Digital encoding of APL symbols

(Redirected from Code page 310)

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)[a]U+234E APL FUNCTIONAL SYMBOL DOWN TACK JOT[a]
SL200000Up Tack Jot (APL)[a]U+2355 APL FUNCTIONAL SYMBOL UP TACK JOT[a]
SL210000Up Shoe Null (APL)U+235D APL FUNCTIONAL SYMBOL UP SHOE JOT
SL220000Up Tack (APL)[a]U+22A4 DOWN TACK[a]
SL230000Down Tack (APL)[a]U+22A5 UP TACK[a]
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)[a]U+22A2 RIGHT TACK[a]
SL350000Right Tack (APL)[a]U+22A3 LEFT TACK[a]
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

EBCDIC code pages

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]
0123456789ABCDEF
0xNULSOHSTXETXSEL HT RNLDEL GE SPSRPT VT  FF  CR  SO  SI  
1xDLEDC1DC2DC3RES/
ENP
 NL   BS POCCAN EM UBSCU1 IFS IGS IRSIUS/
ITB
2x DS SOS FS WUSBYP/
INP
 LF ETBESC SA SFE SM/
SW
CSPMFAENQACKBEL
3xSYN  IR  PP TRNNBSEOTSBS  IT RFFCU3DC4NAKSUB
4x SP 𝐴̲𝐵̲𝐶̲𝐷̲𝐸̲𝐹̲𝐺̲𝐻̲𝐼̲¢.<(+|
5x&𝐽̲𝐾̲𝐿̲𝑀̲𝑁̲𝑂̲𝑃̲𝑄̲𝑅̲!$⋆/*);¬
6x-/−/𝑆̲𝑇̲𝑈̲𝑉̲𝑊̲𝑋̲𝑌̲𝑍̲¦,%_>?
7x⋄/◊/◆∧/⋀¨`:/∶#@'="
8x∼/~abcdefghi
9xjklmnopqr
Ax~stuvwxyz∩/⋂∪/⋃[
Bx⍺/α∊/ε/∈⍳/ι⍴/ρ⍵/ω×\/∖÷]∣/│
Cx{ABCDEFGHI
Dx}JKLMNOPQR!/ǃ
Ex\STUVWXYZ
Fx0123456789 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][b]
0123456789ABCDEF
0x
1x
2x
3x
4x SP 𝐴̲𝐵̲𝐶̲𝐷̲𝐸̲𝐹̲𝐺̲𝐻̲𝐼̲
5x𝐽̲𝐾̲𝐿̲𝑀̲𝑁̲𝑂̲𝑃̲𝑄̲𝑅̲
6x𝑆̲𝑇̲𝑈̲𝑉̲𝑊̲𝑋̲𝑌̲𝑍̲
7x◊/⋄/◆∧/⋀¨
8x∼/~│/⎥
9x█/■⌑/¤±
Ax¯/‾°∙/•∩/⋂∪/⋃[
Bx⍺/α∊/∈/ε⍳/ι⍴/ρ⍵/ω×∖/\÷]∣/│
Cx{⁺/+■/∎§
Dx}⁻/-ǃ/!
Ex[c][c][c][c]
Fx¹²³

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]
0123456789ABCDEF
0xNUL{ HT  FF  CR 
1x NL   BS 
2x} LF §
3x¹²³
4x SP 𝐴̲𝐵̲𝐶̲𝐷̲𝐸̲𝐹̲𝐺̲𝐻̲𝐼̲¢.<(+|
5x&𝐽̲𝐾̲𝐿̲𝑀̲𝑁̲𝑂̲𝑃̲𝑄̲𝑅̲!$*);¬
6x-/𝑆̲𝑇̲𝑈̲𝑉̲𝑊̲𝑋̲𝑌̲𝑍̲¦,%_>?
7x¨°`:#@'="
8xabcdefghi
9xjklmnopqr±
Ax¯~stuvwxyz[
Bx∈/∊×∖ / \÷]
Cx{ABCDEFGHI
Dx}JKLMNOPQRǃ/!
Ex\STUVWXYZ
Fx0123456789

7-bit modified ASCII

Code page 371 (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]

8-bit modified and/or extended ASCII

Code page 907

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

Code page 907[9]
0123456789ABCDEF
0x
1x§
2x SP !/ǃ"#$%&'()⋆/*+,-/−./
3x0123456789:/∶;<=>?
4x@ABCDEFGHIJKLMNO
5xPQRSTUVWXYZ[\/∖]∧/⋀_
6x`abcdefghijklmno
7xpqrstuvwxyz{∣/│}∼/~
8x𝐴̲𝐵̲𝐶̲𝐷̲𝐸̲𝐹̲𝐺̲𝐻̲𝐼̲𝐽̲𝐾̲𝐿̲𝑀̲𝑁̲𝑂̲𝑃̲
9x𝑄̲𝑅̲𝑆̲𝑇̲𝑈̲𝑉̲𝑊̲¢𝑋̲
Ax𝑌̲𝑍̲¬∪/⋃
Bx
Cx
Dx
Ex⍺/αß⍴/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]
0123456789ABCDEF
0x
1x§
2x SP !/ǃ"#$%&'()⋆/*+,-/−./
3x0123456789:/∶;<=>?
4x@ABCDEFGHIJKLMNO
5xPQRSTUVWXYZ[\/∖]∧/⋀_
6x`abcdefghijklmno
7xpqrstuvwxyz{∣/│}∼/~
8xÇüéâäàåçêëèïîìÄÅ
9xôöòûùÖÜ£
AxáíóúñѪº¿¬∪/⋃¡
Bx
Cx
Dx⋄/◊/◆
Ex⍺/αß⍴/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]
0123456789ABCDEF
0x
1x§
2x SP !/ǃ"#$%&'()⋆/*+,-/−./
3x0123456789:/∶;<=>?
4x@ABCDEFGHIJKLMNO
5xPQRSTUVWXYZ[\/∖]∧/⋀_
6x`abcdefghijklmno
7xpqrstuvwxyz{∣/│}∼/~
8xÇüéâäàåçêëèïîìÄÅ
9xôöòûùÖÜø£
AxáíóúñѪº¿¬½∪/⋃¡
Bx
Cx
Dx⋄/◊/◆¦Ì
Ex⍺/αß⍴/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 LATIN CAPITAL LETTER B WITH LINE BELOW
  • U+1E0E LATIN CAPITAL LETTER D WITH LINE BELOW
  • U+1E34 LATIN CAPITAL LETTER K WITH LINE BELOW
  • U+1E3A LATIN CAPITAL LETTER L WITH LINE BELOW
  • U+1E48 LATIN CAPITAL LETTER N WITH LINE BELOW
  • U+1E5E LATIN CAPITAL LETTER R WITH LINE BELOW
  • U+1E6E LATIN CAPITAL LETTER T WITH LINE BELOW
  • U+1E94 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

References