Editing ALGOL 68 (section)

===op: Operators===
The programmer may define new '''[[Operator (programming)|operators]]''' and ''both'' those and the pre-defined ones may be [[overloading (programming)|overloaded]] and their priorities may be changed by the coder. The following example defines operator <code>'''MAX'''</code> with both dyadic and monadic versions (scanning across the elements of an array).

  '''PRIO''' '''MAX''' = 9;
  &nbsp;
  '''OP''' '''MAX''' = ('''INT''' a,b) '''INT''': ( a>b | a | b );
  '''OP''' '''MAX''' = ('''REAL''' a,b) '''REAL''': ( a>b | a | b );
  '''OP''' '''MAX''' = ('''COMPL''' a,b) '''COMPL''': ( '''ABS''' a > '''ABS''' b | a | b );
  &nbsp;
  '''OP''' '''MAX''' = ([]'''REAL''' a) '''REAL''':
     ('''REAL''' out := a['''LWB''' a];
      '''FOR''' i '''FROM''' '''LWB''' a + 1 '''TO''' '''UPB''' a '''DO''' ( a[i]>out | out:=a[i] ) '''OD''';
      out)

====Array, Procedure, Dereference and coercion operations====
{|class="wikitable"
|-
! style="background:#ccc;"|'''PRIO'''rity
! style="background:#ccc;"| Operation <sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]</sup>
! style="background:#ccc;"|+Algol68<sup>G</sup>
|-
|ALIGN=CENTER| Effectively&nbsp;12<br />(Primary) || dereferencing, deproceduring(~,~), subscripting[~], rowing[~,], slicing[~:~], size denotations '''LONG''' & '''SHORT'''
 || proceduring
|ALIGN=CENTER|currying(~,,,), '''DIAG''', '''TRNSP''', '''ROW''', '''COL'''
|-
|ALIGN=CENTER| Effectively&nbsp;11<br />(Secondary) || '''OF''' (selection), '''LOC''' & '''HEAP''' (generators)
 || → (selection)
 || '''NEW''' (generators)
|}
These are technically not operators, rather they are considered "[https://web.archive.org/web/20130101062456/http://jmvdveer.home.xs4all.nl/report.html#52 units associated with names]"
<!-- '''DIAG''', '''TRNSP''', '''ROW''', '''COL''' as per S. G. van der Meulen, M. Veldhorst. TORRIX – A programming language for opera-
tions on vectors and matrices over arbitrary fields and of variable size. Rijksuniver-
siteit Utrecht [1977]. -->

====Monadic operators====
{|class="wikitable"
|-
! style="background:#ccc;"|'''PRIO'''rity<br />(Tertiary)
! style="background:#ccc;"|Algol68 "Worthy characters{{ref|worthy}}"<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>C,G</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]</sup>
|-
|ALIGN=CENTER| 10 || '''NOT''' ~, '''UP''', '''DOWN''', '''LWB''', '''UPB''',
-, '''ABS''', '''ARG''', '''BIN''', '''ENTIER''', '''LENG''', '''LEVEL''', '''ODD''', '''REPR''', '''ROUND''', '''SHORTEN'''
| ¬, ↑, ↓, ⌊, ⌈
| '''NORM''', '''TRACE''', '''T''', '''DET''', '''INV'''
| '''LWS''', '''UPS''', ⎩, ⎧, '''BTB''', '''CTB'''
|}
<!-- '''NORM''', '''TRACE''', '''T''', '''DET''', '''INV''' as per S. G. van der Meulen, M. Veldhorst. TORRIX – A programming language for operations on vectors and matrices over arbitrary fields and of variable size. Rijksuniver-siteit Utrecht [1977]. -->

====Dyadic operators with associated priorities====
{|class="wikitable"
|-
! style="background:#ccc;"|'''PRIO'''rity<br />(Tertiary)
! style="background:#ccc;"|Algol68 "Worthy characters"<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>C,G</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]</sup>
|- style="font-family:monospace"
|ALIGN=CENTER|9 || +*, '''I''' || +×, ⊥ ||  || !
|- style="font-family:monospace"
|ALIGN=CENTER|8 || '''SHL''', '''SHR''', **,  '''UP''', '''DOWN''', '''LWB''', '''UPB''' || ↑, ↓, ⌊, ⌈ ||  || ××, ^, '''LWS''', '''UPS''', ⎩, ⎧
|- style="font-family:monospace"
|ALIGN=CENTER|7 || *, /,  %, '''OVER''',  %*, '''MOD''', '''ELEM''' || ×, ÷, ÷×, ÷*, %×, □ ||  || ÷:
|- style="font-family:monospace"
|ALIGN=CENTER|6 || -, + ||  ||  ||
|- style="font-family:monospace"
|ALIGN=CENTER|5 || <, '''LT''', <=, '''LE''',  >=, '''GE''', >, '''GT''' || ≤, ≥ ||  ||
|- style="font-family:monospace"
|ALIGN=CENTER|4 || '''EQ''' =, '''NE''' ~= /= || ≠, ¬= ||  ||
|- style="font-family:monospace"
|ALIGN=CENTER|3 || &, '''AND''' || ∧ ||  || /\
|- style="font-family:monospace"
|ALIGN=CENTER|2 || '''OR''' || ∨ ||  || \/
|- style="font-family:monospace"
|ALIGN=CENTER|1 || '''MINUSAB''', '''PLUSAB''', '''TIMESAB''', '''DIVAB''', '''OVERAB''', '''MODAB''', '''PLUSTO''',
-:=, +:=, *:=, /:=, %:=, %*:=, +=:
 || ×:=, ÷:=, ÷×:=,  ÷*:=,  %×:= ||  || '''MINUS''', '''PLUS''', '''DIV''', '''OVERB''', '''MODB''', ÷::=, '''PRUS'''
|}
Specific details:
* Tertiaries include names '''NIL''' and ○.  
* '''LWS''': In Algol68<sup>[[#The language of the unrevised report|r0]]</sup> the operators '''LWS''' and ⎩ ... both return '''TRUE''' if the ''lower state'' of the dimension of an array is fixed.
* The '''UPS''' and ⎧ operators are similar on the ''upper state''.
* The '''LWB''' and '''UPB''' operators are automatically available on '''UNION'''s of different orders (and '''MODE'''s) of arrays. eg. '''UPB''' of '''{{code|union([]int, [,]real, flex[,,,]char)}}'''

====Assignation and identity relations, etc.====
These are technically not operators, rather they are considered "[https://web.archive.org/web/20130101062456/http://jmvdveer.home.xs4all.nl/report.html#052 units associated with names]"
{|class="wikitable"
|-
! style="background:#ccc;"|'''PRIO'''rity<br />(Quaternaries)
! style="background:#ccc;"|Algol68 "Worthy characters"<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]&[[#Revisions|r1]]</sup>
! style="background:#ccc;"|+Algol68<sup>C,G,R</sup>
! style="background:#ccc;"|+Algol68<sup>[[#The language of the unrevised report|r0]]</sup>
|-
|ALIGN=CENTER| Effectively 0 || {{tt|1=:=, '''IS''' :=:, '''ISNT''' :/=: :~=:, '''AT'''  @, ":", ";"}} || {{tt|1=:≠: :¬=:}} 
| {{tt|1=:=:=<sup>C</sup>, =:=<sup>R</sup>}} || {{tt|1=..=, .=, '''CT''', ::, '''CTAB''', ::=, .., '''is not''', "..", ".,"}}
|}

Note: Quaternaries include names '''SKIP''' and ~.

{{code|1=:=:}} (alternatively {{tt|1='''IS'''}}) tests if two pointers are equal; {{code|1=:/=:}} (alternatively {{tt|1='''ISNT'''}}) tests if they are unequal.

=====Why {{code|1=:=:}} and {{code|1=:/=:}} are needed=====
Consider trying to compare two pointer values, such as the following variables, declared as pointers-to-integer:

: <code>'''REF''' '''INT''' ip, jp </code>

Now consider how to decide whether these two are pointing to the same location, or whether one of them is pointing to '''NIL'''. The following expression

: <code>ip = jp </code>

will dereference both pointers down to values of type {{tt|1='''INT'''}}, and compare those, since the {{char|{{=}}}} operator is defined for {{tt|1='''INT'''}}, but not {{tt|1='''REF''' '''INT'''}}. It is ''not legal'' to define {{char|{{=}}}} for operands of type {{tt|1='''REF''' '''INT'''}} and {{tt|1='''INT'''}} at the same time, because then calls become ambiguous, due to the implicit coercions that can be applied: should the operands be left as {{tt|1='''REF''' '''INT'''}} and that version of the operator called? Or should they be dereferenced further to {{tt|1='''INT'''}} and that version used instead? Therefore the following expression can never be made legal:

: <code>ip = '''NIL''' </code>

Hence the need for separate constructs not subject to the normal coercion rules for operands to operators. But there is a gotcha. The following expressions:

: <code>ip :=: jp </code>
: <code>ip :=: '''NIL''' </code>

while legal, will probably not do what might be expected. They will always return {{tt|1='''FALSE'''}}, because they are comparing the ''actual addresses of the variables ''<code>ip</code>'' and ''<code>jp</code>'', rather than what they point to''. To achieve the right effect, one would have to write

: <code>ip :=: '''REF''' '''INT'''(jp) </code>
: <code>ip :=: '''REF''' '''INT'''('''NIL''') </code>

====Special characters====
:[[Image:APL-keybd2.svg|600px|thumb|[[IBM 2741]] keyboard with APL symbols]]
Most of Algol's "special" characters (⊂, ≡, ␣, ×, ÷, ≤, ≥, ≠, ¬, ⊃, ≡, ∨, ∧, →, ↓, ↑, ⌊, ⌈, ⎩, ⎧, ⊥, ⏨, ¢, ○ and □) can be found on the [[IBM 2741]] keyboard with the [[APL (programming language)#Hardware|APL]] "golf-ball" print head inserted; these became available in the mid-1960s while ALGOL 68 was being drafted. These characters are also part of the [[Unicode]] standard and most of them are available in several popular [[font]]s.