Unicode

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 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). 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 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+22C6	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+2227	Logical And	No	Yes	Yes	Yes	Yes	Yes
Stile	|	U+007C	Vertical line	Universal						Magnitude	Residue
	∣	U+2223	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
Iota	ι	U+03B9	Greek small letter Iota	No	No	Yes	No	No	No	Left Argument
	⍳	U+2373	APL functional symbol Iota	Universal
Rho	ρ	U+03C1	Greek small letter Rho	No	No	Yes	No	No	No	Left Argument
	⍴	U+2374	APL functional symbol Rho	Universal
Omega	ω	U+03C9	Greek small letter Omega		No	Yes	Yes	No	No	Right Argument
	⍵	U+2375	APL functional symbol Omega		Universal
Epsilon	ϵ	U+03F5	Greek lunate Epsilon symbol	No	No	Yes	No	No	No	Enlist/Type	Membership
	∈	U+2208	Element of	No	No	Yes	Yes	No	No
	∊	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+25AF	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 16⊥0  0  2 10),'1'   ⍝ Star
⍎⎕← '1',(⎕UCS 16⊥2  2 12  6),'1'   ⍝ Star
⍎⎕← '1',(⎕UCS 16⊥0  0  2 13),'1'   ⍝ Minus
⍎⎕← '1',(⎕UCS 16⊥2  2  1  2),'1'   ⍝ Minus
⍎⎕← '1',(⎕UCS 16⊥0  0  5 14),'1'   ⍝ And
⍎⎕← '1',(⎕UCS 16⊥2  2  2  7),'1'   ⍝ And
⍎⎕← '1',(⎕UCS 16⊥0  0  7 12),'1'   ⍝ Modulus
⍎⎕← '1',(⎕UCS 16⊥2  2  2  3),'1'   ⍝ Modulus
⍎⎕←     (⎕UCS 16⊥0  0  7 14),'1'   ⍝ Tilde
⍎⎕←     (⎕UCS 16⊥2  2  3 12),'1'   ⍝ Tilde
⍎⎕←'1{',(⎕UCS 16⊥0  3 11  1),'}1'  ⍝ Alpha
⍎⎕←'1{',(⎕UCS 16⊥2  3  7 10),'}1'  ⍝ Alpha
⍎⎕← '{',(⎕UCS 16⊥0  3 12  9),'}1'  ⍝ Omega
⍎⎕← '{',(⎕UCS 16⊥2  3  7  5),'}1'  ⍝ Omega
⍎⎕← '1',(⎕UCS 16⊥2  2  0  8),'1'   ⍝ Epsilon
⍎⎕← '1',(⎕UCS 16⊥2  2  0 10),'1'   ⍝ Epsilon
⍎⎕← '1',(⎕UCS 16⊥2  2  1  8),'.=1' ⍝ Jot
⍎⎕← '1',(⎕UCS 16⊥2  5 14  6),'.=1' ⍝ Jot
⍎⎕← '1',(⎕UCS 16⊥2  2  6  4),'1'   ⍝ Less than or equal to
⍎⎕← '1',(⎕UCS 16⊥2 10  7 13),'1'   ⍝ Less than or equal to
⍎⎕← '1',(⎕UCS 16⊥2  2  6  5),'1'   ⍝ Greater than or equal to
⍎⎕← '1',(⎕UCS 16⊥2 10  7 14),'1'   ⍝ Greater than or equal to
⍎⎕← '1',(⎕UCS 16⊥2  2 11 13),'1'   ⍝ Nor
⍎⎕← '1',(⎕UCS 16⊥2  3  7  1),'1'   ⍝ Nor
⍎⎕← '1',(⎕UCS 16⊥2  2 11 12),'1'   ⍝ Nand
⍎⎕← '1',(⎕UCS 16⊥2  2 12  4),'1'   ⍝ Diamond
⍎⎕← '1',(⎕UCS 16⊥2  5 12  7),'1'   ⍝ Diamond
⍎⎕← '1',(⎕UCS 16⊥2  5 12 10),'1'   ⍝ Diamond
⍎⎕← '1',(⎕UCS 16⊥2 11  2  6),'1'   ⍝ Diamond
⍎⎕←     (⎕UCS 16⊥2  3  9  5),'←1'  ⍝ Quad
⍎⎕←     (⎕UCS 16⊥2  5 10 15),'←1'  ⍝ Quad
⍎⎕← '1',(⎕UCS 16⊥2  5 12 11),'1'   ⍝ Circle
⍎⎕← '1',(⎕UCS 16⊥2  6 10 10),'1'   ⍝ Circle
⍎⎕← '1',(⎕UCS 16⊥2  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.