ALGOL 68

ALGOL 68, as the name implies, is a follow-on to the ALGOL language that was first formalized in 1960. That same year the International Federation for Information Processing (IFIP) formed and started the Working Group on ALGOL, or WG2.1. This group released an updated ALGOL 60 specification in Rome in April 1962. At a follow-up meeting in March 1964, it was agreed that the group should begin work on two follow-on standards, ALGOL X which would be a redefinition of the language with some additions, and an ALGOL Y, which would have the ability to modify its own programs in the style of the language LISP.[21]

The first meeting of the ALGOL X group was held in Princeton University in May 1965. A report of the meeting noted two broadly supported themes, the introduction of strong typing and interest in Euler's concepts of 'trees' or 'lists' for handling collections.[22]

At the second meeting in October in France, three formal proposals were presented, Niklaus Wirth's ALGOL W along with comments about record structures by C.A.R. (Tony) Hoare, a similar language by Gerhard Seegmüller, and a paper by Adriaan van Wijngaarden on "Orthogonal design and description of a formal language". The latter, written in almost indecipherable "W-Grammar", proved to be a decisive shift in the evolution of the language. The meeting closed with an agreement that van Wijngaarden would re-write the Wirth/Hoare submission using his W-Grammar.[22]

This seemingly simple task ultimately proved more difficult than expected, and the follow-up meeting had to be delayed six months. When it met in April 1966 in Kootwijk, van Wijngaarden's draft remained incomplete and Wirth and Hoare presented a version using more traditional descriptions. It was generally agreed that their paper was "the right language in the wrong formalism".[23] As these approaches were explored, it became clear there was a difference in the way parameters were described that would have real-world effects, and while Wirth and Hoare protested that further delays might become endless, the committee decided to wait for van Wijngaarden's version. Wirth then implemented their current definition as ALGOL W.[24]

At the next meeting in Warsaw in October 1966,[25] there was an initial report from the I/O Subcommittee who had met at the Oak Ridge National Laboratory and the University of Illinois but had not yet made much progress. The two proposals from the previous meeting were again explored, and this time a new debate emerged about the use of pointers; ALGOL W used them only to refer to records, while van Wijngaarden's version could point to any object. To add confusion, John McCarthy presented a new proposal for operator overloading and the ability to string together and or constructs, and Klaus Samelson wanted to allow anonymous functions. In the resulting confusion, there was some discussion of abandoning the entire effort.[24] The confusion continued through what was supposed to be the ALGOL Y meeting in Zandvoort in May 1967.[22]

A draft report was finally published in February 1968. This was met by "shock, horror and dissent",[22] mostly due to the hundreds of pages of unreadable grammar and odd terminology. Charles H. Lindsey attempted to figure out what "language was hidden inside of it",[26] a process that took six man-weeks of effort. The resulting paper, "ALGOL 68 with fewer tears", was widely circulated. At a wider information processing meeting in Zurich in May 1968, attendees complained that the language was being forced upon them and that IFIP was "the true villain of this unreasonable situation" as the meetings were mostly closed and there was no formal feedback mechanism. Wirth and Peter Naur formally resigned their authorship positions in WG2.1 at that time.[26]

The next WG2.1 meeting took place in Tirrenia in June 1968. It was supposed to discuss the release of compilers and other issues, but instead devolved into a discussion on the language. van Wijngaarden responded by saying (or threatening) that he would release only one more version of the report. By this point Naur, Hoare, and Wirth had left the effort, and several more were threatening to do so.[27] Several more meetings followed, North Berwick in August 1968, Munich in December which produced the release of the official Report in January 1969 but also resulted in a contentious Minority Report being written. Finally, at Banff, Alberta in September 1969, the project was generally considered complete and the discussion was primarily on errata and a greatly expanded Introduction to the Report.[28]

The effort took five years, burned out many of the greatest names in computer science, and on several occasions became deadlocked over issues both in the definition and the group as a whole. Hoare released a "Critique of ALGOL 68" almost immediately,[29] which has been widely referenced in many works. Wirth went on to further develop the ALGOL W concept and released this as Pascal in 1970.

The first implementation of the standard, based on the late-1968 draft Report, was introduced by the Royal Radar Establishment in the UK as ALGOL 68-R in July 1970. This was, however, a subset of the full language, and Barry Mailloux, the final editor of the Report, joked that "It is a question of morality. We have a Bible and you are sinning!"[30] This version nevertheless became very popular on the ICL machines, and became a widely-used language in military coding, especially in the UK.[31]

Among the changes in 68-R was the requirement for all variables to be declared before their first use. This had a significant advantage that it allowed the compiler to be one-pass, as space for the variables in the activation record was set aside before it was used. However, this change also had the side-effect of demanding the procs be declared twice, once as a declaration of the types, and then again as the body of code. Another change was to eliminate the assumed void mode, an expression that returns no value (named a statement in other languages) and demanding the word void be added where it would have been assumed. Further, 68-R eliminated the explicit parallel processing commands based on par.[30]

The first full implementation of the language was introduced in 1974 by CDC Netherlands for the Control Data mainframe series. This saw limited use, mostly teaching in Germany and the Netherlands.[31]

A version similar to 68-R was introduced from Carnegie Mellon University in 1976 as 68S, and was again a one-pass compiler based on various simplifications of the original and intended for use on smaller machines like the DEC PDP-11. It too was used mostly for teaching purposes.[31]

A version for IBM mainframes did not become available until 1978, when one was released from Cambridge University. This was "nearly complete". Lindsey released a version for small machines including the IBM PC in 1984.[31]

Two open source Algol 68 implementations are known:[32]

• a68g, GPLv3, written by Marcel van der Veer;
• algol68toc, an open-source software port of ALGOL 68RS.

• "A Shorter History of Algol 68"
• ALGOL 68 – 3rd generation ALGOL

• March 1968: Draft Report on the Algorithmic Language ALGOL 68[38] – Edited by: Adriaan van Wijngaarden, Barry J. Mailloux, John Peck and Cornelis H. A. Koster.

"Van Wijngaarden once characterized the four authors, somewhat tongue-in-cheek, as: Koster: transputter, Peck: syntaxer, Mailloux: implementer, Van Wijngaarden: party ideologist." – Koster.

• October 1968: Penultimate Draft Report on the Algorithmic Language ALGOL 68 – Chapters 1-9[39] Chapters 10-12[40] – Edited by: A. van Wijngaarden, B.J. Mailloux, J. E. L. Peck and C. H. A. Koster.
• December 1968: Report on the Algorithmic Language ALGOL 68 – Offprint from Numerische Mathematik, 14, 79-218 (1969); Springer-Verlag.[41] – Edited by: A. van Wijngaarden, B. J. Mailloux, J. E. L. Peck and C. H. A. Koster.
• March 1970: Minority report, ALGOL Bulletin AB31.1.1 - signed by Edsger Dijkstra, Fraser Duncan, Jan Garwick, Tony Hoare, Brian Randell, Gerhard Seegmüller, Wlad Turski, and Mike Woodger.
• September 1973: Revised Report on the Algorithmic Language Algol 68 – Springer-Verlag 1976[42] – Edited by: A. van Wijngaarden, B. Mailloux, J. Peck, K. Koster, M. Sintzoff, C. H. Lindsey, Lambert Meertens and Richard G. Fisker.
• other WG 2.1 members active in ALGOL 68 design:[18] Friedrich L. Bauer • Hans Bekic • Gerhard Goos • Peter Zilahy Ingerman • Peter Landin • Charles H. Lindsey • John McCarthy • Jack Merner • Peter Naur • Manfred Paul • Willem van der Poel • Doug Ross • Klaus Samelson • Michel Sintzoff • Niklaus Wirth • Nobuo Yoneda.

1968: On 20 December 1968, the "Final Report" (MR 101) was adopted by the Working Group, then subsequently approved by the General Assembly of UNESCO's IFIP for publication. Translations of the standard were made for Russian, German, French and Bulgarian, and then later Japanese and Chinese.[43] The standard was also made available in Braille.

1984: TC97 considered ALGOL 68 for standardisation as "New Work Item" TC97/N1642 . West Germany, Belgium, Netherlands, USSR and Czechoslovakia willing to participate in preparing the standard but the USSR and Czechoslovakia "were not the right kinds of member of the right ISO committees" and Algol 68's ISO standardisation stalled.

1988: Subsequently ALGOL 68 became one of the GOST standards in Russia.

• GOST 27974-88 Programming language ALGOL 68 – Язык программирования АЛГОЛ 68[44]
• GOST 27975-88 Programming language ALGOL 68 extended – Язык программирования АЛГОЛ 68 расширенный[45]

The standard language contains about sixty reserved words, typically bolded in print, and some with "brief symbol" equivalents:

mode, op, prio, proc,
flex, heap, loc, long, ref, short,
bits, bool, bytes, char, compl, int, real, sema, string, void,
channel, file, format, struct, union,
at "@", eitherr0, is ":=:", isnt  is notr0 ":/=:" ":≠:", of "→"r0, true, false, empty, nil "○", skip "~",
co "¢", comment "¢", pr, pragmat,
case ~ in ~ ouse ~ in ~ out ~ esac "( ~ | ~ |: ~ | ~ | ~ )",
for ~ from ~ to ~ by ~ while ~ do ~ od,
if ~ then ~ elif ~ then ~ else ~ fi "( ~ | ~ |: ~ | ~ | ~ )",
par begin ~ end "( ~ )", go to, goto, exit "."r0.

The basic language construct is the unit. A unit may be a formula, an enclosed clause, a routine text or one of several technically needed constructs (assignation, jump, skip, nihil). The technical term enclosed clause unifies some of the inherently bracketing constructs known as block, do statement, switch statement in other contemporary languages. When keywords are used, generally the reversed character sequence of the introducing keyword is used for terminating the enclosure, e.g. ( if ~ then ~ else ~ fi, case ~ in ~ out ~ esac, for ~ while ~ do ~ od ). This Guarded Command syntax was reused by Stephen Bourne in the common Unix Bourne shell. An expression may also yield a multiple value, which is constructed from other values by a collateral clause. This construct just looks like the parameter pack of a procedure call.

The basic data types (called modes in Algol 68 parlance) are real, int, compl (complex number), bool, char, bits and bytes. For example:

int n = 2;
co n is fixed as a constant of 2. co
int m := 3;
co m is a newly created local variable whose value is initially set to 3. co
co    This is short for ref int m = loc int := 3; co
real avogadro = 6.0221415⏨23; co Avogadro's number co
long long real long long pi = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510;
compl square root of minus one = 0 ⊥ 1;

However, the declaration real x; is just syntactic sugar for ref real x = loc real;. That is, x is really the constant identifier for a reference to a newly generated local real variable.

Furthermore, instead of defining both float and double, or int and long and short, etc., ALGOL 68 provides modifiers, so that the presently common double would be written as long real or long long real instead, for example. The prelude constants max real and min long int are provided to adapt programs to different implementations.

All variables need to be declared, but declaration does not have to precede the first use.

primitive-declarer: int, real, compl, complex^G, bool, char, string, bits, bytes, format, file, pipe^G, channel, sema

• bits – a "packed vector" of bool.
• bytes – a "packed vector" of char.
• string – a flexible array of char.
• sema – a semaphore which can be initialised with the operator level.

Complex types can be created from simpler ones using various type constructors:

• ref mode – a reference to a value of type mode, similar to & in C/C++ and ref in Pascal
• struct – used to build structures, like struct in C/C++ and record in Pascal
• union – used to build unions, like in C/C++ and Pascal
• proc – used to specify procedures, like functions in C/C++ and procedures/functions in Pascal

For some examples, see Comparison of ALGOL 68 and C++.

Other declaration symbols include: flex, heap, loc, ref, long, short, event^S

• flex – declare the array to be flexible, i.e. it can grow in length on demand.
• heap – allocate variable some free space from the global heap.
• loc – allocate variable some free space of the local stack.
• long – declare an int, real or compl to be of a longer size.
• short – declare an int, real or compl to be of a shorter size.

A name for a mode (type) can be declared using a mode declaration, which is similar to typedef in C/C++ and type in Pascal:

 int max=99;
 mode newmode = [0:9][0:max]struct (
     long real a, b, c, short int i, j, k, ref real r
 );

This is similar to the following C code:

  const int max=99;
  typedef struct {
      double a, b, c; short i, j, k; float *r;
  } newmode[9+1][max+1];

For ALGOL 68, only the newmode mode-indication appears to the left of the equals symbol, and most notably the construction is made, and can be read, from left to right without regard to priorities. Also, the lower bound of Algol 68 arrays is one by default, but can be any integer from -max int to max int.

Mode declarations allow types to be recursive: defined directly or indirectly in terms of themselves. This is subject to some restrictions – for instance, these declarations are illegal:

 mode A = ref A
 mode A = struct (A a, B b)
 mode A = proc (A a) A

while these are valid:

 mode A = struct (ref A a, B b)
 mode A = proc (ref A a) ref A

The coercions produce a coercee from a coercend according to three criteria: the a priori mode of the coercend before the application of any coercion, the a posteriori mode of the coercee required after those coercions, and the syntactic position or "sort" of the coercee. Coercions may be cascaded.

The six possible coercions are termed deproceduring, dereferencing, uniting, widening, rowing, and voiding. Each coercion, except for uniting, prescribes a corresponding dynamic effect on the associated values. Hence, many primitive actions can be programmed implicitly by coercions.

Context strength – allowed coercions:

• soft – deproceduring
• weak – dereferencing or deproceduring, yielding a name
• meek – dereferencing or deproceduring
• firm – meek, followed by uniting
• strong – firm, followed by widening, rowing or voiding

ALGOL 68 has a hierarchy of contexts which determine the kind of coercions available at a particular point in the program. These contexts are:

INT to LONG INT
INT to REAL
REAL to COMPL
BITS to []BOOL
BYTES to STRING

INT to [1]INT
REAL to [1]REAL

REF REF BOOL to BOOL
REF REF REF INT to INT

REF BOOL to REF BOOL
REF REF INT to REF INT
REF REF REF REAL to REF REAL
REF REF REF REF STRUCT to REF STRUCT

For more details about Primaries, Secondaries, Tertiary & Quaternaries refer to Operator precedence.

Pragmats are directives in the program, typically hints to the compiler; in newer languages these are called "pragmas" (no 't'). e.g.

pragmat heap=32 pragmat
pr heap=32 pr

Comments can be inserted in a variety of ways:

¢ The original way of adding your 2 cents worth to a program ¢
comment "bold" comment comment
co Style i comment co
# Style ii comment #
£ This is a hash/pound comment for a UK keyboard £

Normally, comments cannot be nested in ALGOL 68. This restriction can be circumvented by using different comment delimiters (e.g. use hash only for temporary code deletions).

ALGOL 68 being an expression-oriented programming language, the value returned by an assignment statement is a reference to the destination. Thus, the following is valid ALGOL 68 code:

 real half pi, one pi; one pi := 2 * ( half pi := 2 * arc tan(1) )

This notion is present in C and Perl, among others. Note that as in earlier languages such as Algol 60 and FORTRAN, spaces are allowed in identifiers, so that half pi is a single identifier (thus avoiding the underscores versus camel case versus all lower-case issues).

As another example, to express the mathematical idea of a sum of f(i) from i=1 to n, the following ALGOL 68 integer expression suffices:

 (int sum := 0; for i to n do sum +:= f(i) od; sum)

Note that, being an integer expression, the former block of code can be used in any context where an integer value can be used. A block of code returns the value of the last expression it evaluated; this idea is present in Lisp, among other languages.

Compound statements are all terminated by distinctive closing brackets:

• if choice clauses:

 if condition then statements [ else statements ] fi
 "brief" form:  ( condition | statements | statements )

 if condition1 then statements elif condition2 then statements [ else statements ] fi
 "brief" form:  ( condition1 | statements |: condition2 | statements | statements )

This scheme not only avoids the dangling else problem but also avoids having to use begin and end in embedded statement sequences.

• case choice clauses:

 case switch in statements, statements,... [ out statements ] esac
 "brief" form:  ( switch | statements,statements,... | statements )

 case switch1 in statements, statements,... ouse switch2 in statements, statements,... [ out statements ] esac
 "brief" form of case statement:  ( switch1 | statements,statements,... |: switch2 | statements,statements,... | statements )

Choice clause example with Brief symbols:

proc days in month = (int year, month)int:
  (month|
    31,
    (year÷×4=0 ∧ year÷×100≠0  ∨  year÷×400=0 | 29 | 28 ),
    31, 30, 31, 30, 31, 31, 30, 31, 30, 31
  );

Choice clause example with Bold symbols:

proc days in month = (int year, month)int:
  case month in
    31,
    if year mod 4 eq 0 and year mod 100 ne 0  or  year mod 400 eq 0 then 29 else 28 fi,
    31, 30, 31, 30, 31, 31, 30, 31, 30, 31
  esac;

Choice clause example mixing Bold and Brief symbols:

proc days in month = (int year, month)int:
  case month in
¢Jan¢ 31,
¢Feb¢ ( year mod 4 = 0 and year mod 100 ≠ 0  or  year mod 400 = 0 | 29 | 28 ),
¢Mar¢ 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 ¢ to Dec. ¢
  esac;

Algol68 allowed the switch to be of either type int or (uniquely) union. The latter allows the enforcing strong typing onto union variables. c.f. union below for example.

• do loop clause:

 [ for index ] [ from first ] [ by increment ] [ to last ] [ while condition ] do statements od
 The minimum form of a "loop clause" is thus: do statements od

This was considered the "universal" loop, the full syntax is:

for i from 1 by -22 to -333 while i×i≠4444 do ~ od

The construct have several unusual aspects:

• only the do ~ od portion was compulsory, in which case the loop will iterate indefinitely.
• thus the clause to 100 do ~ od, will iterate only 100 times.
• the while "syntactic element" allowed a programmer to break from a for loop early. e.g.

int sum sq:=0;
for i
while
  print(("So far:",i,newline));
  sum sq≠70↑2
do
  sum sq+:=i↑2
od

Subsequent "extensions" to the standard Algol68 allowed the to syntactic element to be replaced with upto and downto to achieve a small optimisation. The same compilers also incorporated:

• until^(C) – for late loop termination.
• foreach^(S) – for working on arrays in parallel.

Further examples can be found in the code examples below.

ALGOL 68 supports arrays with any number of dimensions, and it allows for the slicing of whole or partial rows or columns.

 mode vector = [1:3]    real;   # vector mode declaration (typedef)  #
 mode matrix = [1:3,1:3]real;   # matrix mode declaration (typedef)  #
 vector v1  := (1,2,3);         # array variable initially (1,2,3)   #
 []real v2   = (4,5,6);         # constant array, type equivalent to vector, bounds are implied  #
 op + = (vector a,b) vector:    # binary operator definition         #
   (vector out; for i from ⌊a to ⌈a do out[i] := a[i]+b[i] od; out);
 matrix m := (v1, v2, v1+v2);
 print ((m[,2:]));              # a slice of the 2nd and 3rd columns #

Matrices can be sliced either way, e.g.:

 ref vector row = m[2,];  # define a ref (pointer) to the 2nd row #
 ref vector col = m[,2];  # define a ref (pointer) to the 2nd column #

ALGOL 68 supports multiple field structures (struct) and united modes. Reference variables may point to any mode including array slices and structure fields.

For an example of all this, here is the traditional linked list declaration:

 mode node = union (void, real, int, compl, string),
      list = struct (node val, ref list next);

Usage example for union case of node:

 node n := "1234";
 real r; int i; compl c; string s
 case r,i,c,s::=n in
   print(("real:", r)),
   print(("int:", i)),
   print(("compl:", c)),
   print(("string:", s))
   out print(("?:", n))
 esac

 node n := "1234";
 # or n := EMPTY; #
  case n in
   (void):     print(("void:", "EMPTY")),
   (real r):   print(("real:", r)),
   (int i):    print(("int:", i)),
   (compl c):  print(("compl:", c)),
   (string s): print(("string:", s))
   out         print(("?:", n))
 esac

Procedure (proc) declarations require type specifications for both the parameters and the result (void if none):

 proc max of real = (real a, b) real:
    if a > b then a else b fi;

or, using the "brief" form of the conditional statement:

 proc max of real = (real a, b) real: (a>b | a | b);

The return value of a proc is the value of the last expression evaluated in the procedure. References to procedures (ref proc) are also permitted. Call-by-reference parameters are provided by specifying references (such as ref real) in the formal argument list. The following example defines a procedure that applies a function (specified as a parameter) to each element of an array:

 proc apply = (ref [] real a, proc (real) real f):
  
    for i from lwb a to upb a do a[i] := f(a[i]) od

This simplicity of code was unachievable in ALGOL 68's predecessor ALGOL 60.

The programmer may define new operators and both those and the pre-defined ones may be overloaded and their priorities may be changed by the coder. The following example defines operator max with both dyadic and monadic versions (scanning across the elements of an array).

 prio max = 9;
  
 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 );
  
 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)

These are technically not operators, rather they are considered "units associated with names"

Note: Tertiaries include names nil and ○.

These are technically not operators, rather they are considered "units associated with names"

Note: Quaternaries include names skip and ~.

":=:" (alternatively "is") tests if two pointers are equal; ":/=:" (alternatively "isnt") tests if they are unequal.

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

ref int ip, jp

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

ip = jp

will dereference both pointers down to values of type int, and compare those, since the "=" operator is defined for int, but not ref int. It is not legal to define "=" for operands of type ref int and 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 ref int and that version of the operator called? Or should they be dereferenced further to int and that version used instead? Therefore the following expression can never be made legal:

ip = nil

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:

ip :=: jp

ip :=: nil

while legal, will probably not do what might be expected. They will always return false, because they are comparing the actual addresses of the variables ip and jp, rather than what they point to. To achieve the right effect, one would have to write

ip :=: ref int(jp)

ip :=: ref int(nil)

IBM 2741 keyboard with APL symbols

Most of Algol's "special" characters (⊂, ≡, ␣, ×, ÷, ≤, ≥, ≠, ¬, ⊃, ≡, ∨, ∧, →, ↓, ↑, ⌊, ⌈, ⎩, ⎧, ⊥, ⏨, ¢, ○ and □) can be found on the IBM 2741 keyboard with the 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 fonts.

Transput is the term used to refer to ALGOL 68's input and output facilities. It includes pre-defined procedures for unformatted, formatted and binary transput. Files and other transput devices are handled in a consistent and machine-independent manner. The following example prints out some unformatted output to the standard output device:

  print ((newpage, "Title", newline, "Value of i is ",
    i, "and x[i] is ", x[i], newline))

Note the predefined procedures newpage and newline passed as arguments.

The transput is considered to be of books, channels and files:

• Books are made up of pages, lines and characters, and may be backed up by files.
  • A specific book can be located by name with a call to match.
• channels correspond to physical devices. e.g. card punches and printers.
  • Three standard channels are distinguished: stand in channel, stand out channel, stand back channel.
• A file is a means of communicating between a program and a book that has been opened via some channel.
  • The mood of a file may be read, write, char, bin, and opened.
  • transput procedures include: establish, create, open, associate, lock, close, scratch.
  • position enquires: char number, line number, page number.
  • layout routines include:
    • space, backspace, newline, newpage.
    • get good line, get good page, get good book, and proc set=(ref file f, int page,line,char)void:
  • A file has event routines. e.g. on logical file end, on physical file end, on page end, on line end, on format end, on value error, on char error.

"Formatted transput" in ALGOL 68's transput has its own syntax and patterns (functions), with formats embedded between two $ characters.[46]

Examples:

 printf (($2l"The sum is:"x, g(0)$, m + n)); ¢ prints the same as: ¢
 print ((new line, new line, "The sum is:", space, whole (m + n, 0))

ALGOL 68 supports programming of parallel processing. Using the keyword par, a collateral clause is converted to a parallel clause, where the synchronisation of actions is controlled using semaphores. In A68G the parallel actions are mapped to threads when available on the hosting operating system. In A68S a different paradigm of parallel processing was implemented (see below).

int initial foot width = 5;
mode foot = struct(
   string name,
   sema width,
   bits toe ¢ packed vector of BOOL ¢
);
 
foot left foot:= foot("Left", level initial foot width, 2r11111),
     right foot:= foot("Right", level initial foot width, 2r11111);
 
¢ 10 round clip in a 1968 Colt Python .357 Magnum ¢
sema rounds = level 10;
 
¢ the Magnum needs more barrels to take full advantage of parallelism ¢
sema acquire target = level 1;
 
prio ∧:= = 1;
op ∧:= = (ref bits lhs, bits rhs)ref bits: lhs := lhs ∧ rhs;
 
proc shoot = (ref foot foot)void: (
  ↓acquire target;
  ↓rounds;
  print("BANG! ");
  ↓width → foot;
  toe → foot ∧:= ¬(bin 1 shl level width → foot);
  printf(($g": Ouch!! – "5(g)l$, name → foot, []bool(toe → foot)[bits width – initial foot width + 1:]));
  ↑acquire target
);
 
¢ do shooting in parallel to cater for someone hoping to stand on just one foot ¢
par (
  for toe to initial foot width do
    shoot (left foot)
  od, ¢ <= a comma is required ¢
  for toe to initial foot width do
    shoot(right foot)
  od
)

This sample program implements the Sieve of Eratosthenes to find all the prime numbers that are less than 100. nil is the ALGOL 68 analogue of the null pointer in other languages. The notation x of y accesses a member x of a struct y.

begin # Algol-68 prime number sieve, functional style #
  
  proc error = (string s) void:
     (print(( newline, " error: ", s, newline)); goto stop);
  proc one to = (int n) list:
     (proc f = (int m,n) list: (m>n | nil | cons(m, f(m+1,n))); f(1,n));
  
  mode list = ref node;
  mode node = struct (int h, list t);
  proc cons = (int n, list l) list: heap node := (n,l);
  proc hd   = (list l) int: ( l is nil | error("hd nil"); skip | h of l );
  proc tl   = (list l) list: ( l is nil | error("tl nil"); skip | t of l );
  proc show = (list l) void: ( l isnt nil | print((" ",whole(hd(l),0))); show(tl(l)));
  
  proc filter = (proc (int) bool p, list l) list:
     if l is nil then nil
     elif p(hd(l)) then cons(hd(l), filter(p,tl(l)))
     else filter(p, tl(l))
     fi;
  
  proc sieve = (list l) list:
     if l is nil then nil
     else
        proc not multiple = (int n) bool: n mod hd(l) ≠ 0;
        cons(hd(l), sieve( filter( not multiple, tl(l) )))
     fi;
  
  proc primes = (int n) list: sieve( tl( one to(n) ));
  
  show( primes(100) )
end

• Cambridge CAP computer – All procedures constituting the operating system were written in ALGOL 68C, although several other closely associated protected procedures, such as a paginator, are written in BCPL.[47]
• Eldon 3 – Developed at Leeds University for the ICL 1900 was written in ALGOL 68-R.[48]
• Flex machine – The hardware was custom and microprogrammable, with an operating system, (modular) compiler, editor, garbage collector and filing system all written in ALGOL 68RS. The command shell Curt[49] was designed to access typed data similar to Algol-68 modes.
• VME – S3 was the implementation language of the operating system VME. S3 was based on ALGOL 68 but with data types and operators aligned to those offered by the ICL 2900 Series.

Note: The Soviet Era computers Эльбрус-1 (Elbrus-1) and Эльбрус-2 were created using high-level language Эль-76 (AL-76), rather than the traditional assembly. Эль-76 resembles Algol-68, The main difference is the dynamic binding types in Эль-76 supported at the hardware level. Эль-76 is used for application, job control, system programming.[50]

Both ALGOL 68C and ALGOL 68-R are written in ALGOL 68, effectively making ALGOL 68 an application of itself. Other applications include:

• ELLA – a hardware description language and support toolset. Developed by the Royal Signals and Radar Establishment during the 1980s and 1990s.
• RAF Strike Command System – "... 400K of error-free ALGOL 68-RT code was produced with three man-years of work. ..."[51]

• NAG Numerical Libraries – a software library of numerical analysis routines. Supplied in ALGOL 68 during the 1980s.
• TORRIX – a programming system for operations on vectors and matrices over arbitrary fields and of variable size by S. G. van der Meulen and M. Veldhorst.[52]

¢ underline or 
   bold typeface ¢
 '''mode''' '''xint''' = '''int''';
 '''xint''' sum sq:=0;
 '''for''' i '''while'''
   sum sq≠70×70
 '''do'''
   sum sq+:=i↑2
 '''od'''

'pr' quote 'pr'
'mode' 'xint' = 'int';
'xint' sum sq:=0;
'for' i 'while'
  sum sq≠70×70
'do'
  sum sq+:=i↑2
'od'

.PR UPPER .PR
MODE XINT = INT;
XINT sum sq:=0;
FOR i WHILE
  sum sq/=70*70
DO
  sum sq+:=i**2
OD

.PR POINT .PR
.MODE .XINT = .INT;
.XINT SUM SQ:=0;
.FOR I .WHILE
  SUM SQ .NE 70*70
.DO
  SUM SQ .PLUSAB I .UP 2
.OD

.PR RES .PR
mode .xint = int;
.xint sum sq:=0;
for i while
  sum sq≠70×70
do
  sum sq+:=i↑2
od

ALGOL 68 allows for every natural language to define its own set of keywords Algol-68. As a result, programmers are able to write programs using keywords from their native language. Below is an example of a simple procedure that calculates "the day following", the code is in two languages: English and German.

 # Next day date - English variant #
 mode date = struct(int day, string month, int year);
 proc the day following = (date x) date:
      if day of  x < length of month (month of x, year of x)
      then (day of x + 1, month of x, year of x)
      elif month of x = "December"
      then (1, "January", year of x + 1)
      else (1, successor of month (month of x), year of x)
      fi;

 # Nachfolgetag - Deutsche Variante #
 menge datum = tupel(ganz tag, wort monat, ganz jahr);
 funktion naechster tag nach = (datum x) datum:
          wenn tag von x < monatslaenge(monat von x, jahr von x)
          dann (tag von x + 1, monat von x, jahr von x)
          wennaber monat von x = "Dezember"
          dann (1, "Januar", jahr von x + 1)
          ansonsten (1, nachfolgemonat(monat von x), jahr von x)
          endewenn;

Russian/Soviet example: In English Algol68's case statement reads case ~ in ~ out ~ esac, in Cyrillic this reads выб ~ в ~ либо ~ быв.

The original language (As per the "Final Report"^r0) differs in syntax of the mode cast, and it had the feature of proceduring, i.e. coercing the value of a term into a procedure which evaluates the term. Proceduring would be intended to make evaluations lazy. The most useful application could have been the short-circuited evaluation of boolean operators. In:

op andf = (bool a,proc bool b)bool:(a | b | false);
op orf = (bool a,proc bool b)bool:(a | true | b);

b is only evaluated if a is true.

As defined in ALGOL 68, it did not work as expected, for example in the code:

if false andf co proc bool: co ( print ("Should not be executed"); true)
then ...

against the programmers naïve expectations the print would be executed as it is only the value of the elaborated enclosed-clause after andf that was procedured. Textual insertion of the commented-out proc bool: makes it work.

Some implementations emulate the expected behaviour for this special case by extension of the language.

Before revision, the programmer could decide to have the arguments of a procedure evaluated serially instead of collaterally by using semicolons instead of commas (gommas).

For example in:

proc test = (real a; real b) :...
...
test (x plus 1, x);

The first argument to test is guaranteed to be evaluated before the second, but in the usual:

proc test = (real a, b) :...
...
test (x plus 1, x);

then the compiler could evaluate the arguments in whatever order it felt like.

After the revision of the report, some extensions to the language have been proposed to widen the applicability:

• partial parametrisation (aka Currying): creation of functions (with fewer parameters) by specification of some, but not all parameters for a call, e.g. a function logarithm of two parameters, base and argument, could be specialised to natural, binary or decadic log,
• module extension: for support of external linkage, two mechanisms were proposed, bottom-up definition modules, a more powerful version of the facilities from ALGOL 68-R and top-down holes, similar to the ENVIRON and USING clauses from ALGOL 68C[55]
• mode parameters: for implementation of limited parametrical polymorphism (most operations on data structures like lists, trees or other data containers can be specified without touching the pay load).

So far, only partial parametrisation has been implemented, in Algol 68 Genie.

The S3 language that was used to write the ICL VME operating system and much other system software on the ICL 2900 Series was a direct derivative of Algol 68. However, it omitted many of the more complex features, and replaced the basic modes with a set of data types that mapped directly to the 2900 Series hardware architecture.

ALGOL 68R^(R) from RRE was the first ALGOL 68 subset implementation, running on the ICL 1900. Based on the original language, the main subset restrictions were definition before use and no parallel processing. This compiler was popular in UK universities in the 1970s, where many computer science students learnt ALGOL 68 as their first programming language; the compiler was renowned for good error messages.

ALGOL 68RS^(RS) from RSRE was a portable compiler system written in ALGOL 68RS (bootstrapped from ALGOL 68R), and implemented on a variety of systems including the ICL 2900/Series 39, Multics and DEC VAX/VMS. The language was based on the Revised Report, but with similar subset restrictions to ALGOL 68R. This compiler survives in the form of an Algol68-to-C compiler.

In ALGOL 68S^(S) from Carnegie Mellon University the power of parallel processing was improved by adding an orthogonal extension, eventing. Any variable declaration containing keyword event made assignments to this variable eligible for parallel evaluation, i.e. the right hand side was made into a procedure which was moved to one of the processors of the C.mmp multiprocessor system. Accesses to such variables were delayed after termination of the assignment.

Cambridge ALGOL 68C^(C) was a portable compiler that implemented a subset of ALGOL 68, restricting operator definitions and omitting garbage collection, flexible rows and formatted transput.

Algol 68 Genie^(G) by M. van der Veer is an ALGOL 68 implementation for today's computers and operating systems.

"Despite good intentions, a programmer may violate portability by inadvertently employing a local extension. To guard against this, each implementation should provide a PORTCHECK pragmat option. While this option is in force, the compiler prints a message for each construct that it recognizes as violating some portability constraint."[62]