[Omitted history]
As with the preliminary Algol report, three different levels of language
are recognized, namely a Reference Language, a Publication Language, and
several Hardware Representations.
It is the working language of the committee.
It is the defining language.
The characters are determined by ease of mutual understanding and
not by any computer limitations, coders notation, or pure
mathematical notation.
It is the basic reference and guide for compiler builders.
It is the guide for all hardware representations.
It is the guide for transliterating from publication language to
any locally appropriate hardware representations.
The main publications of the Algol language itself will use the
reference representation.
The publication language admits variations of the reference
language according to usage of printing and handwriting (e.g.
subscripts, spaces, exponents, Greek letters).
It is used for stating and communicating process.
The characters used may be different in different countries, but
univocal correspondence with reference representation must be
secured.
Each of these is a condensation of the reference language enforced
by the limited number of characters on the standard input
equipment.
Each one of these uses the character set of a particular computer
and is the language accepted by a translator for that computer.
Each of these must by accompanied by a special set of rules for
transliterating from publication or reference language.
For transliteration between the reference language and a language
suitable for publications, among others, the following rules are
recommended.
Reference Language Publication Language
Subscript brackets [ ] Lowering of the line between the
brackets and removal of the brackets.
Exponentiation ^ Raising the exponent.
Parentheses () Any form of parentheses, brackets,
braces.
Basis of ten \ten Raising of the ten and of the following
integral number, inserting of the
intended multiplication sign.
Was sich ueberhaupt sagen laesst, laesst sich
klar sagen; und wovon man nicht reden
kann, darueber muss man schweigen.
Ludwig Wittgenstein
[ Translation of Quote ]
As stated in the introduction, the algorithmic language has three
different kinds of representations -- reference, hardware, and
publication -- and the development described in the sequel is in terms
of the language are represented by a given set of symbols -- and it is
only in the choice of symbols that the other two representations may
differ. Structure and content must be the same for all
representations.
The purpose of the algorithmic language is to describe computational
processes. The basic concept used for the description of calculating
rules is the well known arithmetic expression containing as constituents
numbers, variables, and functions. From such expressions are compounded,
by applying rules of arithmetic composition, self-contained units of the
language -- explicit formulae -- called assignment statements.
To show the flow of computational processes, certain non-arithmetic
statements and statement clauses are added which may describe e.g.,
alternatives, or iterative repetitions of computing statements. Since it
is necessary for the function of the statements that one statement
refers to another, statements may be provided with labels. A sequence of
statements may be enclosed between the statement brackets begin
and end to form a compound statement.
Statements are supported by declarations which are not themselves
computing instructions, but inform the translator of the existence and
certain properties of objects appearing in statements, such as the class
of numbers taken on as values by a variable, the dimension of an array
of numbers, or even the set of rules defining a function. A sequence of
declarations followed by a sequence of statements and enclosed between
begin and end constitutes a block. Every declaration
appears in a block in this way and is valid only for that block.
A program is a block or compound statement which is not contained within
another statement and which makes no use of other statements not
contained within it.
In the sequel the syntax and semantics of the language will be
given
Whenever the precision of arithmetic is stated as being in general
not specified, or the outcome of a certain process is left undefined
or said to be undefined, this is to be interpreted in the sense that
a program only fully defines a computational process if the
accompanying information specifies the precision assumed, the kind
of arithmetic assumed, and the course of action to be taken in all
such cases as may occur during the execution of the computation.
. . . . . . . . . ( end of section 1. Structure of the language) <<Contents | End>>
The reference language is built up from the following basic symbols:
- basic_symbol::= letter | digit | logical_value | delimiter
- letter::= ASCII.letter.
This alphabet may be arbitrarily restricted, or extended with any other
distinctive character (i.e. character not coinciding with any digit,
logical_value or delimiter).
Letters do not have individual meaning. They are used for forming
identifiers and strings
[ Foot note 2 ]
(cf. sections
[ 2.4. Identifiers ]
,
[ 2.6. Strings ]
).
It should be particularly noted that throughout the reference
language underlining (underlined) is used for defining independent basic symbols (see
sections 2.2.2 and 2.3). These are understood to have no relation to
the individual letters of which they are composed. Within the
present report underlining will be used for no other purposes.
- digit::= ASCII.digit
Digits are used for forming numbers, identifiers, and strings.
- logical_value::= true | false.
The logical values have a fixed obvious meaning.
- delimiter::= operator | separator | bracket | declarator | specificator.
- operator::= arithmetic_operator | relational_operator | logical_operator | sequential_operator.
- arithmetic_operator::= "+" | "-" | times | "/" | div | power .
- relational_operator::= "<" | le | "=" | ge | ">" | ne .
- logical_operator::= iff | hook | or | and | not .
- sequential_operator::= goto | if | then | else | for | do.
- separator::= comma | dot | ten | colon | semicolon | ":=" | "_" | step | until | while | comment.
- bracket::= "(" | " | "[" | "]" | "`" | "'" | begin | end
- declarator::= own | Boolean | integer | real | array | switch | procedure
- specificator::= string | label | value
Delimiters have a fixed meaning which for the most part is obvious or else will be given at the appropriate place in the sequel.
Typographical features such as blank space or change to a new line
have no significance in the reference language. They, however, be used
freely for facilitating reading.
For the purpose of including text among the symbols of a program the
following "comment" conventions hold:
- statement_separator::= ";" comment #non(";");"
(comment1): statement_separator = ";".
- block_begining::=begin comment #non(";");"
(comment2): block_begining = begin.
- block_ending::=end #(non(end | ";" | else))
(comment3): block_ending = end.
By equality is here meant that any of the structures shown on
the left hand side may be replaced, in any occurrence outside of
strings, by the symbol shown on the right hand side
without any effect on the action of the program. It is further
understood that the comment structure encountered first in the text
when reading from left to right has precedence in being replaced over
later structures contained in the sequence.
- identifier::= letter #( letter | digit).
q
Soup
V17a
a34kTMNs
MARILYN
Identifiers have no inherent meaning, but serve for
the identification of simple variables, arrays, labels, switches, and
procedures. They may be chosen freely (cf. however section 3.2.4.
Standard functions).
The same identifiers cannot be used to denote two different quantities
except when these quantities have disjoint scopes as defined by the
declarations of the program (cf section 2.7. Quantities, kinds and
scopes and section 5. Declarations).
. . . . . . . . . ( end of section 2.4. Identifiers) <<Contents | End>>
- unsigned_integer::= digit | unsigned_integer digit.
- integer::= unsigned_integer | "+" unsigned_integer | "-" unsigned_integer.
- decimal_fraction::= "." unsigned_integer.
- exponential_part::= \ten integer.
- decimal_number::= unsigned_integer | decimal_fraction | unsigned_integer decimal_fraction.
- unsigned_number::= decimal_number | exponential_part | decimal_number exponential_part.
- number::= unsigned_number | "+" unsigned_number | "-" unsigned_number.
0 -200.084 -.083\ten -02
177 + 07.43\ten 8 -\ten 7
.5384 9.34\ten +10 \ten -4
+0.7300 2\ten -4 +\ten +5
Decimal numbers have their conventional meaning.
The exponent part is scale factor expressed as an integral power of 10.
Integers are of the type integer. All other
numbers are of type real (cf. section 5.1 Type declarations).
. . . . . . . . . ( end of section 2.5. Numbers) <<Contents | End>>
- proper_string::=#non("`" | "'").
- open_string::= proper_string "`" open_string"'" | open_string open_string.
- string_literal::= "`" open_string"'."
`5k,,-`[[[` /\ =/:'Tt''
`This|_|is|_|a|_|`string''
In order to enable the language to handle arbitrary
sequences of basic symbols the string quotes "`" and "'" are introduced.
The Symbol |_| denotes a space. It has no significance outside strings.
Strings are used as actual parameters of procedures (cf. sections 3.2.
Function designators and 4.7. Procedure Statements).
. . . . . . . . . ( end of section 2.6. Strings) <<Contents | End>>
The following kinds of quantities are distinguished: simple variables,
arrays, labels, switches, and procedures.
The scope of a quantity is the set of statements and expressions in
which the declaration of the identifier associated with that quantity is
valid. For labels see section 4.1.3.
A value is an ordered set of numbers (special case: a single number), an
ordered set of logical values (special case: a single logical value), or
a label.
Certain of the syntactic units are said to possess values. These values
will in general change during the execution of the program The values of
expressions and their constituents are defined in section 3. The value
of an array identifier is the ordered set of values of the corresponding
array of subscripted variables (cf. section 3.1.4.1).
The various types'' (integer, real, Boolean)
basically denote properties of values. The types associated with
syntactic units refer to the values of these units.
In the language the primary constituents of the programs describing
algorithmic processes are arithmetic, Boolean, and designational
expressions. Constituents of the expressions, except for certain
delimiters, are logical values, numbers, variables, function designators,
and elementary arithmetic, relational, logical, and sequential
operators. Since the syntactic definition of both variables and
function designators contains expressions, the definition of
expressions, and their constituents, is necessarily recursive.
- expression::= arithmetic_expression | Boolean_expression | designational_expression.
- variable_identifier::= identifier.
- simple_variable::= variable_identifier.
- subscript_expression::= arithmetic_expression.
- subscript_list::= subscript_expression | subscript_list "," subscript_expression.
- array_identifier::= identifier.
- subscripted_value::= array_identifier "["subscripted_list "]".
- variable::= simple_variable | subscripted_variable.
epsilon
detA
a17
Q[7,2]
x[sin(n * pi/2),Q[3,n,4]]
A variable is a designation given to a single value.
This value may be used in expressions for forming other values and may
be changed at will by means of assignment statements (section 4.2). The
type of the value of a particular variable is defined in the declaration
for the variable itself (cf. section 5.1. Type declarations) or for
the corresponding array identifier (cf. section 5.2. Array declarations),
Subscripted variables designate values
which are components of multidimensional arrays (cf. section 5.2.
Array declarations). Each arithmetic expression of the subscript list
occupies one subscript position of the subscripted variable and is
called a subscript. The complete list of subscripts is enclosed in the
subscript brackets [ ]. The array component referred to by a
subscripted variable is specified by the actual numerical value of its
subscripts (cf. section 3.3. Arithmetic expressions).
Each subscript position acts like a variable of type
integer and the evaluation of the subscript is understood to be
equivalent to an assignment to this fictitious variable (cf. section
4.2.4). The value of the subscripted variable is defined only if the
value of the subscript expression is within the subscript bounds of the
array (cf. section 5.2. Array declarations).
. . . . . . . . . ( end of section 3.1.4. Subscripts.) <<Contents | End>>
. . . . . . . . . ( end of section 3.1. Variables) <<Contents | End>>
- procedure_identifier::= identifier.
- actual_parameter::= string_literal | expression | array_identifier | switch_identifier | procedure_identifier.
- letter_string::= letter | letter_string letter.
- parameter_delimiter::= "," | ")" letter_string ":" "(".
- actual_parameter_list::= actual_parameter | actual_parameter_list parameter_delimiter actual_parameter.
- actual_parameter_part::= empty | "(" actual_parameter_list} ")".
- function_designator::= procedure_identifier actual_parameter_part.
sin(a-b)
J(v+s,n)
R
S(s-5) Temperature: (T) Pressure: (P)
Compile (`:=') Stack: (Q)
Function designators define single numerical or
logical values which result through the application of given sets of
rules defined by a procedure declaration (cf. section 5.4. Procedure
declarations) to fixed sets of actual parameters. The rules governing
specification of actual parameters are given in section 4.7. Procedure
statements. Not every procedure declaration defines the value of a
function designator.
Certain identifiers should be reserved for
the standard functions of analysis, which will be expressed as
procedures. It is recommended that this reserved list should contain:
- Reccommended_mathematical_functions::=following
Net
For E: Arithmetic_expression.
- abs(E)::=the modulus (absolute value) of the value of the expression E .
- sign(E)::=the sign of the value of E (+1 for E < 0, 0 for E=0, -1 for E < 0).
- sqrt(E)::=the square root of the value of E.
- sin(E)::=the sine of the value of E.
- cos(E)::=the cosine of the value of E.
- arctan(E)::=the principal value of the arctangent of the value of E.
- ln(E)::=the natural logarithm of the value of E.
- exp(E)::=the exponential function of the value of E (e ^ E).
(End of Net)
These functions are all understood to operate indifferently on arguments
both of type real and integer. They will all yield values
of type real, except for sign (E) which will have values of type
integer. In a particular representation these function may be
available without explicit declarations (cf. section 5. Declarations).
It is understood that transfer functions
between any pair of quantities and expressions my be defined. Among the
standard functions it is recommended that there be one, namely
entier (E),
which transfers'' an expression of real type to one of integer type,
and assigns to it the value which is the largest integer not greater
than the value of E.
. . . . . . . . . ( end of section 3.2. Function designators) <<Contents | End>>
- adding_operator::= "+" | "-".
- multiplying_operator::= timess | "/" | div .
- primary::= unsigned_number | variable | function_designator | "(" arithmetic_expression ")".
- factor::= primary | factor power primary.
- term::= factor | term multiplying_operator factor.
- simple_arithmetic_expression::= term | adding_operator term | simple_arithmetic_expression adding_operator term.
- if_clause::= if Boolean_expression then.
- arithmetic_expression::= simple_arithmetic_expression | if_clause simple_arithmetic_expression else arithmetic_expression.
Primaries:
7.394\ten -8
sum
w[i+2,8]
cos(y+z * 3)
(a-3/y+vu ^ 8)
Factors:
omega
sum ^ cos(y+z * 3)
7.394\ten -8 ^ w[i+2,8] ^ (a-3/y+vu ^ 8)
Terms:
U
omega * sum ^ cos(y+z * 3)/7.394\ten -8 ^ w[i+2,8] ^ (a-3/y+vu ^ 8)
Simple arithmetic expressions:
U-Yu+omega * sum ^ cos(y+z * 3)/7.394\ten -8 ^ w[i+2,8] ^ (a-3/y+vu ^ 8)
Arithmetic expressions:
w * u-Q(S+Cu) ^ 2
if q < 0 then S+3 * Q/A else 2 * S+3 * q
if a < 0 then U+V else if a * b < 17 then U/V else if k <> y then V/U else 0
a * sin(omega * t)
0.57\ten 12 * a[N * (N-1)/2,0]
(A * arctan(y)+Z) ^ (7+Q)
if q then n-1 else n
if a < 0 then A/B else if b=0 then B/A else z
An arithmetic expression is a rule for computing a
numerical value. In case of simple arithmetic expressions this value
is obtained by executing the indicated arithmetic operations on the
actual numerical values of the primaries of the expression, as explained
in detail in section 3.3.4 below. The actual numerical value for a
primary is obvious in the case of numbers. For variables it is the
current value (assigned last in the dynamic sense), and for function
designators it is the value arising from the computing rules defining
the procedure (cf. section 5.4.4. Values of function designators) when
applied to the current values of the procedure parameters given in the
expression. Finally, for arithmetic expressions enclosed in parentheses
the value must through a recursive analysis be expressed in terms of the
values of primaries of the other three kinds.
In the more general arithmetic expression, which include if clauses, one
out of several simple arithmetic expressions is selected on the basis of
the actual values of the Boolean expression (cf. section 3.4. Boolean
expressions). This selection is made as follows: The Boolean expressions
of the if clauses are evaluated one by one in the sequence from left to
right until one having the value true is found. The value of the
arithmetic expression is then the value of the first arithmetic
expression following this Boolean (the largest arithmetic expression
found in this position is understood). The construction:
else simple_arithmetic_expression
is equivalent to the construction:
else if true then simple_arithmetic_expression
Apart from the Boolean expressions of if
clauses, the constituents of simple arithmetic expressions must be of
types real or integer (cf. section 5.1. Type
declarations). The meaning of the basic operators and the types of the
expressions to which they lead are given by the following rules:
The operators +, -, and * have the conventional meaning
(addition, subtraction, and multiplication). The type of the expression
will by integer if both of the operands are of integer
type, otherwise real.
In addition, subtraction, and multiplication, the type of the expression
will by integer if both of the operands are of integer
type, otherwise real.
The operations term / factor and term
% factor both denote division, to be understood as a
multiplication of the term by the reciprocal of the factor with due
regard to the rules of precedence (cf. section 3.3.5). Thus for
example a/b*7/(p-q)*v/s
means ((((a*(b^-1))*7)*((p-q)^-1))*v)*(s^-1)
The operator / is defined for all four combinations of types real
and integer and will yield results of real type in any
case. The operator % is defined only for two operands of type
integer and will yield a result of type integer,
mathematically defined as follows: .
- a % b::= sign(a/b) * entier(abs(a/b))
Compare with sections 3.2.4 and 3.2.5.
The operation factor ^ primary
denotes exponentiation, where the factor is the base and the primary is
the exponent. Thus for example 2 ^ n ^ k means
- (2^n)^k
while
- 2 ^ (n ^ m) means 2^(n^m).
Writing i for a number of integer type, r for a number of
real type, and a for a number of ether integer or
real type, the result is given by the following rules: .
a ^ i
if i>0: a*a*...*a (i times), of the same type as a.
if i=0: if a<>0: 1, of the same type as a.
if a=0: undefined.
if i<0, if a<>0: 1/(a*a*a*...*a) (the denominator has
-i factors), of type $real.
if a=0: undefined.
a ^ r
if a>0: exp(r*ln(a)), of type $real.
if a=0, if r>0: 0.0, of type $real.
if r<=0: undefined.
if a<0: always undefined.
. . . . . . . . . ( end of section 3.3.4. Operators and types.) <<Contents | End>>
The sequence of operations within one
expression is generally from left to right, with the following
additional rules:
According to the syntax given in section 3.3.1 the following
rules of precedence hold:
first: ^
second: * / %
third: + -
The expression between a left parenthesis and the matching
right parenthesis is evaluated by itself and this value is used in
subsequent calculations. Censequently the desired order of execution of
operations within an expression can always be arranged by appropriate
positioning of parenthesis. .
Arithmetics of real quantities. Numbers and variables of
type real must be interpreted in the sense of numerical analysis,
i.e. as entities defined inherently with only a finite accuracy.
Similarly, the possibility of the occurrence of a finite deviation from
the mathematically defined result in any arithmetic expression is
explicitly understood. No exact arithmetic will be specified, however,
and it is indeed understood that different hardware representations may
evaluate arithmetic expressions differently. The control of the
possible consequences of such differences must be carried out by the
methods of numerical analysis. This control must be considered a part
of the process to be described, and will therefore be expressed in terms
of the language itself. .
. . . . . . . . . ( end of section 3.3. Arithmetic expressions) <<Contents | End>>
- relational_operator::= "<" | le | "=" | ge | ">" | ne.
- relation::= simple_arithmetic_expression relational_operator simple_arithmetic_expression.
- Boolean_primary::= logical_value | variable | function_designator | relation | "(" Boolean_expression ")".
- Boolean_secondary::= Boolean_primary | not Boolean_primary.
- Boolean_factor::= Boolean_secondary | Boolean_factor and Boolean_secondary.
- Boolean_term::= Boolean_factor | Boolean_term or Boolean_factor.
- implication::= Boolean_term | implication hook Boolean_term.
- simple_Boolean::= implication | simple_Boolean iff implication.
- Boolean_expression::= simple_Boolean | if_clause simple_Boolean else Boolean_expression.
x=-2
Y>V \/ z<q
a+b>-5 /\ z-d>q^2
p /\ q \/ x<>y
g==~a /\ b /\ ~c \/ d \/ e=> ~f
if k<1 then s<w else h <= c
if if if a then b else c then d else f then g else h < k
A Boolean expression is a rule for computing a
logical value. The principles of evaluation are entirely analogous to
those given for arithmetic expressions in section 3.3.3.
Variables and function designators entered as Boolean
primaries must be declared Boolean (cf. section 5.1. Type
declarations and section 5.4.4. Value of function designators).
Relations take on the value true whenever
the corresponding relation is satisfied for the expressions involved,
otherwise false.
The meaning of the logical operators ~ (not), /\ (and),
\/ (or), => (hook), and == (iff), is given
by the following function table.
b1 | false | false | true | true
b2 | false | true | false | true
----------------------------------------------------------------
~ b1 | true | true | false | false
b1 /\ b2 | false | false | false | true
b1 \/ b2 | false | true | true | true
b1 => b2 | true | true | false | true
b1 == b2 | true | false | false | true
The sequence of operations within one
expression is generally from left to right, with the following
additional rules:
According to the syntax given in section 3.4.1 the following
rules of precedence hold:
first: arithmetic expressions according to section 3.3.5.
second: < <= = >= > <>
third: /\
fourth: /\
fifth: \/
sixth: =>
seventh: ==
The use of parentheses will be interpreted in the sense given
in section 3.3.5.2.
. . . . . . . . . ( end of section 3.4.6. Precedence of operators.) <<Contents | End>>
. . . . . . . . . ( end of section 3.4. Boolean expressions) <<Contents | End>>
- label::= identifier | unsigned_integer.
- switch_identifier::= identifier.
- switch_designator::= switch_identifier l_bracket subscript_expression r_bracket.
- simple_designational_expression::= label | switch_designator | l_paren designational_expression r_paren.
- designational_expression::= simple_designational_expression | if_clause simple_designational_expression else designational_expression.
17
p9
Choose[n-1]
Town [if y<0 then N else N+1]
if Ab<c then 17 else q[if w <= 0 then 2 else n]
A designational expression is a rule for obtaining a
label of a statement (cf. section 4. Statements). Again the principle
of the evaluation is entirely analogous to that of arithmetic
expressions (section 3.3.3). In the general case the Boolean expression
of the if clauses will select a simple designational expression. If
this is a label the desired result is already found. A switch
designator refers refers to the corresponding switch declaration (cf.
section 5.3. Switch declarations) and by the actual numerical value of
its subscript expression selects one of the designational expressions
listed in the switch declaration by counting these from left to right.
Since the designational expression thus selected may again by a switch
designator this evaluation is obviously a recursive process.
The evaluation of the subscript
expression is analogous to that of subscripted variables (cf. section
3.1.4.2). The value of a switch designator is defined only if the
subscript expression assumes one of the positive values 1, 2, 3, ..., n,
where n is the number of entries in the switch list.
Unsigned integers used as labels
have the property that leading zeroes do not affect their meaning, e.g.
00127 denotes the same label as 217.
. . . . . . . . . ( end of section 3.5. Designational expressions) <<Contents | End>>
. . . . . . . . . ( end of section 3. Expressions) <<Contents | End>>
The units of operation within the language are called statements. The
will normally be executed consecutively as written. However, this
sequence of operations may be broken by go to statements, which define
their successor explicitly, and shortened by conditional statements,
which may cause certain statements to be skipped.
In order to make it possible to define a specific dynamic succession,
statements may be provided with labels.
Since sequences of statements may be grouped together into compound
statements and blocks the definition of statement must necessarily be
recursive. Also since declarations, described in section 5, enter
fundamentally into the syntactic structure, the syntactic definition of
statements must suppose declarations to be already defined.
- unlabelled_basic_statement::= assignment_statement | go_to_statement | dummy_statement | procedure_statement.
- basic_statement::= unlabelled_basic_statement | label colon basic_statement.
- unconditional_statement::= basic_statement | compound_statement | block.
- statement::= unconditional_statement | conditional_statement | for_statement.
- compound_tail::= statement end | statement ";" compound_tail.
- block_head::= begin declaration | block_head ";" declaration
- unlabelled_compound::= begin compound_tail.
- compound_statement::= unlabelled_compound | label colon compound_statement.
- block::= unlabelled_block | label colon block.
- program::= block | compound_statement.
This syntax may be illustrated as follows: Denoting arbitrary
statements, declarations, and labels, by the letters S, D, L,
respectively, the basic syntactic units take the forms:
Compound statement:
L:L: ... begin S; S; ... S; S end
Block:
L:L: ... begin D; D; .. D; S; S; ... S; S end
It should by kept in mind that each of the statements S may again be a
complete compound statement or a block.
a:=p+q
goto Naples
Start: Continue: W:=7.993
begin x:=0; for y:=1 step 1 until n do x:=x+A[y];
if x>q then goto STOP else if x>w-2 then goto S;
Aw: St: W:=x+bob end
Q: begin integer i, k; real w;
for i:=1 step 1 until m do
for k:=i+1 step 1 until m do
begin w:=A[i,k];
A[i,k]:=A[k,i];
A[k,i]:=w end for i and k
end block Q
. . . . . . . . . ( end of section 4.1.2. Examples.) <<Contents | End>>
Every block automatically introduces a new level of
nomenclature. This is realized as follows: Any identifier occurring
within the block my through a suitable declaration (cf. section
[ 5. Declarations ]
) be specified to be local to the block in question. This
means (a) that the entity represented by this identifier inside the
blocks has no existence outside it and (b) that any entity represented
by this identifier outside the block is completely inaccessible inside
the block.
Identifiers (except those representing labels) occurring within a block
and not being declared to this block will be non-local to it, i.e. will
represent the same entity inside the block and in the level immediately
outside it. A label separated by a colon from a statement, i.e.
labelling that statement, behaves as though declared in the head of the
smallest embracing block, i.e. the smallest block whose brackets
begin and end enclose that statement. In this context a
procedure body must be considered as if it were enclosed by begin
and end and treated as a block.
Since a statement of a block may again itself be a block the concepts
local and non-local to a block must be understood recursively. Thus an
identifier, which is non-local to a block A, may or may not be non-local
to the block B in which A is one statement.
. . . . . . . . . ( end of section 4.1. Compound statements and blocks) <<Contents | End>>
- left_part::= variable ":=" | procedure_identifier ":=".
- left_part_list::= left_part | left_part_list left_part.
- assignment_statement::= left_part_list arithmetic_expression | left_part_list Boolean_expression.
s:=p[0]:=n:=n+1+s
n:=n+1
A:=B/C-v-q*S
S[v,k+2]:=3-arctan(s*zeta)
V:=Q>Y/\Z
Assignment statements serve for assigning the value
of an expression to one or several variables or procedure identifiers.
Assignment to a procedure_identifier may only occur within the body of a
procedure defining the value of a function designator (cf. section
5.4.4). The process will in the general case be understood to take
place in three steps as follows:
Any subscript expression occurring in the left part variables
are evaluated in sequence from left to right.
The expression of the statement is evaluated.
The value of the expression is assigned to all the left part
variables, with any subscript expressions having values as evaluated in
step 4.2.3.1.
. . . . . . . . . ( end of section 4.2.3. Semantics.) <<Contents | End>>
The type associated with all variables and procedure
identifiers of a left part list must be the same. If the type is
Boolean, the expression must likewise be Boolean. If the
type is real or integer, the expression must be
arithmetic. If the type of the arithmetic expression differs from that
associated with the variables and procedure identifiers, appropriate
transfer functions are understood to be automatically invoked. For
transfer from real to integer type the transfer function
is understood to yield a result equivalent to entier(E+0.5)
where E is the value of the expression. The type associated with a
procedure identifier is given by the declarator which appears as the
first symbol of the corresponding procedure declaration (cf. section
5.4.4).
. . . . . . . . . ( end of section 4.2. Assignment statements) <<Contents | End>>
- go_to_statement::= goto designational_expression.
goto 8
goto exit [n+1]
goto Town [ if y<0 then N else N+1]
goto if Ab<c then 17 else q [ if w\mlt0 then 2 else n]
A go to statement interrupts the normal sequence of
operations, defined by the write-up of statements, by defining its
successor explicitly by the value of a designational expression. Thus
the next statement to be executed will be the one having this value as
its label.
Since labels are inherently local, no go to
statement can lead from outside into a block. A go to statement may,
however, lead from outside into a compound statement.
A go to statement is
equivalent to a dummy statement if the designational expression is a
switch designator whose value is undefined.
. . . . . . . . . ( end of section 4.3. Go to statements) <<Contents | End>>
- dummy_statement::= empty.
L:
begin ....; John: end
A dummy statement executes no operation. It may serve to place a label.
. . . . . . . . . ( end of section 4.4. Dummy statements) <<Contents | End>>
- if_clause::= if Boolean_expression then.
- unconditional_statement::= basic_statement | compound_statement | block.
- if_statement::= if_clause unconditional_statement.
- conditional_statement::= if_statement | if_statement else statement | if_clause for_statement | label colon conditional_statement.
if x>0 then n:=n+1
if s>u then V: q:=n+m else goto R
if s<0 \/ P<=Q then AA: begin if q\mltv then a:=v/s
else y:=2*a end else if v>s then a:=v-q
else if v>s-1 then goto S
Conditional statements cause certain statements to
be executed or skipped depending on the running values of specified
Boolean expressions.
The unconditional statement of an if statement
will be executed if the Boolean expression of the if clause is true.
Otherwise it will be skipped and the operation will be continued with
the next statement.
According to the syntax two different
forms of conditional statements are possible. These may be illustrated
as follows:
if B1 then S1 else if B2 then S2 else S3; S4
if B1 then S1 else if B2 then S2 else if B3 then S3; S4
Here B1 to B3 are Boolean expressions, while S1 to S3 are unconditional
statements. S4 is the statement following the complete conditional
statement.
The execution of a conditional statement may be described as follows:
The Boolean expression of the if clause are evaluated one after the
other in sequence from left to right until one yielding the value
true is found. Then the unconditional statement following this
Boolean is executed. Unless this statement defines its successor
explicitly the next statement to be executed will be S4, i.e. the
statement following the complete complete conditional statement. Thus
the effect of the delimiter else may be described by saying that
it defines the successor of the statement it follows to be the statement
following the complete conditional statement.
The construction
else $unconditional_statement
is equivalent to
else if true then $unconditional_statement
If none of the Boolean expressions of the if clauses is true, the effect
of the whole conditional statement will be equivalent to that of a dummy
statement.
- [Omitted pictures]
. . . . . . . . . ( end of section 4.5.3. Semantics of if.) <<Contents | End>>
The effect of a go to
statement leading into a conditional statement follows directly from the
above explanation of the effect of else.
. . . . . . . . . ( end of section 4.5. Conditional statements) <<Contents | End>>
- for_list_element::= arithmetic_expression | arithmetic_expression step arithmetic_expression until arithmetic_expression | arithmetic_expression while Boolean_expression
- for_list::= for_list_element #( comma for_list_element).
- for_clause::= for variable ":=" for_list do.
- for_statement::= #( label colon) for_clause statement.
for q:=1 step s until n do A[q]:=B[q]
for k:=1,V1*2 while V1<N do
for j:=I+G,L,1 step 1 until N, C+D do A[k,j]:=B[k,j]
A for clause causes the statement S which it precedes
to be repeatedly executed zero or more times. In addition it performs a
sequence of assignments to its controlled variable. The process may be
visualized by means of the following picture:
[Omitted picture]
In this picture the word initialize means: perform the first assignment
of the for clause. Advance means: perform the next assignment of the
for clause. Test determines if the last assignment has been done. If
so, the execution continues with the successor of the for statement. If
not, the statement following the for clause is executed.
The for list gives a rule for obtaining
the values which are consecutively assigned to the controlled variable.
This sequence of values is obtained from the for list elements by taking
these one by one in order in which they are written. The sequence of
values generated by each of the three species of for list elements and
the corresponding execution of the statement S are given by the
following rules:
This element gives rise to one value,
namely the value of the given arithmetic expression as calculated
immediately before the corresponding execution of the statement S.
An element of the form A step B until C, where A, B, and C are arithmetic expressions, gives rise to an execution which may be described most concisely in terms of additional Algol statement as follows:
V := A
L1: if (V-C)*sign(B) > 0 then goto ``Element exhausted'';
Statement S;
V := V+B;
goto L1;
where V is the controlled variable of the for clause and `Element
exhausted' points to the evaluation according to the next element in the
for list, or if the step-until-element is the last of the list, to the
next statement in the program.
The execution governed by a for list element
of the form E while F, where E is an arithmetic and F a Boolean
expression, is most concisely described in terms of additional Algol
statements as follows:
L3: V := E
if ~ F then goto ``Element exhausted'';
Statement S;
goto L3;
where the notation is the same as in 4.6.4.2 above.
Upon exit out
of the statement S (supposed to be compound) through a go to statement
the value of the controlled variable will be the same as it was
immediately preceding the execution of the go to statement.
If the exit is due to exhaustion of the for list, on the other hand, the
value of the controlled variable is undefined after the exit.
The effect of a go to
statement, outside a for statement, which refers to a label within the
for statement, is undefined.
. . . . . . . . . ( end of section 4.6.4. The for list elements.) <<Contents | End>>
. . . . . . . . . ( end of section 4.6. For statements) <<Contents | End>>
- procedure_statement::= procedure_identifier actual_parameter_part.
Spur (A) Order: (7) Result to: (V)
Transpose (W, v+1)
Absmax (A, N, M, Yy, I, K)
Innerproduct (A [t,P,u], B [P], 10, P, Y)
These examples correspond to examples given in section 5.4.2.
[ #5.4.2. Example Procedures ]
A procedure_statement serves to invoke (call for)
the execution of a procedure_body (cf. section 5.4. procedure
declarations). Where the procedure_body is a statement written in Algol
the effect of this execution will be equivalent to the effect of
performing the following operations on the program at the time of
execution of the procedure_statement.
All formal parameters
quoted in the value part of the procedure declaration heading are
assigned the values (cf. section 2.8. Values and types) of the
corresponding actual parameters, these assignments being considers as
being performed explicitly before entering the procedure_body. The
effect is as though an additional block embracing the procedure_body
were created in which these assignments were made to variables local to
this fictitious block with types as given in the corresponding
specifications (cf. section 5.4.5). As a consequence, variables called
by value are to be considered as nonlocal to the body of the procedure,
but local to the fictitious block (cf. section 5.4.3).
Any formal parameter not
quoted in the value list is replaced, throughout the procedure_body, by
the corresponding actual parameter, after enclosing this latter in
parentheses wherever syntactically possible. Possible conflicts between
identifiers inserted through this process and other identifiers already
present within the procedure_body will be avoided by suitable systematic
changes of the formal or local identifiers involved.
Finally the procedure_body,
modified as above, is inserted in place of the procedure_statement and
executed. if the procedure is called from a place outside the scope of
any non-local quantity of the procedure_body the conflicts between the
identifiers inserted through this process of body replacement and the
identifiers whose declarations are valid at the place of the procedure
statement or function designator will be avoided through suitable
systematic changes of the latter identifiers.
. . . . . . . . . ( end of section 4.7.3. Semantics.) <<Contents | End>>
The correspondence between the
actual parameters of the procedure_statement and the formal parameters
of the procedure_heading is established as follows: The actual parameter
list of the procedure_statement must have the same number of entries as
the formal parameter list of the procedure declaration heading. The
correspondence is obtained by taking the entries of these two lists in
the same order.
For a procedure_statement to be defined it is
evidently necessary that the operations on the procedure_body defined in
sections 4.7.3.1 and 4.7.3.2 lead to a correct Algol statement.
This imposes the restriction on any procedure_statement that the kind
and type of each actual parameter to be compatible with the kind and
type of the corresponding formal parameter. Some important particular
cases of this general rule are the following:
If a string is supplied as an actual parameter in a procedure
statement or function designator, whose defining procedure_body is an
Algol 60 statement (as opposed to non-Algol code, cf. section 4.7.8),
then this string can only be used within the procedure_body as an actual
parameter in further procedure calls. Ultimately it can only be used by
a procedure_body expressed in non-Algol code.
A formal parameter which occurs as a left part variable in an
assignment statement within the procedure_body and which is not called
by value can only correspond to an actual parameter which is a variable (special case of expression).
A formal parameter which is used within the procedure_body as
an array identifier can only correspond to an actual parameter which is
an array identifier of an array of the same dimensions. In addition if
the formal parameter is called by value the local array created during
the call will have the same subscript bounds as the actual array.
A formal parameter which is called by value cannot in general
correspond to a switch identifier or a procedure_identifier or a string,
because these latter do not possess values (the exception is the
procedure identifier of a procedure declaration which has an empty
formal parameter part (cf. section 5.4.1) and which defines the value
of a function designator (cf. section 5.4.4). This procedure
identifier is in itself a complete expression).
Any formal parameter may have restrictions on the type of the
corresponding actual parameter associated with it (these restrictions
may, or may not, be given through specifications in the procedure
heading). In the procedure_statement such restrictions must evidently
be observed.
. . . . . . . . . ( end of section 4.7.5. Restrictions.) <<Contents | End>>
All parameter delimiters are understood
to be equivalent. No correspondence between the parameter delimiters
used in a procedure_statement and those used in the procedure_heading is
expected beyond their number is the same. Thus the information conveyed
by using the elaborate ones is entirely optional.
The restrictions imposed on a
procedure statement calling a procedure having its body expressed in
non-Algol code evidently can only be derived from the characteristics of
the code used and the intent of the user and thus fall outside the scope
of the reference language.
. . . . . . . . . ( end of section 4.7. Procedure statements) <<Contents | End>>
. . . . . . . . . ( end of section 4. Statements) <<Contents | End>>
Declarations serve to define certain properties of the quantities used
in the program, and to associate them with identifiers. A declaration
of an identifier is valid for one block. Outside this block the
particular identifier may be used for other purposes (cf. section
4.1.3).
Dynamically this implies the following: at the time of an entry into a
block (through the begin since the labels inside are local and
therefore inaccessible from outside) all identifiers declared for the
block assume the significance implied by the nature of the declarations
given. If these identifiers had already been defined by other
declarations outside they are for the time being given a new
significance. Identifiers which are not declared for the block, on the
other hand, retain their old meaning.
At the time of an exit from an block (through end, or by a go to
statement) all identifiers which are declared for the block lose their
local significance.
A declaration my be marked with the additional declarator own.
This has the following effect: upon a reentry into the block, the values
of own quantities will be unchanged from their values at the last exit,
while the values of declared variables which are not marked as own are
undefined. Apart from labels and formal parameters of procedure
declarations and with the possible exception of those for standard
functions (cf. sections 3.2.4 and 3.2.5) all identifiers of a program
must be declared. No identifier may be declared more than once in any
one block head.
- declaration::= type_declaration | array_declaration | switch_declaration | procedure_declaration.
- type_list::= simple_variable | simple_variable , type_list.
- type::= real | integer | Boolean.
- local_or_own_type::= type | own type.
- type_declaration::= local_or_own_type type_list.
integer p, q, s
own Boolean Acryl, n
Type declarations serve to declare certain
identifiers to represent simple variables of a given type. Real
declared variables may only assume positive or negative values including
zero. Integer declared variables may only assume positive and negative
integral values including zero. Boolean declared variables may only
assume the values true and false.
In arithmetic expressions any position which can be occupied by a real
declared variable may be occupied by an integer declared variable.
For the semantics of own, see the fourth paragraph of section 5
above.
. . . . . . . . . ( end of section 5.1. Type declarations) <<Contents | End>>
- lower_bound::= arithmetic_expression.
- upper_bound::= arithmetic_expression.
- bound_pair::= lower_bound colon upper_bound.
- bound_pair_list::= bound_pair | bound_pair_list comma bound_pair.
- array_segment::= array_identifier l_bracket bound_pair_list r_bracket | array_identifier comma array_segment
- array_list::= array_segment | array_list comma array_segment
- array_declaration::= array array_list | local_or_own_type array array_list
array a, b, c [7:n, 2:m], s [-2:10]
own integer array A [ if c<0 then 2 else 1:20]
real array q [-7:-1]
An array declaration declares one or several
identifiers to represent multidimensional arrays of subscripted
variables and gives the dimensions of the arrays, the bound of the
subscripts, and the types of the variables.
The subscript bounds for any array are
given in the first subscript bracket following the identifier of this
array in the form of a bound pair list. Each item of this list gives
the lower and upper bound of a subscript in the form of two arithmetic
expressions separated by the delimiter :. The bound pair list gives the
bounds of all subscripts taken in order from left to right.
The dimensions are given as the number of entries
in the bound pair list.
All arrays declared in one declaration are of the same
quoted type. If no type declarator is given the type real is
understood.
. . . . . . . . . ( end of section 5.2.3. Semantics of array declarations.) <<Contents | End>>
The expressions will be evaluated in the same way as subscript
expressions (cf. section 3.1.4.2).
The expressions can only depend on variables and procedures
which are non-local to the block for which the array declaration is
valid. Consequently in the outermost block of a program only array
declarations with constant bounds may be declared.
An array identifier id defined only when the values of all
upper subscript bounds are not smaller than those of the corresponding
lower bounds.
The expressions will by evaluated once at each entrace into
the block.
. . . . . . . . . ( end of section 5.2.4. Lower upper bound expressions.) <<Contents | End>>
The identity of a
subscripted variable is not related to the subscript bounds given in the
array declaration. However, even if an array is declared own the
values of the corresponding subscripted variables will, at any time, be
defined only for those of these variables which have subscripts within
the most recently calculated subscript bounds.
. . . . . . . . . ( end of section 5.2. Array declarations) <<Contents | End>>
- switch_list::= designational_expression | switch_list , designational_expression
- switch_declaration::= switch switch_identifier ":=" switch_list
switch S:=S1,S2,Q[m], if v>-5 then S3 else S4
switch Q:=p1,w
A switch declaration defines the set of values of
the corresponding switch designators. These values are given one by one
as the values of the designational expressions entered in the switch
list. With each of these designational expressions there is associated
a positive integer, 1, 2, ..., obtained by counting the items in the
list from left to right. The value of the switch designator
corresponding to a given value of the subscript expression (cf. section
3.5. Designational expressions) is the value of the designational
expression in the switch list having this given value as its associated
integer.
An expression in
the switch list will be evaluated every time the item of the list in
which the expression occurs is referred to, using the current values of
all variables involved.
If a switch designator occurs outside the
scope of a quantity entering into a designational expression in the
switch list, and an evaluation of this switch designator selects this
designational expression, then the conflicts between the identifiers for
the quantities in this expression and the identifiers whose declarations
are valid at the place of the switch designator will be avoided through
suitable systematic changes of the latter identifiers.
. . . . . . . . . ( end of section 5.3. Switch declarations) <<Contents | End>>
- formal_parameter::= identifier .
- formal_parameter_list::= formal_parameter | formal_parameter_list parameter_delimiter formal_parameter.
- formal_parameter_part::= empty | l_paren formal_parameter_list r_paren.
- identifier_list::= identifier | identifier_list comma identifier.
- value_part::= value identifier_list semicolon | empty.
- specifier::= string | type | array | type array | label | switch | procedure | type procedure.
- specification_part::= empty | specifier identifier_list semicolon | specification_part specifier identifier_list.
- procedure_heading::= procedure_identifier formal_parameter_part semicolon value_part specification_part.
- procedure_body::= statement | code.
- procedure_declaration::= procedure procedure_heading procedure_body | type procedure procedure_heading procedure_body.
procedure Spur (a) Order: (n); value n;
array a; integer n; real s;
begin integer k;
s:=0;
for k:=1 step 1 until n do s:=s+a[k,k]
end
procedure Transpose (a) Order: (n); value n;
array a; integer n;
begin real w; integer i, k;
for i := 1 step 1 until n do
for k := 1+i step 1 until n do
begin w:=a[i,k];
a[i,k]:=a[k,i];
a[k,i]:=w
end
end Transpose
integer procedure Step (u); real u;
Step:=if 0<=u/\u<=1 then 1 else 0
procedure Absmax (a) Size: (n, m) Result: (y) Subscripts: (i, k);
comment The absolute greatest element of the matrix a, of size n by m
is transferred to y, and the subscripts of this element to i and k;
array a; integer n, m, i, k; real y;
begin integer p, q;
y := 0;
for p:=1 step 1 until n do for q:=1 step 1 until m do
if abs(a[p,q]])>y then begin y:=abs(a[p,q]);
i:=p; k:=q end end Absmax
procedure Innerproduct (a, b) Order: (k, p) Result: (y); value k;
integer k, p; real y, a, b;
s:=0;
for p:=1 step 1 until k do s:=s+a*b;
y:=s
end Innerproduct
A procedure declaration serves to define the
procedure associated with a procedure_identifier. The principal
constituent of a procedure declaration is a statement or a piece of
code, the procedure_body, which through the use of procedure_statements
and/or function designators may be activated from other parts of the
block in the head of which the procedure declaration appears.
Associated with the body is a heading, which specifies certain
identifiers occurring within the body to represent formal parameters.
Formal parameters in the procedure_body will, whenever the procedure is
activated (cf. section 3.2. Function designators and section 4.7.
Procedure statements) be assigned the values of or replaced by actual
parameters. Identifiers in the procedure_body which are not formal will
be either local or non-local to the body depending on whether they are
declared within the body or not. Those of them which are non-local to
the body may well be local to the block in the head of which the
procedure declaration appears. The procedure_body always acts like a
block, whether it has the form of one or not. Consequently the scope of
any label labelling a statement within the body or the body itself can
never extended beyond the procedure_body. In addition, if the
identifier of a formal parameter is declared anew within
the procedure_body (including the case of its use as a label in section
4.1.3), it is thereby given a local significance and actual parameters
which correspond to it are inaccessible throughout the scope of its
inner local quantity..
5.4.4. Values of function designators.
For a procedure declaration to
define the value of a function designator there must, within the
procedure declaration body, occur one or more explicit assignment
statements with the procedure_identifier in a left part; at least one of
these must be executed, and the type associated with the procedure
identifier must be declared through the appearance of a type declarator
as the very first symbol of the procedure declaration. The last value
so assigned is used to continue the evaluation of the expression in
which the function designator occurs. Any occurrence of the procedure
identifier within the body of the procedure other than in a left part in
an assignment statement denotes activation of the procedure.
5.4.5. Specifications.
In the heading a specification part, giving
information about the kinds and types of the formal parameters by means
of an obvious notation, may be included. In this part no formal
parameter may occur more than once. Specification of formal parameters
called by value (cf. section 4.7.3.1) must be supplied and
specifications of formal parameters called by name (cf. section
4.7.3.2) may be omitted.
It is understood that the procedure
body may be expressed in non-Algol language. Since it is intended that
the use of this feature should be entirely a question of hardware
representation, no further rules concerning this code language can be
given within the reference language.
. . . . . . . . . ( end of section 5.4. Procedure declarations) <<Contents | End>>
. . . . . . . . . ( end of section 5. Declarations) <<Contents | End>>
- [Omitted]
. . . . . . . . . ( end of section Examples) <<Contents | End>>