Open Access Articles- Top Results for ALGOL 68


Revised Report on the Algorithmic Language - Algol 68 Edited by: A. van Wijngaarden & al, Sep 1973
Paradigm multi-paradigm: concurrent, imperative
Designed by A. van Wijngaarden, B.J. Mailloux, J.E.L. Peck and C.H.A. Koster, et al.
First appeared Final Report: 1968r0
Algol 68/RR / Revised Report: 1973r1
static, strong, safe, structural

ALGOL 68 (short for ALGOrithmic Language 1968) is an imperative computer programming language that was conceived as a successor to the ALGOL 60 programming language, designed with the goal of a much wider scope of application and more rigorously defined syntax and semantics.

The contributions of ALGOL 68 to the field of computer science have been deep, wide ranging and enduring, although many of these contributions were only publicly identified when they had reappeared in subsequently developed programming languages.


ALGOL 68 features include expression-based syntax, user-declared types and structures/tagged-unions, a reference model of variables and reference parameters, string, array and matrix slicing, and also concurrency.

ALGOL 68 was designed by IFIP Working Group 2.1. On December 20, 1968, the language was formally adopted by Working Group 2.1 and subsequently approved for publication by the General Assembly of IFIP.

ALGOL 68 was defined using a two-level grammar formalism invented by Adriaan van Wijngaarden. Van Wijngaarden grammars use a context-free grammar to generate an infinite set of productions that will recognize a particular ALGOL 68 program; notably, they are able to express the kind of requirements that in many other programming language standards are labelled "semantics" and have to be expressed in ambiguity-prone natural language prose, and then implemented in compilers as ad hoc code attached to the formal language parser.

The main aims and principles of design of ALGOL 68:

  1. Completeness and clarity of description[7]
  2. Orthogonal design[8]
  3. Security[9]
  4. Efficiency:[10]
    • Static mode checking
    • Mode-independent parsing
    • Independent compilation
    • Loop optimization
    • Representations – in minimal & larger character sets

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C.H.A. Koster, [11]

ALGOL 68 has been criticized, most prominently by some members of its design committee such as C. A. R. Hoare and Edsger Dijkstra, for abandoning the simplicity of ALGOL 60, becoming a vehicle for complex or overly general ideas, and doing little to make the compiler writer's task easy, in contrast to deliberately simple contemporaries (and competitors) such as C, S-algol and Pascal.

In 1970, ALGOL 68R became the first working compiler for ALGOL 68.

In the 1973 revision, certain features – such as proceduring, gommas and formal bounds – were omitted.[12] C.f. The language of the unrevised report.r0

Though European defence agencies (in Britain Royal Signals and Radar Establishment – RSRE) promoted the use of ALGOL 68 for its expected security advantages, the American side of the NATO alliance decided to develop a different project, the Ada programming language, making its use obligatory for US defense contracts.

Steve Bourne, who was on the Algol 68 revision committee, took some of its ideas to his Bourne shell (and thereby, to descendant shells such as Bash) and to C (and thereby to descendants such as C++).

The complete history of the project can be found in C.H. Lindsey's A History of ALGOL 68.[13]

For a full-length treatment of the language, see Programming Algol 68 Made Easy[14] by Dr. Sian Mountbatten, or Learning Algol 68 Genie by Dr. Marcel van der Veer which includes the Revised Report.

Timeline of ALGOL 68

Year Event Contributor
Mar 1959 ALGOL Bulletin Issue 1 (First) Peter Naur / ACM
Feb 1968 Draft Report(DR) Published IFIP Working Group 2.1
Mar 1968 Algol 68 Final Reportr0 Presented at Munich Meeting IFIP Working Group 2.1
Jun 1968 Meeting in Tirrenia, Italy IFIP Working Group 2.1
Aug 1968 Meeting in North Berwick, Scotland IFIP Working Group 2.1
Dec 1968 ALGOL 68 Final Reportr0 Presented at Munich Meeting IFIP Working Group 2.1
Apr 1970 ALGOL 68R(R) under GEORGE 3 on an ICL 1907F Royal Signals and Radar Est.
Sep 1973 Algol 68 Revised Reportr1 Published IFIP Working Group 2.1
1975 ALGOL 68C(C) - transportable compiler (zcode VM) S. Bourne, Andrew Birrell, and Michael Guy
Jun 1977 Strathclyde ALGOL 68 conference, Scotland ACM
May 1978 Proposals for ALGOL H - A Superlanguage of ALGOL 68 A. P. Black, V. J. Rayward-Smith
1984 Full ALGOL 68S(S) compiler for Sun, SPARC, and PCs C.H. Lindsey ea, Manchester
Aug 1988 ALGOL Bulletin Issue 52 (last) Ed. C.H. Lindsey / ACM
May 1997 Algol68 S(S) published on the internet Charles H. Lindsey
Nov 2001 Algol 68 Genie(G) published on the internet (GNU GPL open source licensing) Marcel van der Veer

The Algorithmic Language ALGOL 68 Reports

Timeline of standardization

1968: On December 20, 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.[19] The standard was also made available in Braille.

1984: TC97 considered Algol 68 for standardisation as "New Work Item" TC97/N1642 [2][3]. 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"[4] and Algol 68's ISO standardisation stalled.[5]

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

  • GOST 27974-88 Programming language ALGOL 68 – Язык программирования АЛГОЛ 68[20]
  • GOST 27975-88 Programming language ALGOL 68 extended – Язык программирования АЛГОЛ 68 расширенный[21]

Notable language elements

Bold symbols and reserved words

There are about 60 such reserved words (some with "brief symbol" equivalents) in the standard language:

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.

Units: Expressions

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.

mode: Declarations

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 provided 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, the declaration does not have to appear prior to the first use.

primitive-declarer: int, real, compl, complexG, bool, char, string, bits, bytes, format, file, pipeG, 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.

Other declaration symbols include: flex, heap, loc, ref, long, short, eventS

  • 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.
  • ref - declare the variable to be a pointer, similar to using "&" in a C declaration.
  • 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 new mode (type) may be declared using a mode declaration:

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

This has the similar effect as 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];

Note that 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. Note also that the lower bound of Algol 68 arrays is, by default, one but can be any integer from -max int to max int.

Coercions: casting

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.

There are six possible coercions, termed "deproceduring", "dereferencing", "uniting", "widening", "rowing" and "voiding". Each coercion, except for "uniting", prescribes a corresponding dynamic effect on the associated values. Hence, a number of 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

pr & co: Pragmats and Comments

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).

Expressions and compound statements

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 (and somewhat reverent) 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:
    (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
    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

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. ¢

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 1 to 3 while i≠4 do ~ od

There are several unusual aspects of the construct:

  • 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
  print(("So far:",i,newline));
  sum sq≤1000
  sum sq+:=i↑2

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.

struct, union & [:]: Structures, unions and arrays

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

Usage example for union case of node:

Algol68 as in the 1968 Final Report
 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))
Algol68 as in the 1973 Revised Report
 node n := "1234";
 case n in
   (real r):   print(("real:", r)),
   (int i):    print(("int:", i)),
   (compl c):  print(("compl:", c)),
   (string s): print(("string:", s))
   out         print(("?:", n))

proc: Procedures

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.

op: Operators

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;

Array, Procedure, Dereference and coercion operations

priority Operation r0&r1 +Algol68r0 +Algol68G
Effectively 12
dereferencing, deproceduring(~,~), subscripting[~], rowing[~,], slicing[~:~], size denotations long & short proceduring currying(~,), diag, trnsp, row, col
Effectively 11
of (selection), loc & heap (generators) new (generators)

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

Monadic operators

Algol68 "Worthy characters[6]"r0&r1 +Algol68r0&r1 +Algol68C,G +Algol68r0
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

Dyadic operators with associated priorities

Algol68 "Worthy characters"r0&r1 +Algol68r0&r1 +Algol68C,G +Algol68r0
9 +*, i +×, ⊥  !
8 shl, shr, **, up, down, lwb, upb ↑, ↓, ⌊, ⌈ ××, ^, lws, ups, ⎩, ⎧
7 *, /,  %, over,  %*, mod, elem ×, ÷, ÷×, ÷*, %×, □ ÷:
6 -, +
5 <, lt, <=, le, >=, ge, >, gt ≤, ≥
4 eq =, ne ~= /= ≠, ¬=
3 &, and /\
2 or \/
1 minusab, plusab, timesab, divab, overab, modab, plusto,

-:=, +:=, *:=, /:=, %:=, %*:=, +=:

×:=, ÷:=, ÷×:=, ÷*:=,  %×:= minus, plus, div, overb, modb, ÷::=, prus

Note: Tertiaries include names nil and ○.

Assignation and identity relations etc

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

Algol68 "Worthy characters"r0&r1 +Algol68r0&r1 +Algol68C,G,R +Algol68r0
Effectively 0  :=, is :=:, isnt :/=: :~=:, at @, ":", ";"  :≠: :¬=:  :=:=C, =:=R ..=, .=, ct, ::, ctab, ::=, .., is not, "..", ".,"

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)

Patent application: On 14 May 2003, software patent application No. 20040230959[22] was filed for the ISNOT operator by employees of Microsoft. This patent was granted on 18 November 2004.

Special characters

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: Input and output

Transput is the term used to refer to ALGOL 68's input and output facilities. There are 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.

Books, channels and files

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.
    • There are three standard channels: stand in channel, stand out channel, stand back channel.
  • A file is a means of communicating between a particular 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

"Formatted transput" in ALGOL 68's transput has its own syntax and patterns (functions), with formats embedded between two $ characters.[23]


 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))

par: Parallel processing

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;
  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)

Examples of use

Code sample

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))
  proc sieve = (list l) list:
     if l is nil then nil
        proc not multiple = (int n) bool: n mod hd(l) ≠ 0;
        cons(hd(l), sieve( filter( not multiple, tl(l) )))
  proc primes = (int n) list: sieve( tl( one to(n) ));
  show( primes(100) )

Operating systems written in ALGOL 68

  • Cambridge CAP computer – All procedures constituting the operating system were written in ALGOL 68C, although a number of other closely associated protected procedures – such as a paginator – are written in BCPL.[24]
  • Eldon 3 - Developed at Leeds University for the ICL 1900 was written in ALGOL 68R.[25]
  • 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[26] was designed to access typed data similar to Algol-68 modes.
  • VMES3 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 uЭль-76 (AL-76), rather than the traditional assembly. uЭль-76 resembles Algol-68, The main difference is the dynamic binding types in uЭль-76 supported at the hardware level. uЭль-76 is used for application, job control, system programming.[27]


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

Libraries and APIs

Program representation

A feature of ALGOL 68, inherited from the ALGOL tradition, is its different representations. There is a representation language used to describe algorithms in printed work, a strict language (rigorously defined in the Report) and an official reference language intended to be used in actual compiler input. In the examples you will observe bold typeface words, this is the strict language. ALGOL 68's reserved words are effectively in a different namespace from identifiers, and spaces are allowed in identifiers, so this next fragment is legal:

 int a real int = 3 ;

The programmer who actually writes code does not always have an option of bold typeface or underlining in the code as this may depend on hardware and cultural issues. So different methods to denote these identifiers have been devised. This is called a stropping regime. For example all or some of the following may be available programming representations:

 int a real int = 3; # the strict language #
'INT'A REAL INT = 3; # QUOTE stropping style #
.INT A REAL INT = 3; # POINT stropping style #
 INT a real int = 3; # UPPER stropping style #
 int a_real_int = 3; # RES stropping style, there are 61 accepted reserved words #

All implementations must recognise at least POINT, UPPER and RES inside PRAGMAT sections. Of these, POINT and UPPER stropping are quite common, while RES stropping is in contradiction to the specification (as there are no reserved words). QUOTE (single apostrophe quoting) was the original recommendation, while matched apostrophe quoting, common in ALGOL 60, is not used much in ALGOL 68.[30]

The following characters were recommended for portability, and termed "worthy characters" in the Report on the Standard Hardware Representation of Algol 68:

  • ^ Worthy Characters: ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789 "#$%'()*+,-./:;<=>@[ ]_|

This reflected a problem in the 1960s where some hardware didn't support lower-case, nor some other non-ASCII characters, indeed in the 1973 report it was written: "Four worthy characters — "|", "_", "[", and "]" — are often coded differently, even at installations which nominally use the same character set."

  • Base characters: "Worthy characters" are a subset of "base characters".

Example of different program representations

Algol68 "strict"
as typically published
¢ underline or 
  bold typeface ¢
mode xint = int;
xint sum sq:=0;
for i while
  sum sq≠70×70
  sum sq+:=i↑2
Quote stropping
(like wikitext)
'pr' quote 'pr'
'mode' 'xint' = 'int';
'xint' sum sq:=0;
'for' i 'while'
  sum sq70×70
  sum sq+:=i2
For a 7-bit character code compiler
XINT sum sq:=0;
  sum sq/=70*70
  sum sq+:=i**2
For a 6-bit character code compiler
  SUM SQ .NE 70*70
Algol68 using res stropping
(reserved word)
mode .xint = int;
.xint sum sq:=0;
for i while
  sum sq70×70
  sum sq+:=i2

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.[citation needed]

 # 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)
 # 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)

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

Some Vanitas

For its technical intricacies, ALGOL 68 needs a cornucopia of methods to deny the existence of something:

skip, "~" or "?"C - an undefined value always syntactically valid,
empty - the only value admissible to void, needed for selecting void in a union,
void - syntactically like a mode, but not one,
nil or "○" - a name not denoting anything, of an unspecified reference mode,
() or specifically [1:0]int - a vacuum is an empty array (here specifically of mode []int).
undefined - a standards reports procedure raising an exception in the runtime system.
ℵ - Used in the standards report to inhibit introspection of certain types. e.g. sema

c.f. below for other examples of ℵ.

The term nil is var always evaluates to true for any variable (but see above for correct use of is :/=:), whereas it is not known to which value a comparison x < skip evaluates for any integer x.

ALGOL 68 leaves intentionally undefined what happens in case of integer overflow, the integer bit representation, and the degree of numerical accuracy for floating point. In contrast, the language Java has been criticized for over-specifying the latter.

Both official reports included some advanced features that were not part of the standard language. These were indicated with an ℵ and considered effectively private. Examples include "≮" and "≯" for templates, the outtype/intype for crude duck typing, and the straightout and straightin operators for "straightening" nested arrays and structures.

Extract from the 1973 report:

§ Transput modes
a) modesimplout = union (≮ℒ int≯, ≮ℒ real≯, ≮ℒ compl≯, bool, ≮ℒ bits≯,
           char, [ ] char);
b) modeouttype = ¢ an actual - declarer specifying a mode united
   from a sufficient set of modes none of which is 'void' or contains 'flexible',
   'reference to', 'procedure' or 'union of' ¢;
c) modesimplin = union (≮ref ℒ int≯, ≮ref ℒ real≯, ≮refcompl≯, ref bool,
           ≮ref ℒ bits≯, ref char, ref [ ] char, ref string);
d) modeintype = ¢ ... ¢;
§ Straightening
a) opstraightout = (outtype x) [ ] simplout: ¢ the result of "straightening" 'x' ¢;
b) opstraightin = (intype x) [ ] simplin: ¢ the result of straightening 'x' ¢;

Comparisons with other languages


Except where noted (with a superscript), the language described above is that of the "Revised Report(r1)".

The language of the unrevised report

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.

Extension proposals from IFIP WG 2.1

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 68R and top-down holes, similar to the ENVIRON and USING clauses from ALGOL 68C[32]
  • 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.

True ALGOL 68s specification and implementation timeline

Name Year Purpose State Description Target CPU Licencing Implementation Language
Generalized ALGOL 1962 Scientific NL ALGOL for generalised grammars
ALGOL YY 1966 Draft proposal Intl First version of Algol 68 Specification ACM
ALGOL 68DR 1968 Draft proposal Intl IFIP WG 2.1 Draft Report Specification - March ACM
ALGOL 68r0 1968 Standard Intl IFIP WG 2.1 Final Report Specification - August ACM
ALGOL 68RR 1970 Military UK ICL 1900 ALGOL 60
EPOS ALGOLE 1971 Scientific
ALGOL 68RSRS 1972 Military UK Portable compiler system ICL 2900/Series 39, Multics, VMS & C generator (1993) Crown Copyright ALGOL 68RS
Algol 68 with areas 1972 Experimental & other UK Addition of areas to Algol 68
Mini ALGOL 68 1973 Research NL "An interpreter for simple Algol 68 Programs" Portable interpreter Mathematisch Centrum ALGOL 60
OREGANO 1973 Research US "The importance of implementation models." UCLA
ALGOL 68CC 1975 Scientific UK Cambridge Algol 68 ICL, IBM 360, PDP 10 & Unix, Telefunken, Tesla & Z80(1980)[33] Cambridge ALGOL 68C
ALGOL 68 Revised Reportr1 1975 Standard Intl IFIP WG 2.1 Revised Report Specification ACM
Algol HH 1975 Experimental & other UK Proposed extensions to the mode system of Algol 68 Specification ALGOL W
Odra Algol 68 1976 practical uses USSR/Poland Odra 1204/IL Soviet ALGOL 60
Oklahoma ALGOL 68 1976 programming instruction USA Oklahoma State University implementation[34] IBM 1130 and System/370/158 Unknown ANSI Fortran 66
Berlin ALGOL 68 1977 Research DE "The Berlin ALGOL 68 implementation" &[35] An Abstract ALGOL 68 Machine - machine independent Compiler Technical University of Berlin CDL 2
FLACCF 1977 Multi-purpose CA Revised Report complete implementation with debug features System/370 lease, Chion Corporation Assembler
ALGOL 68-RTRT 1979 Scientific UK Parallel ALGOL 68-R
RS Algolrs 1979 Scientific UK
ALGOL 68+ 1980 Scientific NL Proposed superlanguage of ALGOL 68[36]
M-220 ALGOL 68 USSR M-220 Soviet EPSILON
Leningrad ALGOL 68L 1980 Telecommunications USSR Full Language + Modules IBM, DEC, CAMCOH, PS 1001 & PC Soviet
Interactive ALGOL 68I 1983 UK Incremental compilation PC Noncommercial shareware |
ALGOL 68SS 1985 Scientific Intl Sun version of ALGOL 68 Sun-3, Sun SPARC (under SunOS 4.1 & Solaris 2), Atari ST (under GEMDOS), Acorn Archimedes (under RISC OS), VAX-11 under Ultrix-32
Algol68toC[37] (ctrans) 1985 Electronics UK ctrans from ELLA ALGOL 68RS Portable C generator  Open Sourced & Public Domained 1995 ALGOL 68RS
MK2 Interactive ALGOL 68 1992 UK Incremental compilation PC Noncommercial shareware[38]
Algol 68 GenieG 2001 Full Language NL Includes standard collateral clause Portable interpreter GPL C
Algol 68 Genie Version 2.0.0 2010 Full Language NL Portable interpreter; optional compilation of selected units GPL C

The S3 programming 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.

Implementation specific extensions

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."[39]


  • ... The scheme of type composition adopted by C owes considerable debt to Algol 68, although it did not, perhaps, emerge in a form that Algol's adherents would approve of. The central notion I captured from Algol was a type structure based on atomic types (including structures), composed into arrays, pointers (references), and functions (procedures). Algol 68's concept of unions and casts also had an influence that appeared later. Dennis Ritchie Apr 1993.[1]
  • ... C does not descend from Algol 68 is true, yet there was influence, much of it so subtle that it is hard to recover even when I think hard. In particular, the union type (a late addition to C) does owe to A68, not in any details, but in the idea of having such a type at all. More deeply, the type structure in general and even, in some strange way, the declaration syntax (the type-constructor part) was inspired by A68. And yes, of course, "long". Dennis Ritchie, 18 June 1988[3]
  • "Congratulations, your Master has done it" - Niklaus Wirth[40]
  • The more I see of it, the more unhappy I become - E.W. Dijkstra, 1968[41]
  • [...] it was said that A68's popularity was inversely proportional to [...] the distance from Amsterdam - Guido van Rossum[42]
  • [...] The best we could do was to send with it a minority report, stating our considered view that, "... as a tool for the reliable creation of sophisticated programs, the language was a failure." [...] - C. A. R. Hoare in his Oct 1980 Turing Award Lecture[43]
    • Their actual minority report quote from 1970: "[...] More than ever it will be required from an adequate programming tool that it assists, by structure, the programmer in the most difficult aspects of his job, viz. in the reliable creation of sophisticated programs. In this respect we fail to see how the language proposed here [Algol68] is a significant step forward: on the contrary, we feel that its implicit view of the programmer's task is very much the same as, say, ten years ago. This forces upon us the conclusion that, regarded as a programming tool, the language must be regarded as obsolete. [...]" Signed by: DIJKSTRA, DUNCAN, GARWICK, HOARE, RANDELL, SEEGMUELLER, TURSKI, WOODGER. And then on Dec. 23, 1968, Jan V. Garwick[44]

See also


  1. ^ a b Dennis Ritchie (April 1993). "The Development of the C Language" (PDF). Retrieved April 26, 2007. 
  2. ^ Influence on C: types, structures, arrays, pointers and procedures - Dennis Ritchie[1]
  3. ^ a b Dennis Ritchie (June 1988). "usenet:comp.lang.misc "C and Algol 68"". Retrieved September 15, 2006. 
  4. ^ Influence on C: union, structure, syntax and long precision - Dennis Ritchie[3]
  5. ^ "A History of C++: 1979−1991" (PDF). March 1993. Page 12, 2nd paragraph: Algol68 [gave] operator overloading(§3.3.3), references (§3.3.4), and the ability to declare variables anywhere in a block (§3.3.1). Retrieved May 6, 2008. 
  6. ^ "Interview with Guido van Rossum". July 1998. Archived from the original on 1 May 2007. Retrieved April 29, 2007. 
  7. ^ Completeness and clarity of description
  8. ^ Orthogonal design
  9. ^ Security
  10. ^ Efficiency
  11. ^ "A Shorter History of Algol68". Archived from the original on August 10, 2006. Retrieved September 15, 2006. 
  12. ^ a b Revised Report on the Algorithmic Language Algol 68. (1968-12-20). Retrieved on 2013-07-21.
  13. ^ a b Lindsey, Charles H. (1996). T.J. Bergin & R.G. Gibson, ed. A History of ALGOL 68. History of Programming Languages-II. also in ACM SIGPLAN Notices 28(3), March 1993 (includes a comprehensive bibliography of the meetings and discussions before, during and after development of ALGOL 68). ACM Press. ISBN 0-201-89502-1. 
  14. ^ "PAME". Archived from the original on 2009-10-24. 
  15. ^ "Draft Report on the Algorithmic Language ALGOL 68". March 1968. Archived from the original on September 30, 2007. Retrieved June 22, 2007. 
  16. ^ "Penultimate Draft Report on the Algorithmic Language ALGOL 68 – Chapters 1-9" (PDF). October 1968. Retrieved June 22, 2007. 
  17. ^ "Penultimate Draft Report on the Algorithmic Language ALGOL 68 - Chapters 10-12" (PDF). October 1968. Retrieved June 22, 2007. 
  18. ^ "Revised Report on the Algorithmic Language Algol 68". September 1973. Archived from the original on September 27, 2007. Retrieved April 30, 2007. 
  19. ^ Lu Hu-quan (1971). "The Translation of Algol 68 into Chinese." (PDF). Institute of Mathematics, Academia Sinica - Peking, China. Retrieved August 17, 2012. 
  20. ^ "GOST 27974-88 Programming language ALGOL 68 - Язык программирования АЛГОЛ 68" (PDF) (in Russian). GOST. 1988. Archived (PDF) from the original on 15 November 2008. Retrieved November 15, 2008. 
  21. ^ "GOST 27975-88 Programming language ALGOL 68 extended - Язык программирования АЛГОЛ 68 расширенный" (PDF) (in Russian). GOST. 1988. Retrieved November 15, 2008. 
  22. ^ "IS NOT OPERATOR" - US application 20,040,230,959 
  23. ^ Format syntax in ALGOL 68G
  24. ^
  25. ^ David Holdsworth (Winter 2009/10). "KDF9 Time Sharing: Eldon 2 is not EGDON!". Computer RESURRECTION - Number 49. Computer Conservation Society. Retrieved October 3, 2010.  Check date values in: |date= (help)
  26. ^
  27. ^ Эльбрус Бабаяна и Pentium Пентковского. Retrieved on 2013-07-21.
  28. ^ Oliver, J. R.; Newton, R.S. (1979). "Practical experience with ALGOL 68-RT" (PDF). The Computer Journal 22 (2): 114–118. doi:10.1093/comjnl/22.2.114. Retrieved 2011-04-09. 
  29. ^ Applications, libraries, and test suites — Software Preservation Group. Retrieved on 2013-07-21.
  30. ^ Revised Report, page 123, footnote
  31. ^
  32. ^ Lindsey, C.H.; Boom, H.J. (Dec 1978). "A Modules and Separate Compilation facility for ALGOL 68". ALGOL Bulletin (43). doi:10.1145/1061719.1061724. Retrieved 2011-05-05. 
  33. ^
  34. ^
  35. ^ An abstract ALGOL 68 machine and its application in a machine independent compiler - Springer. Retrieved on 2013-07-21.
  36. ^
  37. ^ Open source Algol 68 implementations - Browse Files at. Retrieved on 2013-07-21.
  38. ^ [1][dead link]
  39. ^
  40. ^ C.H.A. Koster (1993). "The Making of Algol 68" (PDF). Retrieved April 28, 2007. 
  41. ^ E.W. Dijkstra. "To the EDITOR ALGOL 68 Mathematische Centrum". Archived from the original on 21 April 2007. Retrieved April 28, 2007. 
  42. ^ Guido van Rossum (June 2005). "Python-Dev Wishlist: dowhile". Retrieved April 28, 2007. 
  43. ^ Hoare, C. A. R. (February 1981). "The emperor's old clothes" (PDF). Communications of the ACM 24 (2): 75–83. doi:10.1145/358549.358561. Archived from the original on 2010-01-07. 
  44. ^ "ALGOL Bulletin (referred to in AB30.1.1.1)". March 1970. Archived from the original on September 30, 2007. Retrieved March 1, 2007. 
  • Brailsford, D.F. and Walker, A.N., Introductory ALGOL 68 Programming, Ellis Horwood/Wiley, 1979
  • Lindsey, C.H. and van der Meulen, S.G., Informal Introduction to ALGOL 68, North-Holland, 1971
  • McGettrick, A.D., ALGOL 68, A First and Second Course, Cambridge Univ. Press, 1978
  • Peck, J.E.L., An ALGOL 68 Companion, Univ. of British Columbia, October 1971
  • Tanenbaum, A.S., A Tutorial on ALGOL 68, Computing Surveys 8, 155-190, June 1976 and 9, 255-256, September 1977,
  • Woodward, P.M. and Bond, S.G., ALGOL 68-R Userssic Guide, London, Her Majesty's Stationery Office, 1972

External links

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