Digital encoding of APL symbols

The programming language APL uses a number of symbols, rather than words from natural language, to identify operations, similarly to mathematical symbols. Prior to the wide adoption of Unicode, a number of special-purpose EBCDIC and non-EBCDIC code pages were used to represent the symbols required for writing APL.

Character sets

Due to its origins on IBM Selectric-based teleprinters, APL symbols have traditionally been represented on the wire using a unique, non-standard character set. In the 1960s and 1970s, few terminal devices existed which could reproduce them, the most popular ones being the IBM 2741 and IBM 1050 fitted with a specific APL print head. Over time, with the universal use of high-quality graphic display, printing devices and Unicode support, the APL character font problem has largely been eliminated.

Character repertoire

IBM assigns the following character IDs (GCGIDs) to APL syntax, which are used in the definitions of its code pages.[1][2][3]

"SL" (APL functional symbol) series GCGIDs
GCGID[2]IBM name[1][3]UnicodeNotes and other mappings
SL010000Up Stile (APL)U+2308 ⌈ LEFT CEILING
SL020000Down Stile (APL)U+230A ⌊ LEFT FLOOR
SL030000Del (APL)U+2207 ∇ NABLA
SL040000Del Tilde (APL)U+236B ⍫ APL FUNCTIONAL SYMBOL DEL TILDE
SL050000Del Stile (APL)U+2352 ⍒ APL FUNCTIONAL SYMBOL DEL STILE
SL060000Delta (APL)U+2206 ∆ INCREMENT
SL070000Delta Stile (APL)U+234B ⍋ APL FUNCTIONAL SYMBOL DELTA STILE
SL080000Circle (APL)U+25CB ○ WHITE CIRCLE[4][5][6][7]This is SM750000 in a non-APL context, for example, in the C0 replacement graphics from code page 437,[8] which code pages 907, 909 and 910 inherit some or all of, retaining SM750000 in the C0 area and also including SL080000 outside of it.[9][10][11] Both map to U+25CB when APL is represented using Unicode characters, although SL080000 can be mapped to U+F890 in IBM's private use area scheme.[12] Compare SL590000 through SL620000 below.
SL090000Circle Stile (APL)U+233D ⌽ APL FUNCTIONAL SYMBOL CIRCLE STILE
SL100000Circle Slope (APL)U+2349 ⍉ APL FUNCTIONAL SYMBOL CIRCLE BACKSLASH
SL110000Circle Star (APL)U+235F ⍟ APL FUNCTIONAL SYMBOL CIRCLE STAR
SL120000Circle BarU+2296 ⊖ CIRCLED MINUS
SL130000Quad Quote (APL)U+235E ⍞ APL FUNCTIONAL SYMBOL QUOTE QUAD
SL140000Quad Divide (APL)U+2339 ⌹ APL FUNCTIONAL SYMBOL QUAD DIVIDE
SL150000Slash Bar (APL)U+233F ⌿ APL FUNCTIONAL SYMBOL SLASH BAR
SL160000Slope Bar (APL)U+2340 ⍀ APL FUNCTIONAL SYMBOL BACKSLASH BAR
SL170000Up Caret Tilde (APL)U+2372 ⍲ APL FUNCTIONAL SYMBOL UP CARET TILDE
SL180000Down Caret Tilde (APL)U+2371 ⍱ APL FUNCTIONAL SYMBOL DOWN CARET TILDE
SL190000Down Tack Jot (APL)[lower-alpha 1]U+234E ⍎ APL FUNCTIONAL SYMBOL DOWN TACK JOT[lower-alpha 1]
SL200000Up Tack Jot (APL)[lower-alpha 1]U+2355 ⍕ APL FUNCTIONAL SYMBOL UP TACK JOT[lower-alpha 1]
SL210000Up Shoe Null (APL)U+235D ⍝ APL FUNCTIONAL SYMBOL UP SHOE JOT
SL220000Up Tack (APL)[lower-alpha 1]U+22A4 ⊤ DOWN TACK[lower-alpha 1]
SL230000Down Tack (APL)[lower-alpha 1]U+22A5 ⊥ UP TACK[lower-alpha 1]
SL240000Down Tack Up Tack (APL)U+2336 ⌶ APL FUNCTIONAL SYMBOL I-BEAM
SL250000Jot (APL)U+2218 ∘ RING OPERATOR
SL260000Left Bracket Right Bracket (APL)U+2337 ⌷ APL FUNCTIONAL SYMBOL SQUISH QUAD
SL270000Quad Jot (APL)U+233B ⌻ APL FUNCTIONAL SYMBOL QUAD JOT
SL280000Quad Slope (APL)U+2342 ⍂ APL FUNCTIONAL SYMBOL QUAD BACKSLASH
SL290000Ampersand Underbar[3]Not used in any documented code page. Can be represented in Unicode with the sequence U+0026 U+0332 &̲
SL300000Equal Underbar (APL)U+2261 ≡ IDENTICAL TO
SL310000OUT Symbol (APL)[3]Not used in any documented code page. Reference glyph resembles oblique underlined forms of the letters O, U and T overstruck in the same character position.
SL320000Diaeresis Dot (APL)U+2235 ∵ BECAUSE
SL330000Delta Underbar (APL)U+2359 ⍙ APL FUNCTIONAL SYMBOL DELTA UNDERBAR
SL340000Left Tack (APL)[lower-alpha 1]U+22A2 ⊢ RIGHT TACK[lower-alpha 1]
SL350000Right Tack (APL)[lower-alpha 1]U+22A3 ⊣ LEFT TACK[lower-alpha 1]
SL360000Quad (APL)U+2395 ⎕ APL FUNCTIONAL SYMBOL QUAD[4][5]U+25AF ▯ WHITE VERTICAL RECTANGLE[3]
SL370000Less Greater (APL)U+22C4 ⋄ DIAMOND OPERATOR[4][5]U+25CA ◊ LOZENGE,[3] U+25C6 ◆ BLACK DIAMOND[6][15]
SL380000Stile (APL)U+2223 ∣ DIVIDES[4][5]U+2502 │ BOX DRAWINGS LIGHT VERTICAL,[6][15] U+007C | VERTICAL LINE[7]
SL400000Up Shoe (APL)U+2229 ∩ INTERSECTION[4][5][7]U+22C2 ⋂ N-ARY INTERSECTION[15][6]
SL410000Down Shoe (APL)U+222A ∪ UNION[4][5][7]U+22C3 ⋃ N-ARY UNION[15][6]
SL420000Left Shoe (APL)U+2282 ⊂ SUBSET OF
SL430000Right Shoe (APL)U+2283 ⊃ SUPERSET OF
SL440000Underbar (APL)U+005F _ LOW LINE
SL450000Diaeresis (APL)U+00A8 ¨ DIAERESIS
SL460000Tilde (APL)U+223C ∼ TILDE OPERATOR[4][5]U+F88F in IBM's private use area scheme.[12] Also mapped to U+007E ~ TILDE,[15][6][7] although SD190000 (U+007E in a non-APL context) co-occurs at 0xA1 (while SL460000 is at 0x80) in code page 213.[16]
SL480000Circle PlusU+2295 ⊕ CIRCLED PLUS
SL490000Circle xU+2297 ⊗ CIRCLED TIMES
SL500000Down Caret (APL)U+2228 ∨ LOGICAL OR[15][6][4][5][3][7]
SL510000Up Caret (APL)U+2227 ∧ LOGICAL AND[4][5][7]U+22C0 ⋀ N-ARY LOGICAL AND[15][6]
SL520000Less (APL)U+003C < LESS-THAN SIGN
SL530000Greater (APL)U+003E > GREATER-THAN SIGN
SL540000Divide (APL)U+00F7 ÷ DIVISION SIGN
SL550000Times (APL)U+00D7 × MULTIPLICATION SIGN
SL560000Not Greater (APL)U+2264 ≤ LESS-THAN OR EQUAL TO
SL570000Not Less (APL)U+2265 ≥ GREATER-THAN OR EQUAL TO
SL580000Quote Dot (APL)U+0021 ! EXCLAMATION MARK[15][6][5][7]U+F88E in IBM's private use area scheme.[12] SP020000 (U+0021 ! EXCLAMATION MARK in a non-APL context) co-occurs at 0x5A in code page 293 (SL580000 is at 0xDB in code pages 293 and 310).[16] Tachyonsoft lists U+01C3 ǃ LATIN LETTER RETROFLEX CLICK for SL580000.[4]
SL590000Left Arrow (APL)U+2190 ← LEFTWARDS ARROW[4][5][6]These arrows are SM300000, SM310000, SM320000 and SM330000 respectively in a non-APL context, for example, in the C0 replacement graphics from code page 437,[8] which code pages 907, 909 and 910 inherit some or all of. Their APL GCGIDs can be mapped to U+F88D, U+F88C, U+F88B and U+F88A respectively in IBM's private use area scheme.[12]

Code pages 907 and 910 keep the non-APL GCGIDs for the C0 replacements but use the APL GCGIDs where the arrows appear outside of the C0 area, while code page 909 uses the APL GCGIDs multiple times, both for the C0 replacements and for between one and two occurrences of each of these arrows outside of the C0 area.[9][10][11]

Compare SL080000 above. Duplicating C0 replacement graphics outside of the C0 area is not an uncommon practice in DOS code pages: compare, for example, the pilcrow and section sign in code page 850.

SL600000Right Arrow (APL)U+2192 → RIGHTWARDS ARROW[4][5][6]
SL610000Up Arrow (APL)U+2191 ↑ UPWARDS ARROW[4][5][6][7]
SL620000Down Arrow (APL)U+2193 ↓ DOWNWARDS ARROW[4][5][6][7]
SL630000Overbar (APL)U+203E ‾ OVERLINE
SL640000Slope (APL)U+005C \ REVERSE SOLIDUS[15][6][5][7]U+F889 in IBM's private use area scheme.[12] Also mapped to U+2216 ∖ SET MINUS.[4] SM070000 (U+005C \ REVERSE SOLIDUS in a non-APL context) co-occurs at 0x5A (while SL640000 is at 0xB7) in code page 293.[16]
SL650000Star (APL)U+22C6 ⋆ STAR OPERATOR[5]U+002A * ASTERISK[17][7]
SL660000Quote (APL)U+0027 ' APOSTROPHE
SL670000Left Parenthesis (APL)U+0028 ( LEFT PARENTHESIS
SL680000Right Parenthesis (APL)U+0029 ) RIGHT PARENTHESIS
SL690000Bar (APL)U+002D - HYPHEN-MINUS[17][5][6][7]U+2212 − MINUS SIGN
SL700000Query (APL)U+003F ? QUESTION MARKU+F888 in IBM's private use area scheme.[12]
SL710000Alpha (APL)U+237A ⍺ APL FUNCTIONAL SYMBOL ALPHA[4][5]U+03B1 α GREEK SMALL LETTER ALPHA[15][6]
SL720000Epsilon (APL)U+220A ∊ SMALL ELEMENT OF[5][3][7]U+03B5 ε GREEK SMALL LETTER EPSILON,[15][6] U+2208 ∈ ELEMENT OF[4]
SL730000Iota (APL)U+2373 ⍳ APL FUNCTIONAL SYMBOL IOTA[4][5]U+03B9 ι GREEK SMALL LETTER IOTA[15][6]
SL740000Rho (APL)U+2374 ⍴ APL FUNCTIONAL SYMBOL RHO[4][5]U+03C1 ρ GREEK SMALL LETTER RHO[15][6]
SL750000Omega (APL)U+2375 ⍵ APL FUNCTIONAL SYMBOL OMEGA[4][5]U+03C9 ω GREEK SMALL LETTER OMEGA[15][6]
SL760000Slash (APL)U+002F / SOLIDUS
SL770000Left Bracket (APL)U+005B [ LEFT SQUARE BRACKET
SL780000Right Bracket (APL)U+005D ] RIGHT SQUARE BRACKET
SL790000Plus (APL)U+002B + PLUS SIGN
SL800000Semicolon (APL)U+003B ; SEMICOLON
SL810000Equal (APL)U+003D = EQUALS SIGN
SL820000Not Equal (APL)U+2260 ≠ NOT EQUAL TO
SL830000Colon (APL)U+003A : COLON[6][5]Form with fullwidth attribute set (SL830080) is used for 0xA1C3 (i.e. U+2236 ∶ RATIO) in EUC-CN.[18]
SL840000Dot (APL)U+002E . FULL STOP
SL850000Comma (APL)U+002C , COMMA
SL860000Iota Underbar (APL)U+2378 ⍸ APL FUNCTIONAL SYMBOL IOTA UNDERBAR
SL870000Epsilon Underbar (APL)U+2377 ⍷ APL FUNCTIONAL SYMBOL EPSILON UNDERBAR

Code page 293

Code page 293 (CCSID 293),[19] called "APL (USA)", is an EBCDIC code page which includes APL symbols, in addition to preserving the basic Latin letters and Western Arabic numerals at their usual EBCDIC locations.[16][17]

Code page 293[20][16][17]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x NUL SOH STX ETX SEL  HT  RNL DEL  GE  SPS RPT  VT   FF   CR   SO   SI  
1x DLE DC1 DC2 DC3 RES/
ENP		  NL    BS  POC CAN  EM  UBS CU1  IFS  IGS  IRS IUS/
ITB
2x  DS  SOS  FS  WUS BYP/
INP		  LF  ETB ESC  SA  SFE  SM/
SW		 CSP MFA ENQ ACK BEL
3x SYN   IR   PP  TRN NBS EOT SBS   IT  RFF CU3 DC4 NAK SUB
4x  SP  𝐴̲ 𝐵̲ 𝐶̲ 𝐷̲ 𝐸̲ 𝐹̲ 𝐺̲ 𝐻̲ 𝐼̲ ¢ . < ( + |
5x & 𝐽̲ 𝐾̲ 𝐿̲ 𝑀̲ 𝑁̲ 𝑂̲ 𝑃̲ 𝑄̲ 𝑅̲ ! $ ⋆/* ) ; ¬
6x -/− / 𝑆̲ 𝑇̲ 𝑈̲ 𝑉̲ 𝑊̲ 𝑋̲ 𝑌̲ 𝑍̲ ¦ , % _ > ?
7x ⋄/◊/◆ ∧/⋀ ¨ ⌻ ⍸ ⍷ ⊢ ⊣ ∨ ` :/∶ # @ ' = "
8x ∼/~ a b c d e f g h i ↑ ↓ ≤ ⌈ ⌊ →
9x ⎕ j k l m n o p q r ⊃ ⊂ ○ ←
Ax ‾ ~ s t u v w x y z ∩/⋂ ∪/⋃ ⊥ [ ≥ ∘
Bx ⍺/α ∊/ε/∈ ⍳/ι ⍴/ρ ⍵/ω × \/∖ ÷ ∇ ∆ ⊤ ] ≠ ∣/│
Cx { A B C D E F G H I ⍲ ⍱ ⌷ ⌽ ⍂ ⍉
Dx } J K L M N O P Q R ⌶ !/ǃ ⍒ ⍋ ⍞ ⍝
Ex \ ≡ S T U V W X Y Z ⌿ ⍀ ∵ ⊖ ⌹ ⍕
Fx 0 1 2 3 4 5 6 7 8 9 ⍫ ⍙ ⍟ ⍎  EO 
  Differences from Code page 37

Code page 310

Code page 310 ("Graphic Escape APL/TN") includes a larger gamut of symbols, but does not itself include the basic Latin letters or the basic digits.[21][4] It is used alongside Code page 37-2,[22] with the Code page 310 codes being prefixed by the Graphic Escape (EBCDIC 0x08)[23] control character.[6][24]

Code page 310 (prefixed with 0x08)[25][21][4][6][lower-alpha 2]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x
1x
2x
3x
4x  SP  𝐴̲ 𝐵̲ 𝐶̲ 𝐷̲ 𝐸̲ 𝐹̲ 𝐺̲ 𝐻̲ 𝐼̲
5x 𝐽̲ 𝐾̲ 𝐿̲ 𝑀̲ 𝑁̲ 𝑂̲ 𝑃̲ 𝑄̲ 𝑅̲
6x 𝑆̲ 𝑇̲ 𝑈̲ 𝑉̲ 𝑊̲ 𝑋̲ 𝑌̲ 𝑍̲
7x ◊/⋄/◆ ∧/⋀ ¨ ⌻ ⍸ ⍷ ⊢ ⊣ ∨
8x ∼/~ ║ ═ ⎸ ⎹ │/⎥ ↑ ↓ ≤ ⌈ ⌊ →
9x ⎕ ▌ ▐ ▀ ▄ █/■ ⊃ ⊂ ⌑/¤ ○ ± ←
Ax ¯/‾ ° ─ ∙/• ₙ ∩/⋂ ∪/⋃ ⊥ [ ≥ ∘
Bx ⍺/α ∊/∈/ε ⍳/ι ⍴/ρ ⍵/ω × ∖/\ ÷ ∇ ∆ ⊤ ] ≠ ∣/│
Cx { ⁽ ⁺/+ ■/∎ └ ┌ ├ ┴ § ⍲ ⍱ ⌷ ⌽ ⍂ ⍉
Dx } ⁾ ⁻/- ┼ ┘ ┐ ┤ ┬ ⌶ ǃ/! ⍒ ⍋ ⍞ ⍝
Ex ≡ ₁ ₂ ₃ ⍤[lower-alpha 3] ⍥[lower-alpha 3] ⍪[lower-alpha 3] €[lower-alpha 3] ⌿ ⍀ ∵ ⊖ ⌹ ⍕
Fx ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⍫ ⍙ ⍟ ⍎

Code page 351

Code page 351 ("GDDM Default (USA)")[26] contains most of the characters of Code page 293 and Code page 310 (except ⍷, epsilon with underline) in addition to the letters and digits, by replacing several control characters with symbols.

Code page 351[26]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x NUL {  HT  ▀ ⎹  FF   CR 
1x  NL    BS  ▌ █ ▐ │ ┐ ┌ └ ┘
2x ⁽ ⁾ ⁺ ⁻ }  LF  ⍸ ║ ▄ ═ ⎸ § ┼ ─ ⊢ ⊣
3x ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ┬ ├ ┴ ┤
4x  SP  𝐴̲ 𝐵̲ 𝐶̲ 𝐷̲ 𝐸̲ 𝐹̲ 𝐺̲ 𝐻̲ 𝐼̲ ¢ . < ( + |
5x & 𝐽̲ 𝐾̲ 𝐿̲ 𝑀̲ 𝑁̲ 𝑂̲ 𝑃̲ 𝑄̲ 𝑅̲ ! $ * ) ; ¬
6x - / 𝑆̲ 𝑇̲ 𝑈̲ 𝑉̲ 𝑊̲ 𝑋̲ 𝑌̲ 𝑍̲ ¦ , % _ > ?
7x ⋄ ∧ ¨ ₁ ₂ ₃ ₙ ° ∨ ` : # @ ' = "
8x ∼ a b c d e f g h i ↑ ↓ ≤ ⌈ ⌊ →
9x ⎕ j k l m n o p q r ⊃ ⊂ ⌑ ○ ± ←
Ax ¯ ~ s t u v w x y z ∩ ∪ ⊥ [ ≥ ∘
Bx ⍺ ∈/∊ ⍳ ⍴ ⍵ ■ × ∖ / \ ÷ ∙ ∇ ∆ ⊤ ] ≠ ∣
Cx { A B C D E F G H I ⍲ ⍱ ⌷ ⌽ ⍂ ⍉
Dx } J K L M N O P Q R ⌶ ǃ/! ⍒ ⍋ ⍞ ⍝
Ex \ ≡ S T U V W X Y Z ⌿ ⍀ ∵ ⊖ ⌹ ⍕
Fx 0 1 2 3 4 5 6 7 8 9 ⌻ ⍫ ⍙ ⍟ ⍎

Code page 371 (IR-68)
Main article: ISO-IR-68

Code page 371,[27] registered for use with ISO/IEC 2022 as ISO-IR-68,[28][5] is a 7-bit heavily modified ASCII, designed by the APL Working Group of the Canadian Standards Association, intended for use with APL in an environment allowing overstriking of characters using the BS (backspace, 0x08) control code.[28][5]

Code page 907

Code page 907 is used by the IBM 3812, like code page 906.

Code page 907[9]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x ☺ ☻ ♥ ♦ ♣ ♠ • ◘ ○ ◙ ♂ ♀ ♪ ♬ ☼
1x ► ◄ ↕ ‼ § ▬ ↨ ↑ ↓ → ← ∟ ↔ ▲ ▼
2x  SP  !/ǃ " # $ % & ' ( ) ⋆/* + , -/− . /
3x 0 1 2 3 4 5 6 7 8 9 :/∶ ; < = > ?
4x @ A B C D E F G H I J K L M N O
5x P Q R S T U V W X Y Z [ \/∖ ] ∧/⋀ _
6x ` a b c d e f g h i j k l m n o
7x p q r s t u v w x y z { ∣/│ } ∼/~ ⌂
8x 𝐴̲ 𝐵̲ 𝐶̲ 𝐷̲ 𝐸̲ 𝐹̲ 𝐺̲ 𝐻̲ 𝐼̲ 𝐽̲ 𝐾̲ 𝐿̲ 𝑀̲ 𝑁̲ 𝑂̲ 𝑃̲
9x ⎕ ⍞ ⌹ 𝑄̲ 𝑅̲ 𝑆̲ 𝑇̲ 𝑈̲ ⊤ 𝑉̲ 𝑊̲ ¢ 𝑋̲ ⊥ ← ⌶
Ax 𝑌̲ 𝑍̲ ⌈ ¬ → ∪/⋃ ⍕ ⍎
Bx ░ ▒ ▓ │ ┤ ⍷ ⍸ ≡ ∵ ╣ ║ ╗ ╝ ⍂ ⌻ ┐
Cx └ ┴ ┬ ├ ─ ┼ ⌷ ╚ ╔ ╩ ╦ ╠ ═ ╬
Dx ↑ ↓ ⍟ ∆ ∇ ⌊ ┘ ┌ █ ▄ ▌ ▐ ▀
Ex ⍺/α ß ⊂ ⊃ ⍝ ⍲ ⍴/ρ ⍱ ⌽ ⊖ ○ ∨ ⍳/ι ⍉ ∊/ε/∈ ∩/⋂
Fx ⌿ ⍀ ≥ ≤ ≠ × ÷ ⍙ ∘ ⍵/ω ⍫ ⍋ ⍒ ‾ ¨ NBSP
  Differences from code page 437

Code page 909

Code page 909 is another encoding for APL, differing from code page 907 in not including the underlined characters, assigning different codes to the APL characters which fall in the 0xB0–DF range, and replacing some of the C0 replacement graphics from code page 437 with alternative encodings for certain APL symbols.

Code page 909[10]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x ⍷ ⍸ ♥ ♦ ♣ ♠ • ◘ ○ ◙ ≡ ♀ ♪ ♬ ⍟
1x ► ◄ ∵ ⌷ § ⍂ ⌻ ↑ ↓ → ← ⌊ ↔ ∆ ∇
2x  SP  !/ǃ " # $ % & ' ( ) ⋆/* + , -/− . /
3x 0 1 2 3 4 5 6 7 8 9 :/∶ ; < = > ?
4x @ A B C D E F G H I J K L M N O
5x P Q R S T U V W X Y Z [ \/∖ ] ∧/⋀ _
6x ` a b c d e f g h i j k l m n o
7x p q r s t u v w x y z { ∣/│ } ∼/~ ⌂
8x Ç ü é â ä à å ç ê ë è ï î ì Ä Å
9x ⎕ ⍞ ⌹ ô ö ò û ù ⊤ Ö Ü £ ⊥ ← ⌶
Ax á í ó ú ñ Ñ ª º ¿ ⌈ ¬ → ∪/⋃ ¡ ⍕ ⍎
Bx ░ ▒ ▓ │ ┤ ⍟ ∆ ∇ → ╣ ║ ╗ ╝ ← ⌊ ┐
Cx └ ┴ ┬ ├ ─ ┼ ↑ ↓ ╚ ╔ ╩ ╦ ╠ ═ ╬ ≡
Dx ⍸ ⍷ ∵ ⌷ ⍂ ⌻ ⊢ ⊣ ⋄/◊/◆ ┘ ┌ █ ▄ ▀
Ex ⍺/α ß ⊂ ⊃ ⍝ ⍲ ⍴/ρ ⍱ ⌽ ⊖ ○ ∨ ⍳/ι ⍉ ∊/ε/∈ ∩/⋂
Fx ⌿ ⍀ ≥ ≤ ≠ × ÷ ⍙ ∘ ⍵/ω ⍫ ⍋ ⍒ ‾ ¨ NBSP
  Differences from code page 437

Code page 910

Code page 910 is similar to code page 909, but with fewer duplicate horizontal arrows, using the same C0 graphics as code page 437, and including some additional characters.

Code page 910[11]
0 1 2 3 4 5 6 7 8 9 A B C D E F
0x ☺ ☻ ♥ ♦ ♣ ♠ • ◘ ○ ◙ ♂ ♀ ♪ ♬ ☼
1x ► ◄ ↕ ‼ § ▬ ↨ ↑ ↓ → ← ∟ ↔ ▲ ▼
2x  SP  !/ǃ " # $ % & ' ( ) ⋆/* + , -/− . /
3x 0 1 2 3 4 5 6 7 8 9 :/∶ ; < = > ?
4x @ A B C D E F G H I J K L M N O
5x P Q R S T U V W X Y Z [ \/∖ ] ∧/⋀ _
6x ` a b c d e f g h i j k l m n o
7x p q r s t u v w x y z { ∣/│ } ∼/~ ⌂
8x Ç ü é â ä à å ç ê ë è ï î ì Ä Å
9x ⎕ ⍞ ⌹ ô ö ò û ù ⊤ Ö Ü ø £ ⊥ ₧ ⌶
Ax á í ó ú ñ Ñ ª º ¿ ⌈ ¬ ½ ∪/⋃ ¡ ⍕ ⍎
Bx ░ ▒ ▓ │ ┤ ⍟ ∆ ∇ → ╣ ║ ╗ ╝ ← ⌊ ┐
Cx └ ┴ ┬ ├ ─ ┼ ↑ ↓ ╚ ╔ ╩ ╦ ╠ ═ ╬ ≡
Dx ⍸ ⍷ ∵ ⌷ ⍂ ⌻ ⊢ ⊣ ⋄/◊/◆ ┘ ┌ █ ▄ ¦ Ì ▀
Ex ⍺/α ß ⊂ ⊃ ⍝ ⍲ ⍴/ρ ⍱ ⌽ ⊖ ○ ∨ ⍳/ι ⍉ ∊/ε/∈ ∩/⋂
Fx ⌿ ⍀ ≥ ≤ ≠ × ÷ ⍙ ∘ ⍵/ω ⍫ ⍋ ⍒ ‾ ¨ NBSP
  Differences from code page 437

Unicode

Most APL symbols are present in Unicode, in the Miscellaneous Technical range,[29] although some APL products may not yet feature Unicode, and some APL symbols may be unused or unavailable in a given vendor's implementation.

As of 2010, Unicode allows APL to be stored in text files, published in print and on the web, and shared through email and instant messaging. Entering APL characters still requires the use of either a specific input method editor or keyboard mapping, or of a specific touch interface. APL keyboard mappings are available for free for the most common operating systems, or can be obtained by adding the Unicode APL symbols to existing keyboard map.

Underscored alphabetic characters

Missing from Unicode are the traditional underscored alphabetic characters included in some of the APL code pages; their usage has been eliminated or deprecated in most APL implementations. These were produced on APL printing terminals by over-striking a straight capital letter with an underscore character. Some tables show them simulated with underlined and italic markup, not listing Unicode mappings.[4]

IBM assigns them GCGIDs as "LA480000" (which they name "A Line Below Capital/A Underscore (APL)"), "LB480000" ("B Line Below Capital/B Underscore (APL)") and so forth, under the "L" series used for Latin letters.[1] The use of an even number (48) rather than an odd number (47) is due to being uppercase: compare the use of SD110000 for a lone acute accent ´, LA110000 for the lowercase á, and LA120000 for the uppercase Á.[30] They are included in IBM's private use area scheme, encoded in reverse‑alphabetical order in the odd-numbered code points from U+F8BF to U+F8F1.[12]

Homologous uses of 47 include the "SD" (diacritic) series GCGID SD470000 for "Line Below/Discontinuous Underscore"[31]—i.e. macron below, distinct from the ASCII underscore which is SP090000 ("Underline/Continuous Underscore")[30]—and the "A" (Arabic letter) series GCGID AD470009 for the ḏāl,[32] for example. Unicode's Latin Extended Additional block includes the following capital "Line Below" characters with the macron below diacritic, for Semitic transcription (it includes a pre-composed ẖ only in lowercase):

  • U+1E06 Ḇ LATIN CAPITAL LETTER B WITH LINE BELOW
  • U+1E0E Ḏ LATIN CAPITAL LETTER D WITH LINE BELOW
  • U+1E34 Ḵ LATIN CAPITAL LETTER K WITH LINE BELOW
  • U+1E3A Ḻ LATIN CAPITAL LETTER L WITH LINE BELOW
  • U+1E48 Ṉ LATIN CAPITAL LETTER N WITH LINE BELOW
  • U+1E5E Ṟ LATIN CAPITAL LETTER R WITH LINE BELOW
  • U+1E6E Ṯ LATIN CAPITAL LETTER T WITH LINE BELOW
  • U+1E94 Ẕ LATIN CAPITAL LETTER Z WITH LINE BELOW

However, this does not cover the entire ISO basic Latin alphabet, and IBM's reference glyphs for the APL characters show them both underlined and oblique,[2] and tables simulating them with markup may follow suit.[4] Unicode's Mathematical Alphanumeric Symbols block includes italic characters for use in notations where they are contrastive with non-italic characters. Unicode also includes combining forms of the macron below and underscore in the Combining Diacritical Marks block; the characters above canonically decompose with the former:

  • U+0331 ◌̱ COMBINING MACRON BELOW
  • U+0332 ◌̲ COMBINING LOW LINE

Keyboard layout

Note the mnemonics associating an APL character with a letter: ? (question mark) on Q, ⋆ (power) on P, ρ (rho) on R, ⊥ (base value) on B, ⊤ (eNcode) on N, ∣ (modulus) on M and so on. This makes it easier for an English-language speaker to type APL on a non-APL keyboard, providing one has visual feedback on one's screen. Also, decals have been produced for attachment to standard keyboards, either on the front of the keys or on the top of them.

APL keyboard layout.[33]

Later IBM terminals, notably the IBM 3270 display stations, had an alternate keyboard arrangement which is the basis for some of the modern APL keyboard layouts in use today.

Further APL characters were available by overstriking one character with another. For example, the log symbol (⍟) was formed by overstriking ⇧ Shift+P with ⇧ Shift+O. This extended the graphic abilities of the earlier teleprinters, but made it more complex to correct errors and edit program lines.

New overstrikes were introduced by vendors as they produced versions of APL tailored to specific hardware, system features, file systems, and so on. Further, printing terminals and early APL cathode-ray terminals were able to display arbitrary overstrikes, but as personal computers rapidly replaced terminals as a data-entry device, APL character support became provided as an APL Character Generator ROM or a soft character set rendered by the display device. With the advent of the modern PC, APL characters were defined in specific fonts, eliminating the distinction between overstruck characters and standard characters.

Finally, the symbols were ratified in Unicode and given specific code points, with unambiguous interpretations, independently of the graphic font.

See also

Footnotes
  1. There are two naming conventions (which way around "up" and "down" are, and which way around "left" and "right" are) for tack characters, the "London" and "Bosworth" conventions.[13] Which convention is used differs between IBM and Unicode. Naming also differs between composite Unicode characters intended solely for APL (which match IBM naming and use the Bosworth convention) versus plain tacks also intended for other applications (which use the London convention).[13][14] APL specifications subsequently adopted the London convention.[14] The documentation for Dyalog APL notes that the Unicode naming for composite tacks (and thus the IBM naming for all tacks), which follows the lesser-used "Bosworth" convention,[13] runs contrary to convention in the APL community.[7]
  2. Documented mappings vary.[4][6][25][15]
  3. Sharp extension.[6]

References
  1. "Graphic Escape APL2/TN - 138". IBM. GCSGID 00963.
  2. "Graphic Escape APL2/TN - 138 (chart)" (PDF). IBM. GCSGID 00963.
  3. "Graphic character identifiers: Specials, APL symbols". IBM. Archived from the original on 2016-01-22.
  4. Tachyon Software (2007-07-31). Code Page 00310: 3270 APL Graphic Escape.
  5. Cowan, John (2004-06-29). "ISO-IR-68 to Unicode". Unicode.org. Unicode, Inc. Retrieved 19 June 2017.
  6. "x3270 Character Set". x3270 Documentation. Archived from the original on 2018-11-10.
  7. "Dyalog Nomenclature: Functions and Operators" (PDF). Dyalog - Documentation Centre. Dyalog APL.
  8. "Personal Computer". IBM. CPGID 00437.
  9. IBM. Code Page 00907 (PDF). Archived from the original (PDF) on 2017-08-03.
  10. IBM. Code Page 00909 (PDF). Archived from the original (PDF) on 2015-07-08.
  11. IBM. Code Page 00910 (PDF). Archived from the original (PDF) on 2015-07-08.
  12. IBM (1997). unicode.nam: Allow the Unicode characters to be specified using either the IBM or PostScript like names. (Included with Borgendale, Ken, OS/2 Codepage and Keyboard Display Tools)
  13. Dickey, Leroy J. "The Naming of Tack Symbols". University of Waterloo.
  14. Freytag, Asmus; McGowan, Rick; Whistler, Ken (2021-06-14). "Known Anomalies in Unicode Character Names". Unicode Consortium. UTN #27.
  15. "EBCDIC and ASCII Tables". Archived from the original on 2016-08-27.
  16. IBM (1996) [1984]. "Code Page (CPGID) 00293: APL (USA)". REGISTRY, Graphic Character Sets and Code Pages.
  17. Tachyon Software (2007-07-31). Code Page 00293: EBCDIC APL.
  18. "IBM Simplified Chinese Graphic Character Set for Extended UNIX Code (EUC)" (PDF). IBM. 1994. C-H 3-3220-132 1994-06.
  19. "CCSID 293 information document". Archived from the original on 2016-03-27.
  20. Code Page CPGID 00293 (pdf) (PDF), IBM
  21. IBM (1987). "Code Page (CPGID) 00310: Graphic Escape APL/TN". REGISTRY, Graphic Character Sets and Code Pages.
  22. xlate - Transliterate Contents of Records, IBM Corporation, 2010 [1986], archived from the original on 2019-06-16, retrieved 2016-10-18
  23. IBM. "Appendix G-1. EBCDIC control character definitions". IBM Globalization. Archived from the original on 2018-09-11.
  24. "Chapter 5. 3270 Display Station and Printer Code Page Charts (§ APL/APL2 Text Feature Code Page)" (PDF). 3174 Establishment Controller Character Set Reference (3rd ed.). IBM. 1990 [1988]. p. 5·6. GA27-3831-02.
  25. Code Page CPGID 00310 (pdf) (PDF), IBM
  26. Tachyon Software (2007-07-31). Code Page 00351: GDDM Default (USA).
  27. "Code Page 00371" (PDF). IBM. Archived from the original (PDF) on 2015-07-08.
  28. Standards Council of Canada (1983-06-01). APL Character Set for Workspace Interchange (PDF). ITSCJ/IPSJ. ISO-IR-68.
  29. "The Unicode Standard 5.1 Code Charts: Technical Symbols U+2300-U+23FF" (PDF). Unicode Standard 5.1. Unicode Consortium. Archived (PDF) from the original on 2 October 2008. Retrieved October 12, 2008.
  30. "Windows, Latin 1". IBM. CPGID 01252.
  31. "OCR B". IBM. GCSGID 00969.
  32. "Windows, Arabic (PDF)" (PDF). IBM. CPGID 01256.
  33. A more up-to-date keyboard diagram, applicable for APL2 and other modern implementations, is available at WikensOnline Union APL large keyboard layout for Windows Archived March 10, 2012, at the Wayback Machine, actual photo + diagram here Archived April 3, 2015, at the Wayback Machine and NARS2000 APL keyboard layout here.
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