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bqn-mode.el
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bqn-mode.el
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;;; bqn-mode.el --- Emacs mode for BQN -*- lexical-binding: t -*-
;; Emacs bqn-mode is derived from gnu-apl-mode,
;; which is copyright 2013-2015 Elias Mårtenson <lokedhs@gmail.com>.
;; Changes are copyright 2021 Marshall Lochbaum <mwlochbaum@gmail.com>.
;; Author: Marshall Lochbaum <mwlochbaum@gmail.com>
;; Version: 0.1.0
;; Package-Requires: ((emacs "26.1") (compat "30.0.0.0") (eros "0.1.0"))
;; URL: https://github.com/museoa/bqn-mode
;; SPDX-License-Identifier: GPL-3.0-or-later
;;; Commentary:
;; Emacs major mode for BQN programming language.
;;; Code:
(require 'comint)
(require 'quail)
(require 'pulse)
(defvar bqn-keymap-mode-reference
"\
┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬─────────┐
│~ ¬ │! ⎉ │@ ⚇ │# ⍟ │$ ◶ │% ⊘ │^ ⎊ │& │* │( ⟨ │) ⟩ │_ √ │+ ⋆ │Backspace│
│` ˜ │1 ˘ │2 ¨ │3 ⁼ │4 ⌜ │5 ´ │6 ˝ │7 │8 ∞ │9 ¯ │0 • │- ÷ │= × │ │
├────┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬──────┤
│Tab │Q │W 𝕎 │E ⍷ │R 𝕣 │T ⍋ │Y │U │I ⊑ │O ⊒ │P │{ ⊣ │} ⊢ │| │
│ │q ⌽ │w 𝕨 │e ∊ │r ↑ │t ∧ │y │u ⊔ │i ⊏ │o ⊐ │p π │[ ← │] │\\ │
├───────┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴──────┤
│Caps │A │S 𝕊 │D │F 𝔽 │G 𝔾 │H « │J │K ⌾ │L » │: · │\" ˙ │Enter │
│Lock │a ⍉ │s 𝕤 │d ↕ │f 𝕗 │g 𝕘 │h ⊸ │j ∘ │k ○ │l ⟜ │; ⋄ │' ↩ │ │
├────────┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──────────┤
│Shift │Z ⋈ │X 𝕏 │C │V ⍒ │B ⌈ │N │M ≢ │< ≤ │> ≥ │? ⇐ │Shift │
│ │z ⥊ │x 𝕩 │c ↓ │v ∨ │b ⌊ │n │m ≡ │, ∾ │. ≍ │/ ≠ │ │
└───────────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────────────┘
Space: ‿"
"Keyboard map for BQN.")
(defvar bqn-keymap-mode-*buffer-name* "*BQN keymap*"
"Name of the BQN keymap buffer.")
(defun bqn-keymap-mode-show-keyboard ()
"Display the keyboard help."
(interactive)
(let ((keyboard-help (get-buffer bqn-keymap-mode-*buffer-name*)))
(unless (and keyboard-help (get-buffer-window keyboard-help))
;; The buffer is not displayed.
(let* ((buffer (get-buffer-create bqn-keymap-mode-*buffer-name*))
(window (split-window nil)))
(with-current-buffer buffer
(insert bqn-keymap-mode-reference)
(goto-char (point-min))
(bqn-keymap-mode))
(set-window-buffer window buffer)
(fit-window-to-buffer window)))))
(define-derived-mode bqn-keymap-mode special-mode "BQN-Keymap"
"Major mode for displaying the keymap help."
(buffer-face-set 'bqn-default)
(read-only-mode 1)
(setq truncate-lines t))
(defvar bqn-glyph-mode-reference
"┌───┬────────────────┬──────────────┬───┬──────────────────┬────────────────┐
│ @ │ Monadic │ Dyadic │ @ │ Monadic │ Dyadic │
├───┼────────────────┼──────────────┼───┼──────────────────┼────────────────┤
│ + │ Conjugate │ Add │ ⥊ │ Deshape │ Reshape │
│ ─ │ Negate │ Subtract │ ∾ │ Join │ Join to │
│ × │ Sign │ Multiply │ ≍ │ Solo │ Couple │
│ ÷ │ Reciprocal │ Divide │ ⋈ │ Enlist │ Pair │
│ ⋆ │ Exponential │ Power │ ↑ │ Prefixes │ Take │
│ √ │ Square Root │ Root │ ↓ │ Suffixes │ Drop │
│ ⌊ │ Floor │ Minimum │ ↕ │ Range │ Windows │
│ ⌈ │ Ceiling │ Maximum │ » │ Nudge │ Shift Before │
│ ∧ │ Sort Up │ And │ « │ Nudge Back │ Shift After │
│ ∨ │ Sort Down │ Or │ ⌽ │ Reverse │ Rotate │
│ ¬ │ Not │ Span │ ⍉ │ Transpose │ Reorder Axes │
│ │ │ Absolute Value │ Modulus │ / │ Indices │ Replicate │
│ ≤ │ │ No More Than │ ⍋ │ Grade Up │ Bins Up │
│ < │ Enclose │ Less Than │ ⍒ │ Grade Down │ Bins Down │
│ > │ Merge │ Greater Than │ ⊏ │ First Cell │ Select │
│ ≥ │ │ No Less Than │ ⊑ │ First │ Pick │
│ = │ Rank │ Equals │ ⊐ │ Classify │ Index of │
│ ≠ │ Length │ Not Equals │ ⊒ │ Occurrence Count │ Progressive ⊐ │
│ ≡ │ Depth │ Match │ ∊ │ Mark Firsts │ Member of │
│ ≢ │ Shape │ Not Match │ ⍷ │ Deduplicate │ Find │
│ ⊣ │ Identity │ Left │ ⊔ │ Group Indices │ Group │
│ ⊢ │ Identity │ Right │ ! │ Assert │ Assert Message │
└───┴────────────────┴──────────────┴───┴──────────────────┴────────────────┘"
"Glyph Lookup Table for BQN.")
(defvar bqn-glyph-mode-*buffer-name* "*BQN Glyphs*")
(defun bqn-glyph-mode-show-glyphs ()
"Display a table of BQN glyphs."
(interactive)
(let ((glyph-buffer (get-buffer bqn-glyph-mode-*buffer-name*)))
(unless (and glyph-buffer (get-buffer-window glyph-buffer))
;; The buffer is not displayed.
(let* ((buffer (get-buffer-create bqn-glyph-mode-*buffer-name*))
(window (split-window nil)))
(with-current-buffer buffer
(insert bqn-glyph-mode-reference)
(goto-char (point-min))
(bqn-glyph-mode))
(set-window-buffer window buffer)
(fit-window-to-buffer window)))))
(define-derived-mode bqn-glyph-mode special-mode "BQN-Glyphs"
"Major mode for displaying the BQN Glyph help."
(buffer-face-set 'bqn-default)
(read-only-mode 1)
(setq truncate-lines t))
;;; BQN Symbols documentation
;; Arrays and hashes are not very Lispy, however they will be employed here
;; because we want the lowest latency possible for an end-user-facing structure.
;; For all intents and purposes, this table should be regarded as read-only;
;; indeed, it is "cached" at byte-compile time via eval-when-compile.
(defconst bqn--symbols
(eval-when-compile
(let ((table '(
;; top row
(?\` . [ nil
"𝔽` 𝕩: Scan | 𝕨 𝔽` 𝕩: Scan With Initial"
"\
𝔽` 𝕩: Scan
- Scan over 𝕩 with 𝔽 from left to right, producing intermediate values.
𝕨 𝔽` 𝕩: Scan With initial
- Monadic scan, but use 𝕨 as initial left argument."
"\
+` 1‿2‿3
⟨ 1 3 6 ⟩
⟨1, 1+2, (1+2)+3⟩
⟨ 1 3 6 ⟩
-` 1‿2‿3
⟨ 1 ¯1 ¯4 ⟩
⟨1, 1-2, (1-2)-3⟩
⟨ 1 ¯1 ¯4 ⟩
5 +` 1‿2‿3
⟨ 6 8 11 ⟩
⟨5+1, (5+1)+2, ((5+1)+2)+3⟩
⟨ 6 8 11 ⟩
5 -` 1‿2‿3
⟨ 4 2 ¯1 ⟩
⟨5-1, (5-1)-2, ((5-1)-2)-3⟩
⟨ 4 2 ¯1 ⟩"])
(?˜ . [ ?\`
"𝔽˜ 𝕩: Self | 𝕨 𝔽˜ 𝕩: Swap"
"\
𝔽˜ 𝕩: Self
- Supplies 𝕩 as a left argument to 𝔽 (𝕩 𝔽 𝕩).
𝕨 𝔽˜ 𝕩: Swap
- Swaps the arguments of 𝔽 (𝕩 𝔽 𝕨)."
"\
1 + 1
2
+˜ 1
2
1 - 2
¯1
1 -˜ 2
1"])
(?¬ . [ ?~
"¬ 𝕩: Logical Not | 𝕨 ¬ 𝕩: Span"
"\
¬ 𝕩: Logical Not
- Logical Not of 𝕩.
- Pervasive.
𝕨 ¬ 𝕩: Span
- Count of numbers in the inclusive range from 𝕩 to 𝕨.
- Pervasive."
"\
¬ 0
1
¬ 1‿0
⟨ 0 1 ⟩
3 ¬ 1
3
3‿4 ¬ 0‿2
⟨ 4 3 ⟩"])
(?! . [ nil
"! 𝕩: Assert | 𝕨 ! 𝕩: Assert With Message"
"\
! 𝕩: Assert
- Throw an error if 𝕩 is not 1.
𝕨 ! 𝕩: Assert With Message
- Throw an error with message 𝕨 if 𝕩 is not 1."
"\
! 1
1
! 2
Error: Assertion error
! \"hello\"
Error: hello
\"hi\" ! 1
1
\"two\" ! 2
Error: two
\"hello error\" ! \"hello\"
Error: hello error"])
(?˘ . [ ?1
"𝔽˘ 𝕩, 𝕨 𝔽˘ 𝕩: Cells"
"\
𝔽˘ 𝕩, 𝕨 𝔽˘ 𝕩: Cells
- Apply 𝔽 to/between the major cells of the arguments. (𝔽⎉¯1)"
"\
a ← 3‿3 ⥊ ↕9
<˘ a
⟨ ⟨ 0 1 2 ⟩ ⟨ 3 4 5 ⟩ ⟨ 6 7 8 ⟩ ⟩
a ≍˘ a
┌─
╎ 0 1 2
0 1 2
3 4 5
3 4 5
6 7 8
6 7 8
┘"])
(?⎉ . [ ?!
"𝔽⎉𝕘 𝕩, 𝕨 𝔽⎉𝕘 𝕩: Rank"
"\
𝔽⎉𝕘 𝕩, 𝕨 𝔽⎉𝕘 𝕩: Rank
- Apply 𝔽 to cells at ranks given in 𝕘. Non-negative numbers indicate the rank
of the cell and negative ones indicate the difference from full rank.
- The ranks applied are given by the following:
- ⎉ c Rank-c cells of 𝕩 (monadic) or both arguments (dyadic)
- ⎉ b‿c Rank-b cells of 𝕨 and rank-c cells of 𝕩 (dyadic)
- ⎉ a‿b‿c Rank-a cells of 𝕩 (monadic), b-cells of 𝕨 and c-cells of 𝕩 (dyadic)"
"\
a ← 3‿2‿4⥊\"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"
⌽⎉2 a
┌─
╎\"EFGH
ABCD
·MNOP
IJKL
·UVWX
QRST\"
┘"])
(?@ . [ nil
"Null Character"
"\
@: Null Character
- Code point 0 in ASCII.
- Add to a code point number to ger that character."
"\
@+50
'2'
@
@
@+64
'@'"])
(?¨ . [ ?2
"𝔽¨ 𝕩, 𝕨 𝔽¨ 𝕩: Each"
"\
𝔽¨ 𝕩, 𝕨 𝔽¨ 𝕩: Each
- Apply 𝔽 to/between the elements of the arguments. (𝔽⚇¯1)"
"\
<¨ 1‿2‿3
┌─
· ┌· ┌· ┌·
· 1 · 2 · 3
┘ ┘ ┘
┘
4‿5‿6 ∾¨ 1‿2‿3
⟨ ⟨ 4 1 ⟩ ⟨ 5 2 ⟩ ⟨ 6 3 ⟩ ⟩"])
(?⚇ . [ ?@
"𝔽⚇𝕘 𝕩, 𝕨 𝔽⚇𝕘 𝕩: Depth"
"\
𝔽⚇𝕘 𝕩, 𝕨 𝔽⚇𝕘 𝕩: Depth
- Apply 𝔽 to the cells of the arguments at depth given in 𝕘.
- Negative numbers count down from the top level and non-negative ones from the
bottom up."
"\
1⊸↓⚇1 ⟨⟨1,2,3⟩, ⟨4,5,6⟩⟩
⟨ ⟨ 2 3 ⟩ ⟨ 5 6 ⟩ ⟩
1 ↓⚇1 ⟨⟨1,2,3⟩, ⟨4,5,6⟩⟩
⟨ ⟨ 2 3 ⟩ ⟨ 5 6 ⟩ ⟩
(+´↕)⚇0 ⟨2,4‿7,3⟩ # Implements pervasion
⟨ 1 ⟨ 6 21 ⟩ 3 ⟩"])
(?\# . [ nil
"#: Comment"
"\
#: Comment
- Create a comment that extends to the end of the line.
- Anything written in comments is ignored.
"
"\
1 + 2 # + 3 + 4
3
\"Hello world!\" # this is ignored!
\"Hello world!\""])
(?⁼ . [ ?3
"𝔽⁼ 𝕩, 𝕨 𝔽⁼ 𝕩: Undo"
"\
𝔽⁼ 𝕩, 𝕨 𝔽⁼ 𝕩: Undo"
"\
1 - 2
¯1
1 -⁼ 2
¯1
√ 16
4
√⁼ 4
16
⋆ 1
2.718281828459045
⋆⁼ 2.718281828459045
1"])
(?⍟ . [ ?\#
"𝔽⍟𝔾 𝕩, 𝕨 𝔽⍟𝔾 𝕩: Repeat"
"\
𝔽⍟𝔾 𝕩, 𝕨 𝔽⍟𝔾 𝕩: Repeat
- Apply 𝔾 to 𝕨 and 𝕩, then apply 𝔽 to 𝕩 that many times.
- If 𝕨 is given, use it each time as a constant left argument.
- If 𝔾 returns an array, give 𝔽⍟𝕩 for each of its elements."
"\
1 +⍟⊢ 4
8
1 +⍟1‿2‿3 4
⟨ 5 6 7 ⟩
3 ∾⍟{≠𝕩} ⟨4,5,6⟩
⟨ 3 3 3 4 5 6 ⟩"])
(?⌜ . [ ?4
"𝕨 𝔽⌜ 𝕩: Table"
"\
𝕨 𝔽⌜ 𝕩: Table
- Apply 𝔽 between every possible pair of the elements of the arguments."
"\
1‿2‿3‿4 +⌜ 4‿5‿6‿7
┌─
╵ 5 6 7 8
6 7 8 9
7 8 9 10
8 9 10 11
┘
\"abc\" ∾⌜ \"xyz\"
┌─
╵ \"ax\" \"ay\" \"az\"
\"bx\" \"by\" \"bz\"
\"cx\" \"cy\" \"cz\"
┘
"])
(?◶ . [ ?$
"𝔽◶𝕘 𝕩, 𝕨 𝔽◶𝕘 𝕩: Choose"
"\
𝔽◶𝕘 𝕩, 𝕨 𝔽◶𝕘 𝕩: Choose
- Apply 𝔽 to the arguments and use the result to pick (⊑) a function from list
𝕘.
- Apply the picked function to the arguments."
"\
F ← ⊢◶+‿-‿÷‿×
F 0
0
F 1
¯1
F 2
0.5"])
(?´ . [ ?5
"𝔽´ 𝕩: Fold | 𝕨 𝔽´ 𝕩: Fold With Initial"
"\
𝔽´ 𝕩: Fold
- Fold over 𝕩 with 𝔽 from right to left i.e. Insert 𝔽 between the elements of 𝕩.
- 𝕩 must be a simple list (1 = =𝕩).
𝕨 𝔽´ 𝕩: Fold With Initial
- Monadic fold, but use 𝕨 as initial right argument."
"\
+´ 1‿2‿3
6
1+2+3
6
-´ 1‿2‿3
2
1-2-3
2
5 +´ 1‿2‿3
11
1+2+3+5
11
5 -´ 1‿2‿3
¯3
1-2-3-5
¯3"])
(?⊘ . [ ?%
"𝔽⊘𝔾 𝕩: Valences | 𝕨 𝔽⊘𝔾 𝕩: Dyadic Valences"
"\
𝔽⊘𝔾 𝕩: Valences
- Apply 𝔽 to 𝕩.
𝕨 𝔽⊘𝔾 𝕩: Dyadic Valences
- Apply 𝔾 to 𝕨 and 𝕩."
"\
+⊘- 5
5
-⊘+ 5
¯5
4 +⊘- 5
¯1
4 -⊘+ 5
9"])
(?˝ . [ ?6
"𝔽˝ 𝕩: Insert | 𝕨 𝔽˝ 𝕩: Insert With Initial"
"\
𝔽˝ 𝕩: Insert
- Fold over cells of 𝕩 with 𝔽 from end to start, that is, insert 𝔽 between the
major cells of 𝕩.
𝕨 𝔽˝ 𝕩: Insert With Initial
- Monadic insert, but use 𝕨 as initial right argument."
"\
a ← 3‿3 ⥊ ↕9
+˝ a
⟨ 9 12 15 ⟩
0‿1‿2 + 3‿4‿5 + 6‿7‿8
⟨ 9 12 15 ⟩
b ← 3‿3 ⥊ ↕9
1‿1‿1 +˝ b
⟨ 10 13 16 ⟩
1 +˝ b
⟨ 10 13 16 ⟩
0‿1‿2 + 3‿4‿5 + 6‿7‿8 + 1‿1‿1
⟨ 10 13 16 ⟩"])
(?⎊ . [ ?^
"𝔽⎊𝔾 𝕩, 𝕨 𝔽⎊𝔾 𝕩: Catch"
"\
𝔽⎊𝔾 𝕩, 𝕨 𝔽⎊𝔾 𝕩: Catch
- Apply 𝔽 to the arguments.
- If an error happens when 𝔽 is applied, cancel its execution, apply 𝔾 to the
arguments and return its result.
- Otherwise, return the result of 𝔽.
"
"\
∾⎊{\"error occurred with argument: \"∾•Fmt 𝕩} 1
\"error occurred with argument: 1\"
∾⎊{\"error occurred with argument: \"∾•Fmt 𝕩} ⟨⟨1,2⟩, ⟨3,4⟩⟩
⟨ 1 2 3 4 ⟩
"])
(?∞ . [ ?8
"∞: Infinity"
"\
∞: Infinity
- Mathematical constant Infinity, a numeric literal. Can be negative (¯∞)."
"\
∞
∞
¯∞
¯∞
1+∞
∞"])
(?\( . [ nil
"(: Begin Expression"
"\
(: Begin Expression
- Starts an expression, and only one expression.
- Must end with a corresponding ).
- ( supercedes any precedence order, so that an expression in () is evaluated
fully before it can be used in the outer context."
"\
1 + 2 - 3
0
(1 + 2) - 3
0"])
(?¯ . [ ?9
"¯: Minus"
"\
¯: Minus
- Prefix before numbers to indicate that they are negative.
- Note that this is not the same as -, since it is part of the number, rather
than a primitive that negates its value."
"\
-1‿2‿3
⟨ ¯1 ¯2 ¯3 ⟩
¯1‿2‿3
⟨ ¯1 2 3 ⟩"])
(?⟨ . [ ?\(
"⟨: Begin list"
"\
⟨: Begin list
- Starts a list.
- Inner elements must be separated by , or ⋄.
- Lists can be nested in other lists.
- Must end with a corresponding ⟩."
"\
⟨1, 2, 3⟩
⟨ 1 2 3 ⟩
⟨+ ⋄ - ⋄ 56⟩
⟨ + - 56 ⟩"])
(?\) . [ nil
"): End Expression)"
"\
): End Expression
- The closing symbol for (.
- See ( documentation for more details."
"\
1 + 2 - 3
0
(1 + 2) - 3
0"])
(?• . [ ?0
"•: System"
"\
•: System
- A prefix for system functions.
- •listSys gives a list of defined system value names.
- • is ignored when determining the role of the system value."
"\
"])
(?⟩ . [ ?\)
"⟩: End list)"
"\
⟩: End list
- Ends a list started by a ⟨.
- See ⟨ documentation for more details."
"\
⟨1, 2, 3⟩
⟨ 1 2 3 ⟩
⟨+ ⋄ - ⋄ 56⟩
⟨ + - 56 ⟩"])
(?- . [ nil
"- 𝕩: Negate | 𝕨 - 𝕩: Subtract"
"\
- 𝕩: Negate
- Additive Inverse of 𝕩.
𝕨 - 𝕩: Subtract
- Subtract 𝕩 from 𝕨.
- 𝕨 and 𝕩 can be characters or numbers."
"\
- 1
¯1
- ¯1
1
1 - 2
¯1
1 - 2‿3‿4
⟨ ¯1 ¯2 ¯3 ⟩
'a' - 4
']'
'b' - 'a'
1"])
(?÷ . [ ?-
"÷ 𝕩: Reciprocal | 𝕨 ÷ 𝕩: Divide"
"\
÷ 𝕩: Reciprocal
- Gives 1 ÷ 𝕩.
- Pervasive.
𝕨 ÷ 𝕩: Divide
- 𝕨 divided by 𝕩.
- Pervasive."
"\
÷ 5
0.2
5 ÷ 4
1.25
14 ÷ 7
2
"])
(?√ . [ ?_
"√ 𝕩: Square root | 𝕨 √ 𝕩: Root"
"\
√ 𝕩: Square root
- Self-explaining.
- Pervasive.
𝕨 √ 𝕩: Root
- 𝕨 th root of 𝕩.
- Pervasive."
"\
√ 2
1.4142135623730951
2 √ 2
1.4142135623730951
1‿2‿3‿4 √ 4
⟨ 4 2 1.5874010519681994 1.4142135623730951 ⟩"])
(?= . [ nil
"= 𝕩: Rank | 𝕨 = 𝕩: Equal To"
"\
= 𝕩: Rank
- Returns the number of dimensions in 𝕩.
𝕨 = 𝕩: Equal To
- Do argument atoms match?
- Pervasive."
"\
= 0
0
= 3⥊0
1
= 3‿3⥊0
2
3‿3‿3 ⥊ ⟨⟨0⟩⟩
┌─
╎ ⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
⟨ 0 ⟩ ⟨ 0 ⟩ ⟨ 0 ⟩
┘
1 = 3
0
2‿3‿0 = 3‿1‿0
⟨ 0 0 1 ⟩
'a' = 'a'
1"])
(?+ . [ nil
"+ 𝕩: Conjugate | 𝕨 + 𝕩: Add"
"\
+ 𝕩: Conjugate
- Complex conjugate of 𝕩.
- BQN doesn't support complex numbers yet, so it has no effect.
𝕨 + 𝕩: Add
- 𝕨 added to 𝕩.
- Either 𝕨 or 𝕩 can be a character, and if so, the other has to be an integer.
- Pervasive."
"\
+ 1
1
+ ¯1
¯1
1 + 2
3
1 + 2‿3‿4
⟨ 3 4 5 ⟩
'a' + 4
'e'"])
(?× . [ ?=
"× 𝕩: Sign | 𝕨 × 𝕩: Multiply"
"\
× 𝕩: Sign
- Sign of 𝕩.
- ¯1 if 𝕩 < 0
- 0 if 𝕩 = 0
- 1 if 𝕩 > 0
- Pervasive.
𝕨 × 𝕩: Multiply
- 𝕨 multiplied by 𝕩.
- Pervasive."
"\
× ¯5‿0‿5‿1
⟨ ¯1 0 1 1 ⟩
1 × 2
2
2 × 2‿3‿4
⟨ 4 6 8 ⟩
"])
(?⋆ . [ ?+
"⋆ 𝕩: Exponential | 𝕨 ⋆ 𝕩: Power"
"\
⋆ 𝕩: Exponential
- e (Euler's constant) to the power of 𝕩.
- Pervasive.
𝕨 ⋆ 𝕩: Power
- 𝕨 to the power of 𝕩.
- Pervasive."
"\
⋆ 0‿1‿2‿3
⟨ 1 2.718281828459045 7.38905609893065 20.085536923187668 ⟩
2 ⋆ 5
32
8‿5‿9 ⋆ 2
⟨ 64 25 81 ⟩
2‿3 ⋆ 3‿¯4
⟨ 8 0.012345679012345678 ⟩"])
;; first row
(?⌽ . [ ?q
"⌽ 𝕩: Reverse | 𝕨 ⌽ 𝕩: Rotate"
"\
⌽ 𝕩: Reverse
- Reverse 𝕩 along the first axis.
𝕨 ⌽ 𝕩: Rotate
- Move the first 𝕨 elements of 𝕩 to its end. Negative 𝕨 reverses the direction
of rotation."
"\
⌽ 1‿2‿3
⟨ 3 2 1 ⟩
a ← 3‿3 ⥊ ↕9
⌽ a
┌─
╵ 6 7 8
3 4 5
0 1 2
┘
2 ⌽ 1‿2‿3
⟨ 3 1 2 ⟩
b ← 3‿3 ⥊ ↕9
2 ⌽ b
┌─
╵ 6 7 8
0 1 2
3 4 5
┘"])
(?𝕨 . [ ?w
"𝕨: Left Argument"
"\
𝕨: Left Argument
- A variable assigned to the left argument of a block.
- 𝕎 can be used to access the left argument as a function."
"\
5 {𝕨} 1
5
-‿÷ {𝕎𝕩}¨ 4
⟨ ¯4 0.25 ⟩"])
(?𝕎 . [ ?W
"𝕎: Left Argument"
"\
𝕨: Left Argument
- A variable assigned to the left argument of a block.
- 𝕎 can be used to access the left argument as a function."
"\
5 {𝕨} 1
5
-‿÷ {𝕎𝕩}¨ 4
⟨ ¯4 0.25 ⟩"])
(?∊ . [ ?e
"∊ 𝕩: Mark Firsts | 𝕨 ∊ 𝕩: Member Of"
"\
∊ 𝕩: Mark Firsts
- Mark the first occurrence of each major cell in 𝕩 with a 1, and all other
occurrences with a 0.
𝕨 ∊ 𝕩: Member Of
- Is each cell in 𝕨 a major cell of 𝕩?"
"\
∊ 4‿5‿6‿6‿4‿7‿5
⟨ 1 1 1 0 0 1 0 ⟩
a ← 3‿3 ⥊ ↕9
∊ a
⟨ 1 1 1 ⟩
⟨1⟩ ∊ ↕9
⟨ 1 ⟩
b ← 3‿3 ⥊ ↕9
⟨0‿1‿2⟩ ∊ b
┌·
· 0
┘
⟨1‿3 ⥊ 0‿1‿2⟩ ∊ b
┌·
· 0
┘"])
(?⍷ . [ ?E
"⍷ 𝕩: Deduplicate | 𝕨 ⍷ 𝕩: Find"
"\
⍷ 𝕩: Deduplicate
- Unique major cells of 𝕩.
𝕨 ⍷ 𝕩: Find
- Mark the top left location of the occurrences of 𝕨 in 𝕩 with a 1, and other
locations with 0.
- Result is the same shape as (≢𝕨)↕x."
"\
⍷ 4‿5‿6‿6‿4‿7‿5
⟨ 4 5 6 7 ⟩
a ← 3‿3 ⥊ ↕6
⍷ a
┌─
╵ 0 1 2
3 4 5
┘
\"string\" ⍷ \"substring\"
⟨ 0 0 0 1 ⟩
\"loooooong\" ⍷ \"short\"
⟨⟩
b ← 7 (4|⋆˜)⌜○↕ 9
c ← (0‿3‿0≍0‿1‿0)
c ⍷ b
┌─
╵ 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 0 0 0 1
0 0 0 0 0 0 0
0 0 1 0 0 0 1
┘"])
(?↑ . [ ?r
"↑ 𝕩: Prefixes | 𝕨 ↑ 𝕩: Take"
"\
↑ 𝕩: Prefixes
- Prefixes of array 𝕩 along its first axis.
𝕨 ↑ 𝕩: Take
- For each integer in 𝕨, take that many elements from each dimension of 𝕩.
- Negative numbers take from the end.
- If any of the elements in 𝕨 are greater than the length of their respective
dimension, the dimension is extended with a fill value."
"\
↑ 1‿2‿3‿4
⟨ ⟨⟩ ⟨ 1 ⟩ ⟨ 1 2 ⟩ ⟨ 1 2 3 ⟩ ⟨ 1 2 3 4 ⟩ ⟩
a ← 3‿3 ⥊ ↕9
↑ a
┌─
· ↕0‿3 ┌─ ┌─ ┌─
╵ 0 1 2 ╵ 0 1 2 ╵ 0 1 2
┘ 3 4 5 3 4 5
┘ 6 7 8
┘
┘
3 ↑ 1‿3‿5‿67
⟨ 1 3 5 ⟩
b ← 4‿4 ⥊ ↕16
3‿3 ↑ b
┌─
╵ 0 1 2
4 5 6
8 9 10
┘
5‿5 ↑ b
┌─
╵ 0 1 2 3 0
4 5 6 7 0
8 9 10 11 0
12 13 14 15 0
0 0 0 0 0
┘
3‿¯3 ↑ b
┌─
╵ 1 2 3
5 6 7
9 10 11
┘"])
(?𝕣 . [ ?R
"𝕣: Current Modifier"
"\
𝕣: Current Modifier
- A variable assigned to the current modifier block.
- Add underscores to the beginning and/or end (_𝕣, _𝕣_) to use it in a modifier
role."
"\
+{𝕣⊣𝕩} 4
(1-modifier block)"])
(?∧ . [ ?t
"∧ 𝕩: Sort Up | 𝕨 ∧ 𝕩: Logical And"
"\
∧ 𝕩: Sort Up
- Sort array 𝕩 in ascending order.
𝕨 ∧ 𝕩: Logical And
- Logical And of 𝕨 and 𝕩.
- Pervasive."
"\
∧ 3‿1‿4‿1‿5
⟨ 1 1 3 4 5 ⟩
1 ∧ 1
1
1‿0 ∧ 1‿1
⟨ 1 0 ⟩
"])
(?⍋ . [ ?T
"⍋ 𝕩: Grade Up | 𝕨 ⍋ 𝕩: Bins Up"
"\
⍋ 𝕩: Grade Up
- Indices of 𝕩 that would sort its major cells in ascending order.
𝕨 ⍋ 𝕩: Bins Up
- Binary search for each cell of 𝕩 in 𝕨, returning the number of major cells in
𝕨 less than or equal to that cell.
- 𝕨 must be sorted in ascending order."
"\
a ← 3‿2‿1
⍋ a
⟨ 2 1 0 ⟩