | ]
620 | },
621 | "execution_count": null,
622 | "metadata": {},
623 | "output_type": "execute_result"
624 | }
625 | ],
626 | "source": [
627 | "(⊂3 5) ⌷v"
628 | ]
629 | },
630 | {
631 | "cell_type": "code",
632 | "execution_count": null,
633 | "id": "1268fe10",
634 | "metadata": {},
635 | "outputs": [
636 | {
637 | "data": {
638 | "text/html": [
639 | "┌→─────────┐\n",
640 | "↓1 2 3 4│\n",
641 | "│5 6 7 8│\n",
642 | "│9 10 11 12│\n",
643 | "└~─────────┘\n",
644 | "
"
645 | ]
646 | },
647 | "execution_count": null,
648 | "metadata": {},
649 | "output_type": "execute_result"
650 | }
651 | ],
652 | "source": [
653 | "⎕ ← mat ← 3 4 ⍴⍳12"
654 | ]
655 | },
656 | {
657 | "cell_type": "code",
658 | "execution_count": null,
659 | "id": "137a5f5f",
660 | "metadata": {},
661 | "outputs": [
662 | {
663 | "data": {
664 | "text/html": [
665 | " \n",
666 | "7\n",
667 | " \n",
668 | "
"
669 | ]
670 | },
671 | "execution_count": null,
672 | "metadata": {},
673 | "output_type": "execute_result"
674 | }
675 | ],
676 | "source": [
677 | "2 3 ⌷ mat"
678 | ]
679 | },
680 | {
681 | "cell_type": "markdown",
682 | "id": "3b2eaa84",
683 | "metadata": {},
684 | "source": [
685 | "### `⍒` (Grade Down)"
686 | ]
687 | },
688 | {
689 | "cell_type": "markdown",
690 | "id": "09ab35bf",
691 | "metadata": {},
692 | "source": [
693 | "#### monadic `⍒` (Grade Down)"
694 | ]
695 | },
696 | {
697 | "cell_type": "code",
698 | "execution_count": null,
699 | "id": "2e77203d",
700 | "metadata": {},
701 | "outputs": [
702 | {
703 | "data": {
704 | "text/html": [
705 | "┌→────────┐\n",
706 | "│4 3 1 5 2│\n",
707 | "└~────────┘\n",
708 | "
"
709 | ]
710 | },
711 | "execution_count": null,
712 | "metadata": {},
713 | "output_type": "execute_result"
714 | }
715 | ],
716 | "source": [
717 | "⍒ 33 11 44 66 22"
718 | ]
719 | },
720 | {
721 | "cell_type": "code",
722 | "execution_count": null,
723 | "id": "6df7fa75",
724 | "metadata": {},
725 | "outputs": [],
726 | "source": [
727 | "a ← 33 11 44 66 22"
728 | ]
729 | },
730 | {
731 | "cell_type": "code",
732 | "execution_count": null,
733 | "id": "6ca39670",
734 | "metadata": {},
735 | "outputs": [
736 | {
737 | "data": {
738 | "text/html": [
739 | "┌→─────────────┐\n",
740 | "│66 44 33 22 11│\n",
741 | "└~─────────────┘\n",
742 | "
"
743 | ]
744 | },
745 | "execution_count": null,
746 | "metadata": {},
747 | "output_type": "execute_result"
748 | }
749 | ],
750 | "source": [
751 | "a[⍒a]"
752 | ]
753 | },
754 | {
755 | "cell_type": "code",
756 | "execution_count": null,
757 | "id": "c3dd94c3",
758 | "metadata": {},
759 | "outputs": [
760 | {
761 | "data": {
762 | "text/html": [
763 | "┌→─────────────┐\n",
764 | "│66 44 33 22 11│\n",
765 | "└~─────────────┘\n",
766 | "
"
767 | ]
768 | },
769 | "execution_count": null,
770 | "metadata": {},
771 | "output_type": "execute_result"
772 | }
773 | ],
774 | "source": [
775 | "a⌷⍨⊂⍒a"
776 | ]
777 | },
778 | {
779 | "cell_type": "markdown",
780 | "id": "0bec4127",
781 | "metadata": {},
782 | "source": [
783 | "`{⍵[⍋⍵]}` and `{(⊂⍋⍵)⌷⍵}` are sort idioms (special cased for performance)"
784 | ]
785 | },
786 | {
787 | "cell_type": "code",
788 | "execution_count": null,
789 | "id": "ff298201",
790 | "metadata": {},
791 | "outputs": [],
792 | "source": [
793 | "sort ← ⌷⍨∘⊂∘⍒⍨"
794 | ]
795 | },
796 | {
797 | "cell_type": "code",
798 | "execution_count": null,
799 | "id": "710685d5",
800 | "metadata": {},
801 | "outputs": [
802 | {
803 | "data": {
804 | "text/html": [
805 | "┌→─────────────┐\n",
806 | "│66 44 33 22 11│\n",
807 | "└~─────────────┘\n",
808 | "
"
809 | ]
810 | },
811 | "execution_count": null,
812 | "metadata": {},
813 | "output_type": "execute_result"
814 | }
815 | ],
816 | "source": [
817 | "sort a"
818 | ]
819 | },
820 | {
821 | "cell_type": "code",
822 | "execution_count": null,
823 | "id": "dafc738a",
824 | "metadata": {},
825 | "outputs": [],
826 | "source": [
827 | "tsort ← (⊂∘⍒)⌷⊢ ⍝ h/t Rory Kemp"
828 | ]
829 | },
830 | {
831 | "cell_type": "code",
832 | "execution_count": null,
833 | "id": "92af3196",
834 | "metadata": {},
835 | "outputs": [
836 | {
837 | "data": {
838 | "text/html": [
839 | "┌→─────────────┐\n",
840 | "│66 44 33 22 11│\n",
841 | "└~─────────────┘\n",
842 | "
"
843 | ]
844 | },
845 | "execution_count": null,
846 | "metadata": {},
847 | "output_type": "execute_result"
848 | }
849 | ],
850 | "source": [
851 | "tsort a"
852 | ]
853 | },
854 | {
855 | "cell_type": "markdown",
856 | "id": "815f2ca9",
857 | "metadata": {},
858 | "source": [
859 | "#### dyadic `⍒` (Dyadic Grade Down)"
860 | ]
861 | },
862 | {
863 | "cell_type": "code",
864 | "execution_count": null,
865 | "id": "834b4267",
866 | "metadata": {},
867 | "outputs": [],
868 | "source": [
869 | "a ← 'abcdefgabcdefg'"
870 | ]
871 | },
872 | {
873 | "cell_type": "code",
874 | "execution_count": null,
875 | "id": "ed3d0a25",
876 | "metadata": {},
877 | "outputs": [],
878 | "source": [
879 | "b ← 'cgf' ⍒ a"
880 | ]
881 | },
882 | {
883 | "cell_type": "code",
884 | "execution_count": null,
885 | "id": "16954655",
886 | "metadata": {},
887 | "outputs": [
888 | {
889 | "data": {
890 | "text/html": [
891 | "┌→─────────────┐\n",
892 | "│abdeabdeffggcc│\n",
893 | "└──────────────┘\n",
894 | "
"
895 | ]
896 | },
897 | "execution_count": null,
898 | "metadata": {},
899 | "output_type": "execute_result"
900 | }
901 | ],
902 | "source": [
903 | "a⌷⍨⊂b"
904 | ]
905 | },
906 | {
907 | "cell_type": "markdown",
908 | "id": "6462e384",
909 | "metadata": {},
910 | "source": [
911 | "### `⍋` (Grade Up)"
912 | ]
913 | },
914 | {
915 | "cell_type": "markdown",
916 | "id": "325836fc",
917 | "metadata": {},
918 | "source": [
919 | "#### monadic `⍋` (Grade Up)"
920 | ]
921 | },
922 | {
923 | "cell_type": "code",
924 | "execution_count": null,
925 | "id": "4659cd30",
926 | "metadata": {},
927 | "outputs": [
928 | {
929 | "data": {
930 | "text/html": [
931 | "┌→────────┐\n",
932 | "│2 5 1 3 4│\n",
933 | "└~────────┘\n",
934 | "
"
935 | ]
936 | },
937 | "execution_count": null,
938 | "metadata": {},
939 | "output_type": "execute_result"
940 | }
941 | ],
942 | "source": [
943 | "⍋ 33 11 44 66 22"
944 | ]
945 | },
946 | {
947 | "cell_type": "code",
948 | "execution_count": null,
949 | "id": "6e85eeeb",
950 | "metadata": {},
951 | "outputs": [],
952 | "source": [
953 | "a ← 33 11 44 66 22"
954 | ]
955 | },
956 | {
957 | "cell_type": "code",
958 | "execution_count": null,
959 | "id": "670053ed",
960 | "metadata": {},
961 | "outputs": [
962 | {
963 | "data": {
964 | "text/html": [
965 | "┌→─────────────┐\n",
966 | "│11 22 33 44 66│\n",
967 | "└~─────────────┘\n",
968 | "
"
969 | ]
970 | },
971 | "execution_count": null,
972 | "metadata": {},
973 | "output_type": "execute_result"
974 | }
975 | ],
976 | "source": [
977 | "a[⍋a]"
978 | ]
979 | },
980 | {
981 | "cell_type": "code",
982 | "execution_count": null,
983 | "id": "8b0eb4bd",
984 | "metadata": {},
985 | "outputs": [
986 | {
987 | "data": {
988 | "text/html": [
989 | "┌→─────────────┐\n",
990 | "│11 22 33 44 66│\n",
991 | "└~─────────────┘\n",
992 | "
"
993 | ]
994 | },
995 | "execution_count": null,
996 | "metadata": {},
997 | "output_type": "execute_result"
998 | }
999 | ],
1000 | "source": [
1001 | "a⌷⍨⊂⍋a"
1002 | ]
1003 | },
1004 | {
1005 | "cell_type": "markdown",
1006 | "id": "a717b1f2",
1007 | "metadata": {},
1008 | "source": [
1009 | "#### dyadic `⍒` (Dyadic Grade Down)"
1010 | ]
1011 | },
1012 | {
1013 | "cell_type": "code",
1014 | "execution_count": null,
1015 | "id": "90ad8673",
1016 | "metadata": {},
1017 | "outputs": [
1018 | {
1019 | "data": {
1020 | "text/html": [
1021 | "┌→─────────────┐\n",
1022 | "│ccggffabdeabde│\n",
1023 | "└──────────────┘\n",
1024 | "
"
1025 | ]
1026 | },
1027 | "execution_count": null,
1028 | "metadata": {},
1029 | "output_type": "execute_result"
1030 | }
1031 | ],
1032 | "source": [
1033 | "a ← 'abcdefgabcdefg'\n",
1034 | "b ← 'cgf' ⍋ a\n",
1035 | "a⌷⍨⊂b"
1036 | ]
1037 | },
1038 | {
1039 | "cell_type": "markdown",
1040 | "id": "484bc54f",
1041 | "metadata": {},
1042 | "source": [
1043 | "## Rotate / transpose / flip"
1044 | ]
1045 | },
1046 | {
1047 | "cell_type": "markdown",
1048 | "id": "39dcdf7b",
1049 | "metadata": {},
1050 | "source": [
1051 | "### `⌽` (Circle Stile)"
1052 | ]
1053 | },
1054 | {
1055 | "cell_type": "markdown",
1056 | "id": "9799fd42",
1057 | "metadata": {},
1058 | "source": [
1059 | "#### monadic `⌽` (Reverse)"
1060 | ]
1061 | },
1062 | {
1063 | "cell_type": "code",
1064 | "execution_count": null,
1065 | "id": "d8cf03d6",
1066 | "metadata": {},
1067 | "outputs": [
1068 | {
1069 | "data": {
1070 | "text/html": [
1071 | "┌→────┐\n",
1072 | "│smart│\n",
1073 | "└─────┘\n",
1074 | "
"
1075 | ]
1076 | },
1077 | "execution_count": null,
1078 | "metadata": {},
1079 | "output_type": "execute_result"
1080 | }
1081 | ],
1082 | "source": [
1083 | "⌽ 'trams'"
1084 | ]
1085 | },
1086 | {
1087 | "cell_type": "code",
1088 | "execution_count": null,
1089 | "id": "c3007ccf",
1090 | "metadata": {},
1091 | "outputs": [
1092 | {
1093 | "data": {
1094 | "text/html": [
1095 | "┌→─────────┐\n",
1096 | "↓1 2 3 4│\n",
1097 | "│5 6 7 8│\n",
1098 | "│9 10 11 12│\n",
1099 | "└~─────────┘\n",
1100 | "
"
1101 | ]
1102 | },
1103 | "execution_count": null,
1104 | "metadata": {},
1105 | "output_type": "execute_result"
1106 | }
1107 | ],
1108 | "source": [
1109 | "⎕ ← mat ← 3 4 ⍴⍳12"
1110 | ]
1111 | },
1112 | {
1113 | "cell_type": "code",
1114 | "execution_count": null,
1115 | "id": "076ec08c",
1116 | "metadata": {},
1117 | "outputs": [
1118 | {
1119 | "data": {
1120 | "text/html": [
1121 | "┌→─────────┐\n",
1122 | "↓ 4 3 2 1│\n",
1123 | "│ 8 7 6 5│\n",
1124 | "│12 11 10 9│\n",
1125 | "└~─────────┘\n",
1126 | "
"
1127 | ]
1128 | },
1129 | "execution_count": null,
1130 | "metadata": {},
1131 | "output_type": "execute_result"
1132 | }
1133 | ],
1134 | "source": [
1135 | "⌽ mat"
1136 | ]
1137 | },
1138 | {
1139 | "cell_type": "markdown",
1140 | "id": "8912e595",
1141 | "metadata": {},
1142 | "source": [
1143 | "#### dyadic `⌽` (Rotate)"
1144 | ]
1145 | },
1146 | {
1147 | "cell_type": "code",
1148 | "execution_count": null,
1149 | "id": "d10daf7d",
1150 | "metadata": {},
1151 | "outputs": [
1152 | {
1153 | "data": {
1154 | "text/html": [
1155 | "┌→───────┐\n",
1156 | "│atStandH│\n",
1157 | "└────────┘\n",
1158 | "
"
1159 | ]
1160 | },
1161 | "execution_count": null,
1162 | "metadata": {},
1163 | "output_type": "execute_result"
1164 | }
1165 | ],
1166 | "source": [
1167 | "1 ⌽ 'HatStand'"
1168 | ]
1169 | },
1170 | {
1171 | "cell_type": "code",
1172 | "execution_count": null,
1173 | "id": "3c9acd25",
1174 | "metadata": {},
1175 | "outputs": [
1176 | {
1177 | "data": {
1178 | "text/html": [
1179 | "┌→───────┐\n",
1180 | "│StandHat│\n",
1181 | "└────────┘\n",
1182 | "
"
1183 | ]
1184 | },
1185 | "execution_count": null,
1186 | "metadata": {},
1187 | "output_type": "execute_result"
1188 | }
1189 | ],
1190 | "source": [
1191 | "3 ⌽ 'HatStand'"
1192 | ]
1193 | },
1194 | {
1195 | "cell_type": "code",
1196 | "execution_count": null,
1197 | "id": "5fbabe11",
1198 | "metadata": {},
1199 | "outputs": [
1200 | {
1201 | "data": {
1202 | "text/html": [
1203 | "┌→──────────┐\n",
1204 | "│5 6 1 2 3 4│\n",
1205 | "└~──────────┘\n",
1206 | "
"
1207 | ]
1208 | },
1209 | "execution_count": null,
1210 | "metadata": {},
1211 | "output_type": "execute_result"
1212 | }
1213 | ],
1214 | "source": [
1215 | "¯2 ⌽ 1 2 3 4 5 6"
1216 | ]
1217 | },
1218 | {
1219 | "cell_type": "code",
1220 | "execution_count": null,
1221 | "id": "4a5246f2",
1222 | "metadata": {},
1223 | "outputs": [
1224 | {
1225 | "data": {
1226 | "text/html": [
1227 | "┌→─────────┐\n",
1228 | "↓1 2 3 4│\n",
1229 | "│5 6 7 8│\n",
1230 | "│9 10 11 12│\n",
1231 | "└~─────────┘\n",
1232 | "
"
1233 | ]
1234 | },
1235 | "execution_count": null,
1236 | "metadata": {},
1237 | "output_type": "execute_result"
1238 | }
1239 | ],
1240 | "source": [
1241 | "⎕ ← mat ← 3 4 ⍴⍳12"
1242 | ]
1243 | },
1244 | {
1245 | "cell_type": "code",
1246 | "execution_count": null,
1247 | "id": "ec0be1f9",
1248 | "metadata": {},
1249 | "outputs": [
1250 | {
1251 | "data": {
1252 | "text/html": [
1253 | "┌→─────────┐\n",
1254 | "↓ 4 1 2 3│\n",
1255 | "│ 8 5 6 7│\n",
1256 | "│12 9 10 11│\n",
1257 | "└~─────────┘\n",
1258 | "
"
1259 | ]
1260 | },
1261 | "execution_count": null,
1262 | "metadata": {},
1263 | "output_type": "execute_result"
1264 | }
1265 | ],
1266 | "source": [
1267 | "¯1 ⌽ mat"
1268 | ]
1269 | },
1270 | {
1271 | "cell_type": "code",
1272 | "execution_count": null,
1273 | "id": "86a51ea9",
1274 | "metadata": {},
1275 | "outputs": [
1276 | {
1277 | "data": {
1278 | "text/html": [
1279 | "┌→─────────┐\n",
1280 | "↓ 2 3 4 1│\n",
1281 | "│ 8 5 6 7│\n",
1282 | "│11 12 9 10│\n",
1283 | "└~─────────┘\n",
1284 | "
"
1285 | ]
1286 | },
1287 | "execution_count": null,
1288 | "metadata": {},
1289 | "output_type": "execute_result"
1290 | }
1291 | ],
1292 | "source": [
1293 | "1 ¯1 2 ⌽ mat"
1294 | ]
1295 | },
1296 | {
1297 | "cell_type": "markdown",
1298 | "id": "7b284ee6",
1299 | "metadata": {},
1300 | "source": [
1301 | "### `⊖` (Circle Bar)"
1302 | ]
1303 | },
1304 | {
1305 | "cell_type": "markdown",
1306 | "id": "45a8f3e7",
1307 | "metadata": {},
1308 | "source": [
1309 | "#### monadic `⊖` (Reverse First)"
1310 | ]
1311 | },
1312 | {
1313 | "cell_type": "code",
1314 | "execution_count": null,
1315 | "id": "606bbe70",
1316 | "metadata": {},
1317 | "outputs": [
1318 | {
1319 | "data": {
1320 | "text/html": [
1321 | "┌→────┐\n",
1322 | "│smart│\n",
1323 | "└─────┘\n",
1324 | "
"
1325 | ]
1326 | },
1327 | "execution_count": null,
1328 | "metadata": {},
1329 | "output_type": "execute_result"
1330 | }
1331 | ],
1332 | "source": [
1333 | "⊖ 'trams'"
1334 | ]
1335 | },
1336 | {
1337 | "cell_type": "code",
1338 | "execution_count": null,
1339 | "id": "68ab5beb",
1340 | "metadata": {},
1341 | "outputs": [
1342 | {
1343 | "data": {
1344 | "text/html": [
1345 | "┌→─────────┐\n",
1346 | "↓9 10 11 12│\n",
1347 | "│5 6 7 8│\n",
1348 | "│1 2 3 4│\n",
1349 | "└~─────────┘\n",
1350 | "
"
1351 | ]
1352 | },
1353 | "execution_count": null,
1354 | "metadata": {},
1355 | "output_type": "execute_result"
1356 | }
1357 | ],
1358 | "source": [
1359 | "mat ← 3 4 ⍴⍳12\n",
1360 | "⊖ mat"
1361 | ]
1362 | },
1363 | {
1364 | "cell_type": "markdown",
1365 | "id": "ae5a17ec",
1366 | "metadata": {},
1367 | "source": [
1368 | "#### dyadic `⊖` (Rotate First)"
1369 | ]
1370 | },
1371 | {
1372 | "cell_type": "code",
1373 | "execution_count": null,
1374 | "id": "cd078b60",
1375 | "metadata": {},
1376 | "outputs": [
1377 | {
1378 | "data": {
1379 | "text/html": [
1380 | "┌→───────┐\n",
1381 | "│StandHat│\n",
1382 | "└────────┘\n",
1383 | "
"
1384 | ]
1385 | },
1386 | "execution_count": null,
1387 | "metadata": {},
1388 | "output_type": "execute_result"
1389 | }
1390 | ],
1391 | "source": [
1392 | "3 ⊖ 'HatStand'"
1393 | ]
1394 | },
1395 | {
1396 | "cell_type": "code",
1397 | "execution_count": null,
1398 | "id": "cdf5770c",
1399 | "metadata": {},
1400 | "outputs": [
1401 | {
1402 | "data": {
1403 | "text/html": [
1404 | "┌→─────────┐\n",
1405 | "↓9 10 11 12│\n",
1406 | "│1 2 3 4│\n",
1407 | "│5 6 7 8│\n",
1408 | "└~─────────┘\n",
1409 | "
"
1410 | ]
1411 | },
1412 | "execution_count": null,
1413 | "metadata": {},
1414 | "output_type": "execute_result"
1415 | }
1416 | ],
1417 | "source": [
1418 | "mat ← 3 4 ⍴⍳12\n",
1419 | "¯1 ⊖ mat"
1420 | ]
1421 | },
1422 | {
1423 | "cell_type": "markdown",
1424 | "id": "db239b56",
1425 | "metadata": {},
1426 | "source": [
1427 | "### `⍉` (Circle Bar)"
1428 | ]
1429 | },
1430 | {
1431 | "cell_type": "markdown",
1432 | "id": "307d55a9",
1433 | "metadata": {},
1434 | "source": [
1435 | "#### monadic `⍉` (Transpose)"
1436 | ]
1437 | },
1438 | {
1439 | "cell_type": "code",
1440 | "execution_count": null,
1441 | "id": "a8e58b17",
1442 | "metadata": {},
1443 | "outputs": [
1444 | {
1445 | "data": {
1446 | "text/html": [
1447 | "┌→─────┐\n",
1448 | "↓1 5 9│\n",
1449 | "│2 6 10│\n",
1450 | "│3 7 11│\n",
1451 | "│4 8 12│\n",
1452 | "└~─────┘\n",
1453 | "
"
1454 | ]
1455 | },
1456 | "execution_count": null,
1457 | "metadata": {},
1458 | "output_type": "execute_result"
1459 | }
1460 | ],
1461 | "source": [
1462 | "mat ← 3 4 ⍴⍳12\n",
1463 | "⍉ mat"
1464 | ]
1465 | },
1466 | {
1467 | "cell_type": "code",
1468 | "execution_count": null,
1469 | "id": "edde848f",
1470 | "metadata": {},
1471 | "outputs": [
1472 | {
1473 | "data": {
1474 | "text/html": [
1475 | "┌┌→──────────┐\n",
1476 | "↓↓ 1 2 3 4│\n",
1477 | "││ 5 6 7 8│\n",
1478 | "││ 9 10 11 12│\n",
1479 | "││ │\n",
1480 | "││13 14 15 16│\n",
1481 | "││17 18 19 20│\n",
1482 | "││21 22 23 24│\n",
1483 | "└└~──────────┘\n",
1484 | "
"
1485 | ]
1486 | },
1487 | "execution_count": null,
1488 | "metadata": {},
1489 | "output_type": "execute_result"
1490 | }
1491 | ],
1492 | "source": [
1493 | "⎕←cube ← 2 3 4 ⍴⍳24"
1494 | ]
1495 | },
1496 | {
1497 | "cell_type": "code",
1498 | "execution_count": null,
1499 | "id": "c46169dd",
1500 | "metadata": {},
1501 | "outputs": [
1502 | {
1503 | "data": {
1504 | "text/html": [
1505 | "┌┌→────┐\n",
1506 | "↓↓ 1 13│\n",
1507 | "││ 5 17│\n",
1508 | "││ 9 21│\n",
1509 | "││ │\n",
1510 | "││ 2 14│\n",
1511 | "││ 6 18│\n",
1512 | "││10 22│\n",
1513 | "││ │\n",
1514 | "││ 3 15│\n",
1515 | "││ 7 19│\n",
1516 | "││11 23│\n",
1517 | "││ │\n",
1518 | "││ 4 16│\n",
1519 | "││ 8 20│\n",
1520 | "││12 24│\n",
1521 | "└└~────┘\n",
1522 | "
"
1523 | ]
1524 | },
1525 | "execution_count": null,
1526 | "metadata": {},
1527 | "output_type": "execute_result"
1528 | }
1529 | ],
1530 | "source": [
1531 | "⍉ cube"
1532 | ]
1533 | },
1534 | {
1535 | "cell_type": "code",
1536 | "execution_count": null,
1537 | "id": "440ad418",
1538 | "metadata": {},
1539 | "outputs": [
1540 | {
1541 | "data": {
1542 | "text/html": [
1543 | "┌→────┐\n",
1544 | "│4 3 2│\n",
1545 | "└~────┘\n",
1546 | "
"
1547 | ]
1548 | },
1549 | "execution_count": null,
1550 | "metadata": {},
1551 | "output_type": "execute_result"
1552 | }
1553 | ],
1554 | "source": [
1555 | "⍴⍉ cube"
1556 | ]
1557 | },
1558 | {
1559 | "cell_type": "markdown",
1560 | "id": "000eaa59",
1561 | "metadata": {},
1562 | "source": [
1563 | "#### dyadic `⊖` (Rotate First)"
1564 | ]
1565 | },
1566 | {
1567 | "cell_type": "code",
1568 | "execution_count": null,
1569 | "id": "30e4a317",
1570 | "metadata": {},
1571 | "outputs": [
1572 | {
1573 | "data": {
1574 | "text/html": [
1575 | "┌→─────┐\n",
1576 | "↓1 5 9│\n",
1577 | "│2 6 10│\n",
1578 | "│3 7 11│\n",
1579 | "│4 8 12│\n",
1580 | "└~─────┘\n",
1581 | "
"
1582 | ]
1583 | },
1584 | "execution_count": null,
1585 | "metadata": {},
1586 | "output_type": "execute_result"
1587 | }
1588 | ],
1589 | "source": [
1590 | "mat ← 3 4 ⍴⍳12\n",
1591 | "2 1 ⍉ mat"
1592 | ]
1593 | },
1594 | {
1595 | "cell_type": "code",
1596 | "execution_count": null,
1597 | "id": "9dc16c94",
1598 | "metadata": {},
1599 | "outputs": [
1600 | {
1601 | "data": {
1602 | "text/html": [
1603 | "┌→─────┐\n",
1604 | "│1 6 11│\n",
1605 | "└~─────┘\n",
1606 | "
"
1607 | ]
1608 | },
1609 | "execution_count": null,
1610 | "metadata": {},
1611 | "output_type": "execute_result"
1612 | }
1613 | ],
1614 | "source": [
1615 | "1 1 ⍉ mat "
1616 | ]
1617 | },
1618 | {
1619 | "cell_type": "code",
1620 | "execution_count": null,
1621 | "id": "b8f77a8e",
1622 | "metadata": {},
1623 | "outputs": [
1624 | {
1625 | "data": {
1626 | "text/html": [
1627 | "┌┌→──────────┐\n",
1628 | "↓↓ 1 2 3 4│\n",
1629 | "││ 5 6 7 8│\n",
1630 | "││ 9 10 11 12│\n",
1631 | "││ │\n",
1632 | "││13 14 15 16│\n",
1633 | "││17 18 19 20│\n",
1634 | "││21 22 23 24│\n",
1635 | "└└~──────────┘\n",
1636 | "
"
1637 | ]
1638 | },
1639 | "execution_count": null,
1640 | "metadata": {},
1641 | "output_type": "execute_result"
1642 | }
1643 | ],
1644 | "source": [
1645 | "⎕ ← cube ← 2 3 4 ⍴⍳24"
1646 | ]
1647 | },
1648 | {
1649 | "cell_type": "code",
1650 | "execution_count": null,
1651 | "id": "9035bd1e",
1652 | "metadata": {},
1653 | "outputs": [
1654 | {
1655 | "data": {
1656 | "text/html": [
1657 | "┌→────┐\n",
1658 | "│3 2 4│\n",
1659 | "└~────┘\n",
1660 | "
"
1661 | ]
1662 | },
1663 | "execution_count": null,
1664 | "metadata": {},
1665 | "output_type": "execute_result"
1666 | }
1667 | ],
1668 | "source": [
1669 | "⍴ 2 1 3 ⍉ cube"
1670 | ]
1671 | },
1672 | {
1673 | "cell_type": "code",
1674 | "execution_count": null,
1675 | "id": "80684b4c",
1676 | "metadata": {},
1677 | "outputs": [
1678 | {
1679 | "data": {
1680 | "text/html": [
1681 | "┌→───┐\n",
1682 | "│1 18│\n",
1683 | "└~───┘\n",
1684 | "
"
1685 | ]
1686 | },
1687 | "execution_count": null,
1688 | "metadata": {},
1689 | "output_type": "execute_result"
1690 | }
1691 | ],
1692 | "source": [
1693 | "1 1 1⍉ cube"
1694 | ]
1695 | },
1696 | {
1697 | "cell_type": "code",
1698 | "execution_count": null,
1699 | "id": "755c266d",
1700 | "metadata": {},
1701 | "outputs": [
1702 | {
1703 | "data": {
1704 | "text/html": [
1705 | "┌→────┐\n",
1706 | "↓ 1 13│\n",
1707 | "│ 6 18│\n",
1708 | "│11 23│\n",
1709 | "└~────┘\n",
1710 | "
"
1711 | ]
1712 | },
1713 | "execution_count": null,
1714 | "metadata": {},
1715 | "output_type": "execute_result"
1716 | }
1717 | ],
1718 | "source": [
1719 | "2 1 1⍉ cube"
1720 | ]
1721 | },
1722 | {
1723 | "cell_type": "markdown",
1724 | "id": "617899d6",
1725 | "metadata": {},
1726 | "source": [
1727 | "## Other operators"
1728 | ]
1729 | },
1730 | {
1731 | "cell_type": "markdown",
1732 | "id": "240784d0",
1733 | "metadata": {},
1734 | "source": [
1735 | "### `⌺` (Quad Diamond)"
1736 | ]
1737 | },
1738 | {
1739 | "cell_type": "markdown",
1740 | "id": "afd147ca",
1741 | "metadata": {},
1742 | "source": [
1743 | "#### Dyadic operator `⌺` (Stencil)"
1744 | ]
1745 | },
1746 | {
1747 | "cell_type": "code",
1748 | "execution_count": null,
1749 | "id": "21fb8418",
1750 | "metadata": {},
1751 | "outputs": [
1752 | {
1753 | "data": {
1754 | "text/html": [
1755 | "┌→──────────────────────────────────────────────────────────┐\n",
1756 | "↓ ┌→──────────────┐ ┌→──────────────┐ ┌→───────────────┐ │\n",
1757 | "│ │ ┌→──┐ ┌→────┐ │ │ ┌→──┐ ┌→────┐ │ │ ┌→───┐ ┌→────┐ │ │\n",
1758 | "│ │ │1 1│ ↓0 0 0│ │ │ │1 0│ ↓0 0 0│ │ │ │1 ¯1│ ↓0 0 0│ │ │\n",
1759 | "│ │ └~──┘ │0 1 2│ │ │ └~──┘ │1 2 3│ │ │ └~───┘ │2 3 0│ │ │\n",
1760 | "│ │ │0 4 5│ │ │ │4 5 6│ │ │ │5 6 0│ │ │\n",
1761 | "│ │ └~────┘ │ │ └~────┘ │ │ └~────┘ │ │\n",
1762 | "│ └∊──────────────┘ └∊──────────────┘ └∊───────────────┘ │\n",
1763 | "│ ┌→──────────────┐ ┌→──────────────┐ ┌→───────────────┐ │\n",
1764 | "│ │ ┌→──┐ ┌→────┐ │ │ ┌→──┐ ┌→────┐ │ │ ┌→───┐ ┌→────┐ │ │\n",
1765 | "│ │ │0 1│ ↓0 1 2│ │ │ │0 0│ ↓1 2 3│ │ │ │0 ¯1│ ↓2 3 0│ │ │\n",
1766 | "│ │ └~──┘ │0 4 5│ │ │ └~──┘ │4 5 6│ │ │ └~───┘ │5 6 0│ │ │\n",
1767 | "│ │ │0 7 8│ │ │ │7 8 9│ │ │ │8 9 0│ │ │\n",
1768 | "│ │ └~────┘ │ │ └~────┘ │ │ └~────┘ │ │\n",
1769 | "│ └∊──────────────┘ └∊──────────────┘ └∊───────────────┘ │\n",
1770 | "│ ┌→───────────────┐ ┌→───────────────┐ ┌→────────────────┐ │\n",
1771 | "│ │ ┌→───┐ ┌→────┐ │ │ ┌→───┐ ┌→────┐ │ │ ┌→────┐ ┌→────┐ │ │\n",
1772 | "│ │ │¯1 1│ ↓0 4 5│ │ │ │¯1 0│ ↓4 5 6│ │ │ │¯1 ¯1│ ↓5 6 0│ │ │\n",
1773 | "│ │ └~───┘ │0 7 8│ │ │ └~───┘ │7 8 9│ │ │ └~────┘ │8 9 0│ │ │\n",
1774 | "│ │ │0 0 0│ │ │ │0 0 0│ │ │ │0 0 0│ │ │\n",
1775 | "│ │ └~────┘ │ │ └~────┘ │ │ └~────┘ │ │\n",
1776 | "│ └∊───────────────┘ └∊───────────────┘ └∊────────────────┘ │\n",
1777 | "└∊──────────────────────────────────────────────────────────┘\n",
1778 | "
"
1779 | ]
1780 | },
1781 | "execution_count": null,
1782 | "metadata": {},
1783 | "output_type": "execute_result"
1784 | }
1785 | ],
1786 | "source": [
1787 | "{⊂⍺ ⍵}⌺3 3⊢3 3⍴⍳12"
1788 | ]
1789 | },
1790 | {
1791 | "cell_type": "code",
1792 | "execution_count": null,
1793 | "id": "05b866d9",
1794 | "metadata": {},
1795 | "outputs": [
1796 | {
1797 | "data": {
1798 | "text/html": [
1799 | "┌→────────────────────┐\n",
1800 | "↓ ┌→────┐ ┌→────┐ │\n",
1801 | "│ ↓0 0 0│ ↓0 0 0│ │\n",
1802 | "│ │0 1 2│ │2 3 4│ │\n",
1803 | "│ │0 5 6│ │6 7 8│ │\n",
1804 | "│ └~────┘ └~────┘ │\n",
1805 | "│ ┌→─────┐ ┌→───────┐ │\n",
1806 | "│ ↓0 5 6│ ↓ 6 7 8│ │\n",
1807 | "│ │0 9 10│ │10 11 12│ │\n",
1808 | "│ │0 0 0│ │ 0 0 0│ │\n",
1809 | "│ └~─────┘ └~───────┘ │\n",
1810 | "└∊────────────────────┘\n",
1811 | "
"
1812 | ]
1813 | },
1814 | "execution_count": null,
1815 | "metadata": {},
1816 | "output_type": "execute_result"
1817 | }
1818 | ],
1819 | "source": [
1820 | "s←2 2⍴3 3 2 2 ⍝ 2x2 stride with 3x3 kernel\n",
1821 | "({⊂⍵}⌺s)3 4⍴⍳12"
1822 | ]
1823 | },
1824 | {
1825 | "cell_type": "markdown",
1826 | "id": "78544c22",
1827 | "metadata": {},
1828 | "source": [
1829 | "### `@` (At)"
1830 | ]
1831 | },
1832 | {
1833 | "cell_type": "markdown",
1834 | "id": "0543baf4",
1835 | "metadata": {},
1836 | "source": [
1837 | "#### Dyadic `@` (At)"
1838 | ]
1839 | },
1840 | {
1841 | "cell_type": "code",
1842 | "execution_count": null,
1843 | "id": "d3befbc4",
1844 | "metadata": {},
1845 | "outputs": [
1846 | {
1847 | "data": {
1848 | "text/html": [
1849 | "┌→──────────┐\n",
1850 | "│1 0 3 0 5 6│\n",
1851 | "└~──────────┘\n",
1852 | "
"
1853 | ]
1854 | },
1855 | "execution_count": null,
1856 | "metadata": {},
1857 | "output_type": "execute_result"
1858 | }
1859 | ],
1860 | "source": [
1861 | "(0@2 4) ⍳6"
1862 | ]
1863 | },
1864 | {
1865 | "cell_type": "code",
1866 | "execution_count": null,
1867 | "id": "e9971f12",
1868 | "metadata": {},
1869 | "outputs": [
1870 | {
1871 | "data": {
1872 | "text/html": [
1873 | "┌→──────────┐\n",
1874 | "│1 3 3 1 5 6│\n",
1875 | "└~──────────┘\n",
1876 | "
"
1877 | ]
1878 | },
1879 | "execution_count": null,
1880 | "metadata": {},
1881 | "output_type": "execute_result"
1882 | }
1883 | ],
1884 | "source": [
1885 | "(3 1@2 4) ⍳6"
1886 | ]
1887 | },
1888 | {
1889 | "cell_type": "code",
1890 | "execution_count": null,
1891 | "id": "780a3c01",
1892 | "metadata": {},
1893 | "outputs": [
1894 | {
1895 | "data": {
1896 | "text/html": [
1897 | "┌→───────────────┐\n",
1898 | "│1 0.5 3 0.25 5 6│\n",
1899 | "└~───────────────┘\n",
1900 | "
"
1901 | ]
1902 | },
1903 | "execution_count": null,
1904 | "metadata": {},
1905 | "output_type": "execute_result"
1906 | }
1907 | ],
1908 | "source": [
1909 | "÷@2 4 ⍳6"
1910 | ]
1911 | },
1912 | {
1913 | "cell_type": "code",
1914 | "execution_count": null,
1915 | "id": "96945f30",
1916 | "metadata": {},
1917 | "outputs": [
1918 | {
1919 | "data": {
1920 | "text/html": [
1921 | "┌→──────────┐\n",
1922 | "│1 20 3 40 5│\n",
1923 | "└~──────────┘\n",
1924 | "
"
1925 | ]
1926 | },
1927 | "execution_count": null,
1928 | "metadata": {},
1929 | "output_type": "execute_result"
1930 | }
1931 | ],
1932 | "source": [
1933 | "10 (×@2 4) ⍳5"
1934 | ]
1935 | },
1936 | {
1937 | "cell_type": "code",
1938 | "execution_count": null,
1939 | "id": "29afcb4e",
1940 | "metadata": {},
1941 | "outputs": [
1942 | {
1943 | "data": {
1944 | "text/html": [
1945 | "┌→──────────┐\n",
1946 | "│0 2 0 4 0 6│\n",
1947 | "└~──────────┘\n",
1948 | "
"
1949 | ]
1950 | },
1951 | "execution_count": null,
1952 | "metadata": {},
1953 | "output_type": "execute_result"
1954 | }
1955 | ],
1956 | "source": [
1957 | "0@(2∘|)⍳6"
1958 | ]
1959 | },
1960 | {
1961 | "cell_type": "code",
1962 | "execution_count": null,
1963 | "id": "26943cf8",
1964 | "metadata": {},
1965 | "outputs": [
1966 | {
1967 | "data": {
1968 | "text/html": [
1969 | "┌→──────────┐\n",
1970 | "│5 2 3 4 1 6│\n",
1971 | "└~──────────┘\n",
1972 | "
"
1973 | ]
1974 | },
1975 | "execution_count": null,
1976 | "metadata": {},
1977 | "output_type": "execute_result"
1978 | }
1979 | ],
1980 | "source": [
1981 | "⌽@(2∘|)⍳6"
1982 | ]
1983 | },
1984 | {
1985 | "cell_type": "markdown",
1986 | "id": "e81d5acb",
1987 | "metadata": {},
1988 | "source": [
1989 | "## Special non-math glyphs"
1990 | ]
1991 | },
1992 | {
1993 | "cell_type": "markdown",
1994 | "id": "071dbcaf",
1995 | "metadata": {},
1996 | "source": [
1997 | "### `&` (Ampersand)"
1998 | ]
1999 | },
2000 | {
2001 | "cell_type": "markdown",
2002 | "id": "4825fc15",
2003 | "metadata": {},
2004 | "source": [
2005 | "#### Monadic `&` (Spawn)"
2006 | ]
2007 | },
2008 | {
2009 | "cell_type": "markdown",
2010 | "id": "59a65bcc",
2011 | "metadata": {},
2012 | "source": [
2013 | "`&` spawns a new thread in which f is applied to its argument(s)."
2014 | ]
2015 | },
2016 | {
2017 | "cell_type": "code",
2018 | "execution_count": null,
2019 | "id": "e173b86e",
2020 | "metadata": {},
2021 | "outputs": [],
2022 | "source": [
2023 | "÷&4 ⍝ Reciprocal in background"
2024 | ]
2025 | },
2026 | {
2027 | "cell_type": "markdown",
2028 | "id": "1bcfcaaf",
2029 | "metadata": {},
2030 | "source": [
2031 | "### `→` (Branch)"
2032 | ]
2033 | },
2034 | {
2035 | "cell_type": "markdown",
2036 | "id": "46dc51a2",
2037 | "metadata": {},
2038 | "source": [
2039 | "Branching is superseded by the more modern control structures such as :If ... :EndIf."
2040 | ]
2041 | },
2042 | {
2043 | "cell_type": "markdown",
2044 | "id": "46f81f2f",
2045 | "metadata": {},
2046 | "source": [
2047 | "### `⍞` (Print without CR, or stdin)"
2048 | ]
2049 | },
2050 | {
2051 | "cell_type": "markdown",
2052 | "id": "20e2f64f",
2053 | "metadata": {},
2054 | "source": [
2055 | "When ⍞ is assigned with a vector or a scalar, the array is displayed without the normal ending new-line character."
2056 | ]
2057 | },
2058 | {
2059 | "cell_type": "code",
2060 | "execution_count": null,
2061 | "id": "795c17d9",
2062 | "metadata": {},
2063 | "outputs": [
2064 | {
2065 | "data": {
2066 | "text/html": [
2067 | "2+2=4\n",
2068 | "
"
2069 | ]
2070 | },
2071 | "execution_count": null,
2072 | "metadata": {},
2073 | "output_type": "execute_result"
2074 | }
2075 | ],
2076 | "source": [
2077 | "⍞←'2+2' ⋄ ⍞←'=' ⋄ ⍞←2+2"
2078 | ]
2079 | },
2080 | {
2081 | "cell_type": "markdown",
2082 | "id": "7e407d30",
2083 | "metadata": {},
2084 | "source": [
2085 | "When ⍞ is referenced, terminal input is expected without any specific prompt, and the response is returned as a character vector (however this doesn't work in Jupyter)."
2086 | ]
2087 | },
2088 | {
2089 | "cell_type": "code",
2090 | "execution_count": null,
2091 | "id": "4fd129ff",
2092 | "metadata": {},
2093 | "outputs": [
2094 | {
2095 | "data": {
2096 | "text/html": [
2097 | "┌→─────┐\n",
2098 | "↓{ │\n",
2099 | "│\"a\":1,│\n",
2100 | "│\"b\":42│\n",
2101 | "│} │\n",
2102 | "└──────┘\n",
2103 | ""
2104 | ]
2105 | },
2106 | "execution_count": null,
2107 | "metadata": {},
2108 | "output_type": "execute_result"
2109 | }
2110 | ],
2111 | "source": [
2112 | "⎕←j ← 4 6 ⍴ '{ \"a\":1,\"b\":42} '"
2113 | ]
2114 | },
2115 | {
2116 | "cell_type": "markdown",
2117 | "id": "3c2e8abd",
2118 | "metadata": {},
2119 | "source": [
2120 | "### `⍠` Variant"
2121 | ]
2122 | },
2123 | {
2124 | "cell_type": "markdown",
2125 | "id": "9efca324",
2126 | "metadata": {},
2127 | "source": [
2128 | "Used to pass options/variants to some system functions, such as [JSON convert](https://help.dyalog.com/latest/index.htm#Language/System%20Functions/json.htm)."
2129 | ]
2130 | },
2131 | {
2132 | "cell_type": "code",
2133 | "execution_count": null,
2134 | "id": "b7e7347a",
2135 | "metadata": {},
2136 | "outputs": [
2137 | {
2138 | "data": {
2139 | "text/html": [
2140 | "┌→────────────┐\n",
2141 | "↓ ┌⊖┐ ┌⊖┐ │\n",
2142 | "│ 0 │ │ │0│ 1 │\n",
2143 | "│ └─┘ └~┘ │\n",
2144 | "│ ┌→┐ │\n",
2145 | "│ 1 │a│ 1 3 │\n",
2146 | "│ └─┘ │\n",
2147 | "│ ┌→┐ │\n",
2148 | "│ 1 │b│ 42 3 │\n",
2149 | "│ └─┘ │\n",
2150 | "└∊────────────┘\n",
2151 | "
"
2152 | ]
2153 | },
2154 | "execution_count": null,
2155 | "metadata": {},
2156 | "output_type": "execute_result"
2157 | }
2158 | ],
2159 | "source": [
2160 | "⎕←mat←(⎕JSON⍠('Format' 'M'))j"
2161 | ]
2162 | },
2163 | {
2164 | "cell_type": "code",
2165 | "execution_count": null,
2166 | "id": "3e27d184",
2167 | "metadata": {},
2168 | "outputs": [
2169 | {
2170 | "data": {
2171 | "text/html": [
2172 | "┌→─────────────┐\n",
2173 | "│{\"a\":1,\"b\":42}│\n",
2174 | "└──────────────┘\n",
2175 | ""
2176 | ]
2177 | },
2178 | "execution_count": null,
2179 | "metadata": {},
2180 | "output_type": "execute_result"
2181 | }
2182 | ],
2183 | "source": [
2184 | "1(⎕JSON⍠('Format' 'M')) mat"
2185 | ]
2186 | },
2187 | {
2188 | "cell_type": "markdown",
2189 | "id": "f72ad6b6",
2190 | "metadata": {},
2191 | "source": [
2192 | "### `⌶` (I-Beam)"
2193 | ]
2194 | },
2195 | {
2196 | "cell_type": "markdown",
2197 | "id": "f551cbf3",
2198 | "metadata": {},
2199 | "source": [
2200 | "I-Beam is a monadic operator that provides a range of system related services. WARNING: Although documentation is provided for I-Beam functions, any service provided using I-Beam should be considered as \"experimental\" and subject to change. As at Aug-2022 services include SVD, probability distributions, and much more."
2201 | ]
2202 | },
2203 | {
2204 | "cell_type": "markdown",
2205 | "id": "29015349",
2206 | "metadata": {},
2207 | "source": [
2208 | "### `⍎` (Hydrant)"
2209 | ]
2210 | },
2211 | {
2212 | "cell_type": "markdown",
2213 | "id": "c53de407",
2214 | "metadata": {},
2215 | "source": [
2216 | "#### Monadic `⍎` (Execute expression)"
2217 | ]
2218 | },
2219 | {
2220 | "cell_type": "code",
2221 | "execution_count": null,
2222 | "id": "273d73cc",
2223 | "metadata": {},
2224 | "outputs": [
2225 | {
2226 | "data": {
2227 | "text/html": [
2228 | " \n",
2229 | "2\n",
2230 | " \n",
2231 | "
"
2232 | ]
2233 | },
2234 | "execution_count": null,
2235 | "metadata": {},
2236 | "output_type": "execute_result"
2237 | }
2238 | ],
2239 | "source": [
2240 | "⍎ '1+1'"
2241 | ]
2242 | },
2243 | {
2244 | "cell_type": "code",
2245 | "execution_count": null,
2246 | "id": "d0c35053",
2247 | "metadata": {},
2248 | "outputs": [
2249 | {
2250 | "data": {
2251 | "text/html": [
2252 | "┌→────┐\n",
2253 | "│1 2 3│\n",
2254 | "└~────┘\n",
2255 | "
"
2256 | ]
2257 | },
2258 | "execution_count": null,
2259 | "metadata": {},
2260 | "output_type": "execute_result"
2261 | }
2262 | ],
2263 | "source": [
2264 | "V ← 1 2 3\n",
2265 | "⍎ 'V'"
2266 | ]
2267 | },
2268 | {
2269 | "cell_type": "code",
2270 | "execution_count": null,
2271 | "id": "c7f0e353",
2272 | "metadata": {},
2273 | "outputs": [
2274 | {
2275 | "data": {
2276 | "text/html": [
2277 | " \n",
2278 | "2\n",
2279 | " \n",
2280 | "
"
2281 | ]
2282 | },
2283 | "execution_count": null,
2284 | "metadata": {},
2285 | "output_type": "execute_result"
2286 | }
2287 | ],
2288 | "source": [
2289 | "A← ⍎'1+1 ⋄ 2+2'"
2290 | ]
2291 | },
2292 | {
2293 | "cell_type": "code",
2294 | "execution_count": null,
2295 | "id": "9d4bd38a",
2296 | "metadata": {},
2297 | "outputs": [
2298 | {
2299 | "data": {
2300 | "text/html": [
2301 | " \n",
2302 | "4\n",
2303 | " \n",
2304 | "
"
2305 | ]
2306 | },
2307 | "execution_count": null,
2308 | "metadata": {},
2309 | "output_type": "execute_result"
2310 | }
2311 | ],
2312 | "source": [
2313 | "A"
2314 | ]
2315 | },
2316 | {
2317 | "cell_type": "markdown",
2318 | "id": "b883202f",
2319 | "metadata": {},
2320 | "source": [
2321 | "#### Dyadic `⍎` (Execute expression in given namespace)"
2322 | ]
2323 | },
2324 | {
2325 | "cell_type": "markdown",
2326 | "id": "62259083",
2327 | "metadata": {},
2328 | "source": [
2329 | "X must be a namespace reference or a simple character scalar or vector representing the name of a namespace in which the expression is to be executed."
2330 | ]
2331 | },
2332 | {
2333 | "cell_type": "markdown",
2334 | "id": "df1830bc",
2335 | "metadata": {},
2336 | "source": [
2337 | "### `⍕` (Thorn)"
2338 | ]
2339 | },
2340 | {
2341 | "cell_type": "markdown",
2342 | "id": "79cfa777",
2343 | "metadata": {},
2344 | "source": [
2345 | "#### Monadic `⍕` (Format)"
2346 | ]
2347 | },
2348 | {
2349 | "cell_type": "code",
2350 | "execution_count": null,
2351 | "id": "3a899b68",
2352 | "metadata": {},
2353 | "outputs": [
2354 | {
2355 | "data": {
2356 | "text/html": [
2357 | "┌→────┐\n",
2358 | "│4 5 6│\n",
2359 | "└~────┘\n",
2360 | "
"
2361 | ]
2362 | },
2363 | "execution_count": null,
2364 | "metadata": {},
2365 | "output_type": "execute_result"
2366 | }
2367 | ],
2368 | "source": [
2369 | "4 5 6 ⍝ These are numbers (see the `~` in bottom left)"
2370 | ]
2371 | },
2372 | {
2373 | "cell_type": "code",
2374 | "execution_count": null,
2375 | "id": "efb6d04a",
2376 | "metadata": {},
2377 | "outputs": [
2378 | {
2379 | "data": {
2380 | "text/html": [
2381 | "┌→────┐\n",
2382 | "│4 5 6│\n",
2383 | "└─────┘\n",
2384 | "
"
2385 | ]
2386 | },
2387 | "execution_count": null,
2388 | "metadata": {},
2389 | "output_type": "execute_result"
2390 | }
2391 | ],
2392 | "source": [
2393 | "⍕ 4 5 6 ⍝ These are characters (no `~` in bottom left)"
2394 | ]
2395 | },
2396 | {
2397 | "cell_type": "markdown",
2398 | "id": "787be6ff",
2399 | "metadata": {},
2400 | "source": [
2401 | "#### Dyadic `⍕` (Format By Specification)"
2402 | ]
2403 | },
2404 | {
2405 | "cell_type": "markdown",
2406 | "id": "b58d9b26",
2407 | "metadata": {},
2408 | "source": [
2409 | "Field-width and number of decimal places:"
2410 | ]
2411 | },
2412 | {
2413 | "cell_type": "code",
2414 | "execution_count": null,
2415 | "id": "1bc94bba",
2416 | "metadata": {},
2417 | "outputs": [
2418 | {
2419 | "data": {
2420 | "text/html": [
2421 | "┌→───────────┐\n",
2422 | "│ 3.13 0.00│\n",
2423 | "└────────────┘\n",
2424 | "
"
2425 | ]
2426 | },
2427 | "execution_count": null,
2428 | "metadata": {},
2429 | "output_type": "execute_result"
2430 | }
2431 | ],
2432 | "source": [
2433 | "6 2 ⍕ 3.125 0.002"
2434 | ]
2435 | },
2436 | {
2437 | "cell_type": "code",
2438 | "execution_count": null,
2439 | "id": "4d632ed2",
2440 | "metadata": {},
2441 | "outputs": [],
2442 | "source": []
2443 | }
2444 | ],
2445 | "metadata": {
2446 | "kernelspec": {
2447 | "display_name": "Dyalog APL",
2448 | "language": "apl",
2449 | "name": "dyalog-kernel"
2450 | }
2451 | },
2452 | "nbformat": 4,
2453 | "nbformat_minor": 5
2454 | }
2455 |
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/MANIFEST.in:
--------------------------------------------------------------------------------
1 | include settings.ini
2 | include LICENSE
3 | include CONTRIBUTING.md
4 | include README.md
5 | recursive-exclude * __pycache__
6 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | APL Study Group
2 | ================
3 |
4 |
5 |
6 | Check out [the
7 | forum](https://forums.fast.ai/t/apl-array-programming/97188) for meeting
8 | time and resources!
9 |
10 | You’ll find here a walkthru of what will eventually be all the glyphs in
11 | Dyalog APL, in an order where no glyph is used in an example until it’s
12 | been introduced. So far there’s no prose – the explanations are purely
13 | through examples for now (but we’ll add prose later).
14 |
15 | There’s also a [Python equivalents](python.ipynb) notebook, which has
16 | explanations using python of some APL ideas, including `bind`/`partial`
17 | and APL operators (aka higher-order functions).
18 |
--------------------------------------------------------------------------------
/_quarto.yml:
--------------------------------------------------------------------------------
1 | project:
2 | type: website
3 |
4 | format:
5 | html:
6 | theme: cosmo
7 | css: styles.css
8 | toc: true
9 | resources: '*.woff2'
10 |
11 | website:
12 | twitter-card: true
13 | open-graph: true
14 | repo-actions: [issue]
15 | navbar:
16 | background: primary
17 | search: true
18 | sidebar:
19 | style: floating
20 |
21 | metadata-files: [nbdev.yml, sidebar.yml]
22 |
--------------------------------------------------------------------------------
/aplstudy/__init__.py:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/fastai/apl-study/115c5b1468823884889b3eb966ceaf2acfc68266/aplstudy/__init__.py
--------------------------------------------------------------------------------
/aplstudy/_modidx.py:
--------------------------------------------------------------------------------
1 | # Autogenerated by nbdev
2 |
3 | d = { 'settings': { 'branch': 'master',
4 | 'doc_baseurl': '/apl-study/',
5 | 'doc_host': 'https://fastai.github.io',
6 | 'git_url': 'https://github.com/fastai/apl-study/tree/master/',
7 | 'lib_path': 'aplstudy'},
8 | 'syms': {}}
--------------------------------------------------------------------------------
/index.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# APL Study Group\n",
8 | "\n",
9 | "> This blog is a work in progress to document and share learning that the Fastai APL Study Group has as they learn Dyalog APL. If you are interested, join us!"
10 | ]
11 | },
12 | {
13 | "cell_type": "markdown",
14 | "metadata": {},
15 | "source": [
16 | "Check out [the forum](https://forums.fast.ai/t/apl-array-programming/97188) for meeting time and resources!\n",
17 | "\n",
18 | "You'll find here a walkthru of what will eventually be all the glyphs in Dyalog APL, in an order where no glyph is used in an example until it's been introduced. So far there's no prose -- the explanations are purely through examples for now (but we'll add prose later).\n",
19 | "\n",
20 | "There's also a [Python equivalents](python.ipynb) notebook, which has explanations using python of some APL ideas, including `bind`/`partial` and APL operators (aka higher-order functions). "
21 | ]
22 | }
23 | ],
24 | "metadata": {
25 | "kernelspec": {
26 | "display_name": "Python 3 (ipykernel)",
27 | "language": "python",
28 | "name": "python3"
29 | }
30 | },
31 | "nbformat": 4,
32 | "nbformat_minor": 4
33 | }
34 |
--------------------------------------------------------------------------------
/nbdev.yml:
--------------------------------------------------------------------------------
1 | project:
2 | output-dir: _docs
3 |
4 | website:
5 | title: "apl-study"
6 | site-url: "https://fastai.github.io/apl-study/"
7 | description: "fast.ai APL study group notes"
8 | repo-branch: master
9 | repo-url: "https://github.com/fastai/apl-study/tree/master/"
10 |
--------------------------------------------------------------------------------
/python.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "raw",
5 | "id": "6857289c",
6 | "metadata": {},
7 | "source": [
8 | "---\n",
9 | "title: \"Python equivalents\"\n",
10 | "---"
11 | ]
12 | },
13 | {
14 | "cell_type": "markdown",
15 | "id": "82d44d43",
16 | "metadata": {},
17 | "source": [
18 | "## Decorators"
19 | ]
20 | },
21 | {
22 | "cell_type": "code",
23 | "execution_count": null,
24 | "id": "8ae42943",
25 | "metadata": {},
26 | "outputs": [
27 | {
28 | "data": {
29 | "text/plain": [
30 | "4"
31 | ]
32 | },
33 | "execution_count": null,
34 | "metadata": {},
35 | "output_type": "execute_result"
36 | }
37 | ],
38 | "source": [
39 | "def add1(x): return x+1\n",
40 | "add1(3)"
41 | ]
42 | },
43 | {
44 | "cell_type": "markdown",
45 | "id": "1c1cbc34",
46 | "metadata": {},
47 | "source": [
48 | "A function that returns a function:"
49 | ]
50 | },
51 | {
52 | "cell_type": "code",
53 | "execution_count": null,
54 | "id": "28e83e74",
55 | "metadata": {},
56 | "outputs": [],
57 | "source": [
58 | "def logargs(f):\n",
59 | " \"Print arguments to `f` before calling it\"\n",
60 | " def _inner(*args, **kwargs):\n",
61 | " print(f\"Received: {args=}; {kwargs=}\")\n",
62 | " return f(*args, **kwargs)\n",
63 | " return _inner"
64 | ]
65 | },
66 | {
67 | "cell_type": "markdown",
68 | "id": "f140baf4",
69 | "metadata": {},
70 | "source": [
71 | "Using `logargs` to modify a function:"
72 | ]
73 | },
74 | {
75 | "cell_type": "code",
76 | "execution_count": null,
77 | "id": "9fca0a51",
78 | "metadata": {},
79 | "outputs": [
80 | {
81 | "name": "stdout",
82 | "output_type": "stream",
83 | "text": [
84 | "Received: args=(3,); kwargs={}\n"
85 | ]
86 | },
87 | {
88 | "data": {
89 | "text/plain": [
90 | "6"
91 | ]
92 | },
93 | "execution_count": null,
94 | "metadata": {},
95 | "output_type": "execute_result"
96 | }
97 | ],
98 | "source": [
99 | "def _mult2(x): return x*2\n",
100 | "mult2 = logargs(_mult2)\n",
101 | "mult2(3)"
102 | ]
103 | },
104 | {
105 | "cell_type": "markdown",
106 | "id": "74c1368e",
107 | "metadata": {},
108 | "source": [
109 | "Exactly the same thing but using a decorator as syntax sugar:"
110 | ]
111 | },
112 | {
113 | "cell_type": "code",
114 | "execution_count": null,
115 | "id": "02759326",
116 | "metadata": {},
117 | "outputs": [
118 | {
119 | "name": "stdout",
120 | "output_type": "stream",
121 | "text": [
122 | "Received: args=(3,); kwargs={}\n"
123 | ]
124 | },
125 | {
126 | "data": {
127 | "text/plain": [
128 | "6"
129 | ]
130 | },
131 | "execution_count": null,
132 | "metadata": {},
133 | "output_type": "execute_result"
134 | }
135 | ],
136 | "source": [
137 | "@logargs\n",
138 | "def mult2(x): return x*2\n",
139 | "mult2(3)"
140 | ]
141 | },
142 | {
143 | "cell_type": "markdown",
144 | "id": "72c5a968",
145 | "metadata": {},
146 | "source": [
147 | "A class that takes a function and returns a function:"
148 | ]
149 | },
150 | {
151 | "cell_type": "code",
152 | "execution_count": null,
153 | "id": "482f917d",
154 | "metadata": {},
155 | "outputs": [],
156 | "source": [
157 | "class logargs:\n",
158 | " def __init__(self, prefix='Received: '): self.prefix=prefix\n",
159 | " def __call__(self, f): \n",
160 | " def _inner(*args, **kwargs):\n",
161 | " print(f\"{self.prefix}{args=}; {kwargs=}\")\n",
162 | " return f(*args, **kwargs)\n",
163 | " return _inner"
164 | ]
165 | },
166 | {
167 | "cell_type": "markdown",
168 | "id": "c45d150f",
169 | "metadata": {},
170 | "source": [
171 | "Here's how to use it:"
172 | ]
173 | },
174 | {
175 | "cell_type": "code",
176 | "execution_count": null,
177 | "id": "8013666a",
178 | "metadata": {},
179 | "outputs": [
180 | {
181 | "name": "stdout",
182 | "output_type": "stream",
183 | "text": [
184 | "Logging: args=(3,); kwargs={}\n"
185 | ]
186 | },
187 | {
188 | "data": {
189 | "text/plain": [
190 | "4"
191 | ]
192 | },
193 | "execution_count": null,
194 | "metadata": {},
195 | "output_type": "execute_result"
196 | }
197 | ],
198 | "source": [
199 | "def _add1(x): return x+1\n",
200 | "o = logargs('Logging: ')\n",
201 | "add1 = o(_add1)\n",
202 | "add1(3)"
203 | ]
204 | },
205 | {
206 | "cell_type": "markdown",
207 | "id": "f52282a2",
208 | "metadata": {},
209 | "source": [
210 | "Exactly the same thing but using a decorator as syntax sugar:"
211 | ]
212 | },
213 | {
214 | "cell_type": "code",
215 | "execution_count": null,
216 | "id": "22bd8c62",
217 | "metadata": {},
218 | "outputs": [
219 | {
220 | "name": "stdout",
221 | "output_type": "stream",
222 | "text": [
223 | "Logging: args=(3,); kwargs={}\n"
224 | ]
225 | },
226 | {
227 | "data": {
228 | "text/plain": [
229 | "4"
230 | ]
231 | },
232 | "execution_count": null,
233 | "metadata": {},
234 | "output_type": "execute_result"
235 | }
236 | ],
237 | "source": [
238 | "@logargs('Logging: ')\n",
239 | "def add1(x): return x+1\n",
240 | "add1(3)"
241 | ]
242 | },
243 | {
244 | "cell_type": "markdown",
245 | "id": "3e96dc9e",
246 | "metadata": {},
247 | "source": [
248 | "## partial"
249 | ]
250 | },
251 | {
252 | "cell_type": "code",
253 | "execution_count": null,
254 | "id": "30a6ba64",
255 | "metadata": {},
256 | "outputs": [],
257 | "source": [
258 | "from functools import partial"
259 | ]
260 | },
261 | {
262 | "cell_type": "code",
263 | "execution_count": null,
264 | "id": "a4175712",
265 | "metadata": {},
266 | "outputs": [
267 | {
268 | "data": {
269 | "text/plain": [
270 | "9"
271 | ]
272 | },
273 | "execution_count": null,
274 | "metadata": {},
275 | "output_type": "execute_result"
276 | }
277 | ],
278 | "source": [
279 | "def pow(x,y): return x**y\n",
280 | "pow(3,2)"
281 | ]
282 | },
283 | {
284 | "cell_type": "code",
285 | "execution_count": null,
286 | "id": "3395ce77",
287 | "metadata": {},
288 | "outputs": [
289 | {
290 | "data": {
291 | "text/plain": [
292 | "9"
293 | ]
294 | },
295 | "execution_count": null,
296 | "metadata": {},
297 | "output_type": "execute_result"
298 | }
299 | ],
300 | "source": [
301 | "squared = partial(pow, y=2)\n",
302 | "squared(3)"
303 | ]
304 | },
305 | {
306 | "cell_type": "code",
307 | "execution_count": null,
308 | "id": "78cd2374",
309 | "metadata": {},
310 | "outputs": [],
311 | "source": []
312 | }
313 | ],
314 | "metadata": {
315 | "kernelspec": {
316 | "display_name": "Python 3 (ipykernel)",
317 | "language": "python",
318 | "name": "python3"
319 | }
320 | },
321 | "nbformat": 4,
322 | "nbformat_minor": 5
323 | }
324 |
--------------------------------------------------------------------------------
/settings.ini:
--------------------------------------------------------------------------------
1 | [DEFAULT]
2 | # All sections below are required unless otherwise specified
3 | # see https://github.com/fastai/nbdev/blob/master/settings.ini for examples
4 | host = github
5 | lib_name = apl-study
6 | description = fast.ai APL study group notes
7 | copyright = Jeremy Howard, 2022 onwards
8 | keywords = nbdev apl dyalog
9 | user = fastai
10 | author = Jeremy Howard
11 | author_email = info@fast.ai
12 | branch = master
13 | version = 0.0.1
14 | min_python = 3.9
15 | audience = Developers
16 | language = English
17 | license = apache2
18 | status = 2
19 | nbs_path = .
20 | doc_path = _docs
21 | recursive = True
22 | tst_flags = notest
23 |
24 | ### Inferred From Other Values ###
25 | doc_host = https://%(user)s.github.io
26 | doc_baseurl = /%(lib_name)s/
27 | git_url = https://github.com/%(user)s/%(lib_name)s/tree/%(branch)s/
28 | lib_path = aplstudy
29 | title = %(lib_name)s
30 |
31 | ### OPTIONAL ### see https://github.com/fastai/nbdev/blob/master/settings.ini for examples
32 |
33 | # requirements = fastcore pandas
34 | # dev_requirements =
35 | # console_scripts =
36 |
37 |
--------------------------------------------------------------------------------
/setup.py:
--------------------------------------------------------------------------------
1 | from pkg_resources import parse_version
2 | from configparser import ConfigParser
3 | import setuptools
4 | assert parse_version(setuptools.__version__)>=parse_version('36.2')
5 |
6 | # note: all settings are in settings.ini; edit there, not here
7 | config = ConfigParser(delimiters=['='])
8 | config.read('settings.ini')
9 | cfg = config['DEFAULT']
10 |
11 | cfg_keys = 'version description keywords author author_email'.split()
12 | expected = cfg_keys + "lib_name user branch license status min_python audience language".split()
13 | for o in expected: assert o in cfg, "missing expected setting: {}".format(o)
14 | setup_cfg = {o:cfg[o] for o in cfg_keys}
15 |
16 | licenses = {
17 | 'apache2': ('Apache Software License 2.0','OSI Approved :: Apache Software License'),
18 | 'mit': ('MIT License', 'OSI Approved :: MIT License'),
19 | 'gpl2': ('GNU General Public License v2', 'OSI Approved :: GNU General Public License v2 (GPLv2)'),
20 | 'gpl3': ('GNU General Public License v3', 'OSI Approved :: GNU General Public License v3 (GPLv3)'),
21 | 'bsd3': ('BSD License', 'OSI Approved :: BSD License'),
22 | }
23 | statuses = [ '1 - Planning', '2 - Pre-Alpha', '3 - Alpha',
24 | '4 - Beta', '5 - Production/Stable', '6 - Mature', '7 - Inactive' ]
25 | py_versions = '3.6 3.7 3.8 3.9 3.10'.split()
26 |
27 | requirements = cfg.get('requirements','').split()
28 | min_python = cfg['min_python']
29 | lic = licenses.get(cfg['license'].lower(), (cfg['license'], None))
30 | dev_requirements = (cfg.get('dev_requirements') or '').split()
31 |
32 | setuptools.setup(
33 | name = cfg['lib_name'],
34 | license = lic[0],
35 | classifiers = [
36 | 'Development Status :: ' + statuses[int(cfg['status'])],
37 | 'Intended Audience :: ' + cfg['audience'].title(),
38 | 'Natural Language :: ' + cfg['language'].title(),
39 | ] + ['Programming Language :: Python :: '+o for o in py_versions[py_versions.index(min_python):]] + (['License :: ' + lic[1] ] if lic[1] else []),
40 | url = cfg['git_url'],
41 | packages = setuptools.find_packages(),
42 | include_package_data = True,
43 | install_requires = requirements,
44 | extras_require={ 'dev': dev_requirements },
45 | dependency_links = cfg.get('dep_links','').split(),
46 | python_requires = '>=' + cfg['min_python'],
47 | long_description = open('README.md').read(),
48 | long_description_content_type = 'text/markdown',
49 | zip_safe = False,
50 | entry_points = {
51 | 'console_scripts': cfg.get('console_scripts','').split(),
52 | 'mkdocs.plugins': [ 'rm_num_prefix = nbdev.mkdocs:RmNumPrefix' ],
53 | 'nbdev': [f'{cfg.get("lib_path")}={cfg.get("lib_path")}._modidx:d']
54 | },
55 | **setup_cfg)
56 |
57 |
58 |
--------------------------------------------------------------------------------
/sidebar.yml:
--------------------------------------------------------------------------------
1 | website:
2 | sidebar:
3 | contents:
4 | - index.ipynb
5 | - 01_APL.ipynb
6 | - 02_functions.ipynb
7 | - 03_operators.ipynb
8 | - 04_competition.ipynb
9 | - 05_the_rest.ipynb
10 | - python.ipynb
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/styles.css:
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1 | pre.language-APL {
2 | line-height: 1.05;
3 | }
4 |
5 | .cell-output pre {
6 | padding: 3px 0px 3px 9px;
7 | margin-left: 0.8rem;
8 | margin-top: 0;
9 | background: none;
10 | border-left: 2px solid lightsalmon;
11 | border-top-left-radius: 0;
12 | border-top-right-radius: 0;
13 | }
14 |
15 | .cell-output .sourceCode {
16 | background: none;
17 | margin-top: 0;
18 | }
19 |
20 | .cell > .sourceCode {
21 | margin-bottom: 0;
22 | }
23 |
24 | @font-face {
25 | font-family: 'sax2';
26 | src: url('www/SAX2.woff2') format('woff2');
27 | font-weight: normal;
28 | font-style: normal;
29 | }
30 |
31 | pre.language-APL {
32 | font-family: 'sax2' !important;
33 | }
34 |
35 | .apl code {
36 | font-family: 'sax2' !important;
37 | }
38 |
39 |
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