Unicode

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The advent of Unicode solved many problems with dealing with APL characters, however there was still some wiggle room as to which Unicode codepoint were to be used in a Unicode implementation of APL, and different implementors made different choices. This article, which documents these differences, is adapted from an original paper by Bob Smith[1] that attempted to raise awareness of these issues because the differences impede transfer of information.

The relevant document for the APL character set is the APL Character Repertoire (ACR)[2]. For whatever reasons, that document never became a standard, but it does provide some guidance, and is better than each implementor making separate choices.

Introduction

There are a surprising number of similar APL characters in Unicode and in several cases some implementors went one way, others the other way. The following table lists the characters in question, along with the way APL2, Dyalog, GNU APL, NARS2000, ngn/apl, and dzaima/APL behave. APL2000 states that Generally the default codepoint scheme for the VisualAPL product follows the IBM APL2 workstation scheme. Please edit the table if you believe there are other characters that should be included in the table, or to add another dialect.

When there are differences among APL implementations, users can become confused. They type something into one APL system, copy it to another and are greeted by a SYNTAX ERROR or the like.

The whole basis for the confusion in a lengthy thread on comp.lang.apl entitled caret vs and[3] was that in some implementations the symbol for the logical And function was U+005E only, in some implementations it was U+2227 only, and in some both characters worked. The original poster encountered some APL text from the APL Wiki that had been produced by a system that supports U+005E and copied it into a system that used U+2227 only and failed on U+005E.

When systems differ in the set of acceptable characters for the same function, it serves only to confuse the end user to the detriment of the community. The cautious APL programmer can avoid such problems by choosing symbols that work across dialects. Note that in the below table, there is exactly one universally accepted codepoint for each symbol (these have been indicated by a single "Universal" cell stretching across the row), except for And where APL2 doesn't recognise the otherwise universal U+2227. However, APL2 does not have And extended to Least Common Multiple, so it is equivalent to Times (×) which can therefore be used instead for truly portable code.

Comparison of implementations

The following characters are included have been encountered in APL code displayed somewhere on the Internet or in a PDF file. Blindly copying them into an APL session can produce an error which might well confuse the user.

APL name Glyph Codepoint Unicode name APL2 Dyalog
APL
GNU
APL
NARS
2000
ngn/
apl
dzaima/
APL
Monadic Dyadic
Star * U+002A Asterisk Universal Exponential Power
U+26AA Star operator No No Yes Yes Yes No
Minus - U+002D Hyphen-minus Universal Negate Minus
U+2212 Minus sign No No Yes Yes Yes No
Logical And ^ U+005E Circumflex accent Yes Yes Yes Yes Yes No And
U+22BD Logical And No[4] Yes Yes Yes Yes Yes
Stile | U+007C Vertical line Universal Magnitude Residue
U+2212 Divides Yes Yes Yes Yes Yes No
Tilde ~ U+007E Tilde Universal Not Without
U+223C Tilde operator No No Yes Yes No No
Alpha α U+03B1 Greek small letter Alpha No Yes Yes No No Left Argument
U+237A APL functional symbol Alpha Universal
Omega ω U+03C9 Greek small letter Omega No Yes Yes No No Right Argument
U+237A APL functional symbol Omega Universal
Epsilon [5] U+2208 Element of No No Yes Yes No No Enlist/Type Membership
U+220A Small Element of Universal
Jot U+2218 Ring operator Universal Outer product Beside/Bind
U+25E6 White bullet No No Yes Yes No No
Less than or
equal to
U+2264 Less-than or equal to Universal Less than or
equal to
U+2A7D Less than or slanted equal to No No Yes Yes No No
Greater than or
equal to
U+2265 Greater than or equal to Universal Greater than or
equal to
U+2A7E Greater than or slanted equal to No No Yes Yes No No
Logical Nor U+22BD Nor No No Yes Yes No No Nor
U+2371 APL functional symbol down caret tilde Universal
Logical Nand U+22BC Nand No No Yes Yes No No Nand
U+2372 APL functional symbol up caret tilde Universal
Diamond U+22C4 Diamond operator Universal Statement Separator
U+25C7 White Diamond No No No Yes No No
U+25CA Lozenge No No Yes Yes No No
U+2B26 Diamond No No Yes Yes No No
Quad U+2395 APL functional symbol Quad Universal Quad name
U+26AA White vertical rectangle Yes No Yes Yes No No
Circle U+25CB White circle Universal Pi Times Circular
U+26AA Medium white circle No No Yes Yes No No

Functionality

The following statements can be used to test the functionality of the symbols:

 '1',(⎕UCS 160  0  2 10),'1'   ⍝ Star
 '1',(⎕UCS 162  2 12  6),'1'   ⍝ Star
 '1',(⎕UCS 160  0  2 13),'1'   ⍝ Minus
 '1',(⎕UCS 162  2  1  2),'1'   ⍝ Minus
 '1',(⎕UCS 160  0  5 14),'1'   ⍝ And
 '1',(⎕UCS 162  2  2  7),'1'   ⍝ And
 '1',(⎕UCS 160  0  7 12),'1'   ⍝ Modulus
 '1',(⎕UCS 162  2  2  3),'1'   ⍝ Modulus
     (⎕UCS 160  0  7 14),'1'   ⍝ Tilde
     (⎕UCS 162  2  3 12),'1'   ⍝ Tilde
'1{',(⎕UCS 160  3 11  1),'}1'  ⍝ Alpha
'1{',(⎕UCS 162  3  7 10),'}1'  ⍝ Alpha
 '{',(⎕UCS 160  3 12  9),'}1'  ⍝ Omega
 '{',(⎕UCS 162  3  7  5),'}1'  ⍝ Omega
 '1',(⎕UCS 162  2  0  8),'1'   ⍝ Epsilon
 '1',(⎕UCS 162  2  0 10),'1'   ⍝ Epsilon
 '1',(⎕UCS 162  2  1  8),'.=1' ⍝ Jot
 '1',(⎕UCS 162  5 14  6),'.=1' ⍝ Jot
 '1',(⎕UCS 162  2  6  4),'1'   ⍝ Less than or equal to
 '1',(⎕UCS 162 10  7 13),'1'   ⍝ Less than or equal to
 '1',(⎕UCS 162  2  6  5),'1'   ⍝ Greater than or equal to
 '1',(⎕UCS 162 10  7 14),'1'   ⍝ Greater than or equal to
 '1',(⎕UCS 162  2 11 13),'1'   ⍝ Nor
 '1',(⎕UCS 162  3  7  1),'1'   ⍝ Nor
 '1',(⎕UCS 162  2 11 12),'1'   ⍝ Nand
 '1',(⎕UCS 162  2 12  4),'1'   ⍝ Diamond
 '1',(⎕UCS 162  5 12  7),'1'   ⍝ Diamond
 '1',(⎕UCS 162  5 12 10),'1'   ⍝ Diamond
 '1',(⎕UCS 162 11  2  6),'1'   ⍝ Diamond
     (⎕UCS 162  3  9  5),'←1'  ⍝ Quad
     (⎕UCS 162  5 10 15),'←1'  ⍝ Quad
 '1',(⎕UCS 162  5 12 11),'1'   ⍝ Circle
 '1',(⎕UCS 162  6 10 10),'1'   ⍝ Circle
 '1',(⎕UCS 162  3  7  2),'1'   ⍝ Nand

Note that the last four lines will not work on a system that doesn’t support dfns.

Atomic Vector

If the Atomic vector (⎕AV) has no room in which to include these new characters, an implementation can translate them on entry to the corresponding symbol that is in ⎕AV. NARS2000 even has a means of translating symbols on the way out via Copy (Ctrl+C in Windows) to various other APL systems that don't support the same set of principal characters NARS2000 uses for the functions in the above table.

Considerations

Unicode was a great start to enabling APL characters to be used, however in order for there to be interoperability, implementors have to agree upon which characters are functional. It doesn't matter if one's system can change the mapping of glyphs to codepoints as the vast majority of users won't change from the default behavior. Implementors therefore have to decide if it is worthwhile to support the above codepoints.

References

  1. Smith, Bob. APL Characters and Their Aliases. 14 Dec 2013–25 Dec 2019. Sudley Place Software.
  2. ISO-IEC/JTC1/SC22/WG3. N3067: APL Character Repertoire. 28 Dec 1999.
  3. comp.lang.apl. caret vs and. 28 Oct 2013–9 Dec 2013
  4. × (U+00D7) is a universally supported substitute
  5. Found by Hanspeter Moser in The Toronto Toolkit
APL glyphs [edit]
Information GlyphTyping glyphs (on Linux) ∙ UnicodeFontsMnemonics
Individual glyphs Jot () ∙ Right Shoe () ∙ Up Arrow () ∙ Zilde () ∙ High minus (¯) ∙ Dot (.)