Rexx is used as a command language for operating, dialog,
database management, network systems, as a scripting language for automating
and integrating applications in these systems and as a macro language for
arbitrary application programs. In this article I would like to show that
Rexx is an interesting high-level programming language, too. This is an
original introduction. I will concentrate only on features of the language
Rexx which are not included, in whole, in the others programming languages.
Instead the chapter "Types, Constants and Variables"
Declarations or types are missing in Rexx programs because:
  • All data are in the form of strings of characters.
  • The meaning of a constant depends entirely on its usage. Operations are
    applicable on the basis of instantaneous values.
  • A variable is a symbol that represents a value. Variables are considered
    to be varying-length character strings allowed to hold any binary value
    of any length between zero and an implementation maximum (the length of
    the evaluated result of an expression is limited by the available storage).
    Variables are automatically initialized at their first use. A variable which
    has not been assigned a value is not initialized. It will contain the default
    value of the symbol, which is the symbol's own name in uppercase letters.
  • If the characters in a string form is a valid number, optionally with
    leading or trailing blanks, that string may participate in arithmetic
    operations. Numbers may be specified in exponential
    notation if desired.
  • The numeric instruction may be used to select the arbitrary
    precision of calculations, which, for example, may calculate with 1000
    or more significant digits.
Precision of Calculation
How many digits are in N-factorial? And the first thirteen are? For N equals
16 we compute 16-factorial, then we add of number of digits and finally
we read the first 13 digits from the left. And for N equals 1000? The
program UHLER displays answer on a screen by the say instruction.

/* UHLER */

Factorial = NFACT(1000)

say "Number of digits =" LENGTH(Factorial)

say "The first thirteen =" LEFT(Factorial, 13)
The blank character followed the constant "Number of digits =" is the blank
that concatenates two data strings together with a blank between them. The
program is so short because I used the built-in functions (a rich set of functions
supplied with the language) LEFT and LENGTH. But the
function NFACT is not the
built-in function. If anyone didn't write it, we had to write this function ourself:

/* NFACT - computing of factorials */

N = ARG(1)

numeric digits 3000

Nfactorial = 1

do J = 2 to N

Nfactorial = Nfactorial * J


return Nfactorial
The ARG(number) built-in function returns the value of a
specific argument.
If the text of the NFACT function is saved on disk,
then this
file is an external function. When we add to the text of the
UHLER program following rows:


NFACT: procedure

and the text of the NFACT function, then NFACT is
an internal function.
The exit instruction terminates immediately the UHLER program. The procedure instruction, without the keyword expose,
prevents the
subroutine from knowing anything about the caller's variables and vice versa.
The UHLER program displays on a screen:

Number of digits = 2568

The first thirteen = 4023872600770
In the solution of the fourth exercise in the chapter 1.2.5 of The Art of
Computer Programming
, Vol. 1, Donald E. Knuth notes that Horace S. Uhler
was the first who examined the exact value of 1000!. His
result was published in the journal Scripta Mathematica 21 (1955),
pp. 266-267, it begins: 402 38 726 00 770 ...

Exercise 1

The ** (power) operator raises a number to a whole power, which may be positive or negative. How many digits
has nine to the ninth to the ninth, i.e. 9 ** (9 ** 9)?
Work with Words
When a Rexx program deals with words, it always means a list of
blank-delimited tokens in a string. A work with words is facilitated by
built-in functions and by the parse instruction. For example, the
WORDS(string) function returns the number words in
I would like to demonstrate the WORDS function by the modified G. G. Berry's paradox: The phrases of a language
that refer to numbers can be ordered, alphabetically and according to length.
There will be a definite set of integers named by those phrases of less than
any given length. In particular there will be some integer which is the least
integer not namable in fewer than eleven words. The phrase "the least integer
not namable in fewer than eleven words" is the definition of a natural number.
If in the variable Sentence is stored this definition:
"the least integer not namable in fewer than eleven words"
then the WORDS(Sentence) function returns the number of words
in Sentence. Check it with the say WORDS(Sentence) instruction.
I think, that the result compels everybody to re-count carefully
number of words in Sentence!

But what if a delimiter is a different character from blank (also called a space character)?
Suppose, that any character is stored in the Delimiter variable.
character is the delimiter of words. Then following fragment of a program
writes all words of the Sentence variable in this common case:

Db = Delimiter || " "; Bd = REVERSE(Db)

Sentence = TRANSLATE(Sentence, Db, Bd)

do J = 1 to WORDS(Sentence)

say TRANSLATE(WORD(Sentence, J), Db, Bd)

We use the || operator to force concatenation without a blank.
The WORD(string, number) function returns a specific
word from a string.
The REVERSE(string) function returns the input string with the characters
reversed end-for-end. Can you remember A Tale Of The Ragged
by E.A.Poe? ... for Bedloe, without the e, what is it but
Oldeb conversed!

The following program BEDLO displays
OLDEB on a screen.

/* BEDLO */ say REVERSE(LEFT(Bedloe, 5))

The TRANSLATE(string, cipher_alphabet,
plain_alphabet) function replaces
every occurence of a character from the plain_alphabet in the string by the corresponding character from the cipher_alphabet (i. e. simple substitution cipher). When in the Parchment variable
will stored the cryptogram of Captain Kidd starting with a
string 53++!305))6*; then the following instruction:

say TRANSLATE(Parchment, ,/* to be continued */

"adeghinortlsbpvwmuycf", "5!8346*+(;0)2.']9?:-1")

bring us the solution of this enigma (Edgar Allan Poe - The Gold-Bug)
starting with agoodglassint.
The interpret instruction
The interpret expression instruction executes one or more
instructions that are generated as the value of an expression.
A useful instrument for learning and teaching of the
language Rexx is a simple variation on the program REXXTRY from a manual:

/* USHER */

do forever

say 'Enter Rexx instructions:'

parse pull String_of_Instructions

call INTERPRETATION String_of_Instructions


/* INTERPRETATION subroutine */


interpret ARG(1)


The parse pull String_of_Instructions instruction stores a line of input read
from the standard input stream (assume the keyboard) to the String_of_Instructions variable and the interpret instruction this fragment executes. We
can write:

if RANDOM(1, 2) = 1 then say "Head"; else say "Tail"

The following fragment hepls us understand
evaluating expressions and built-in functions:

do until Exp = ""; say "?"; parse pull Exp; interpret "say" Exp; end

The example of a possible conversation follows:


1 + (2 * 12)



"[" || SPACE(" Edgar Allan Poe ") || "]"

[Edgar Allan Poe]

Note, that variables, as the Exp variable, can come and go (using
the drop Exp instruction) dynamically. Names of variables can be generated at run time, using all
power of expression evaluation of the language. The procedure instruction, in
the INTERPRETATION subroutine, creates a local environment and a
name of
a variable is created and existed only during an execution of the subroutine.
The scope of variables is controlled by the procedure instruction.
If a routine is declared with the procedure instruction, only
those variables exposed using the expose instruction are
available to
the routine. The first instruction of the INTERPRETATION subroutine

INTERPRETATION: procedure expose Global

allows to see a value of the Global variable in a next subroutine

Try imagine an action of an interpreter, when a string:

/* A Descent Into The Maelström */ interpret ARG(1)

is stored (from a keyboard) into the String_of_Instructions variable.

Exercise 2

How can be ended the infinite loop in USHER?

Exercise 3

F. M. Whyte's system of classification is used to describe the wheel
arrangement of conventional steam locomotives. In this system, the first
number is the number of leading wheels, and the last is the number of
trailing wheels. The middle number (or numbers) gives the number and
arrangement of drivers. For instance the wheel arrangement of the Santa Fe
steam locomotive class 3700, built 1917, can be described as 4-8-2 (look at
the figure).
Santa Fe 3700 (4-8-2) has 14 wheels
Please, write only one instruction to determine
a number of wheels from the description of the wheel arrangement stored in
the Arrangement variable and to display of a result on the screen.
The SOURCELINE function
Ken Thompson in his paper Reflection on Trusting Trust, CACM,
August 1984, Vol. 27, No 8, pp. 761-763 writes:
In college, before video games, we would amuse ourselves by posing
programming exercises. One of the favorites was to write the shortest
self-reproducing program... More precisely stated, the problem is to write a
source program that, when ... executed, will produce as output an exact copy
of its source
. The solution in Rexx follows:

/**/say SOURCELINE(1)

The SOURCELINE(number) function returns
the specified line of the program's source code. The SOURCELINE()
function returns number of lines in the program. Assume that we need display
on a screen the message:


| Important message |


We can write a program including three instructions say. An
advantage of the
most complicated program ATTENTION we will appreciate after many changes
of the message.



| Important message |



do J = 2 while SOURCELINE(J) <> "*/"



Rows of a program can be data as well.
Multiple Exits and sparse array
G. V. Bochmann argued a usefulness of this kind of control flow on
the example: Given a vector V of n integers, and an integer I; if I is one
of the integers in V, print its order in V; otherwise print "non in V"
Bochmann: Multiple Exits from a Loop Without the GOTO, CACM,
July 1973, Vol.
16, No 7, pp. 443-444).
Forteen years later F. Rubin submitted a letter-to-CACM form titled: "'GOTO Considered Harmful' Considered Harmful" (CACM, March 1987, Vol.
30, No 3, pp. 195-196) and reopened the discussion by showing a clearcut
instance where GOTOs significantly reduce program complexity.
His example:
"Let X be an N x N matrix of integers. Write a program that will print the
number of the first all-zero row of X, if any."

May be in the year 2001 (1987 + 14) I will read a paper dealing with advantages
of a miserable traveling with GOTO that will include the following example:
"Let X be an N x N x N threedimensional array of integers. Find the number
of the first all-zero matrix of X, if any." The following ODYSSEY program
shows the solution now.


N = 100; X. = 0

X.1.1.1 = 1; X.2.94.15 = 1; X.3.16.8 = 1

X.4.5.2 = 1; X.5.16.30 = 0; X.6.86.3 = 1

do I = 1 to M

do J = 1 to N

do K = 1 to N

if X.I.J.K <> 0 then iterate I



leave I


if I<=M then say "The first all-zero matrix in X is" I

else say "Non all-zero matrix is in X"

The iterate I instruction causes control to pass to the top of an
do-group with the I control variable. The I control
variable will be
incremented appropriately and the terminating conditions will be tested as
if the end instruction closing the do-group had been encountered.
The leave I instruction causes control to pass to the instruction
following the end of an iterative do-group with the I control variable.
These structures and their variants conform to programs for which transfers of control
can only be made to the end or beginning of an enclosing control loop (see the following figure).

do-while/until-leave/iterate-end structures

Associative arrays
Rexx has one easy-to-use facility for building higher-level data
structures such as arrays - the compound variable. A name of compound variable has
two parts: a stem and a tail. A stem is like any other variable name
except that it ends in a period. A tail is a string of one or more symbols.
When the tail is made up of more than one symbol, each symbol is separated
from the next by a period. When Rexx retrieves the value of a compound
variable it first generates a derived variable name. The name is derived by
replacing any simple variables in the tail name by their values. The value
of the compound variable is then the value associated with the derived name.
You can set all possible compound variables derived from a given stem by
assigning a value to the stem, for example

X. = 0

After setting a stem variable this way, a reference to any compound variable
with that stem to which you do not assign another value will return the
value zero. Note, that X array in the ODYSSEY program
is a sparse array,
only six elements allocate memory.

Given a document and a natural number K, display on a screen all words
occur at least K-times in the document. The following internal subroutine
provides the answer:

/* K_TIMES subroutine */

K_TIMES: procedure expose Document K

Times. = 0

do J = 1 to WORDS(Document)

Oneword = WORD(Document, J)

Times.Oneword = Times.Oneword + 1

if Times.Oneword = K then say Oneword



The Times array using a non-numeric subscript. Note, that it does
not have
to declare the size of the Times array.
Why learn Rexx?

It is a portable language across platforms (for a proof look at the home
page of the creator of the Rexx language - M. F. Cowlishaw).

Instructions do-(iterate, leave)-end, numeric, interpret, parse, built-in
functions, compound variables, recursion, allow complex algorithms to be
expressed in simple programs.

Simple programs make useful prototypes.

I use Rexx as an environment for design and testing algorithms as in my article FIND, SELECT, MODIFIND.

Compound variables can represent many data structures quite naturally
(one and multidimensional arrays using a numeric or non-numeric subscript,
structures, stacks and queues, lists, symbol tables, graphs).

It is suitable for learning and teaching programming, compiler
construction (look at my implementation of the Universal Turing Machine)
etc. Album of Algorithms and Techniques proves that the Rexx language is the suitable vehicle to writing useful,
educational, and entertaining routines, translating from excellent texts,
in clean, succint, and uniform code.
All magics of the language REXX are
results of a
consistent application of only a few, ingeniously chosen
general features. Can you remember of The Fall Of The House
Of Usher
"I have just spoken of that morbid condition of the auditory
nerve which rendered all music intolerable to the sufferer,
with the exception of certain effects of stringed instruments.
It was, perhaps, the narrow limits to which he thus confined
himself upon the guitar, which gave birth, in great measure,
to the fantastic character of his performances."
Solutions of the excercises
1. The following HOWMANY program

/* HOWMANY */ say 9 ** (9 ** 9)

displays on a screen 4.28124773E+369693099, so 9**(9**9) has 369 693 100
2. Syntax error, user interrupting, interpretation of the exit instruction.

3. If in the Arrangement variable is stored "4-8-2" then the following instructrion displays
the number of wheels, i.e. 14:

interpret "say -(-" Arrangement ")"

What is pronunciation of the word "Rexx"?

Gerard Shildberger from Hankinson, North Dakota, wrote me: REXX is pronounced as "hex" would with an "R". Also, rhymes with flex or lex. The REXX language was originally
called REX, but because of a copyright conflict with another (software)
program, an "X" was added, and it became REXX.

Notes and Acknowledgments.
first version of my "An Introduction ..." was published in the Czech journal
Softwarove noviny, Vol. 6, No. 12 (1995), 114-118. I used for translation my emails
in Archive of REXXLIST REXX & E. A. Poe 98/10/09, Complements to Words, words, words 98/10/26 and the English texts:

M. F. Cowlishaw: The REXX Language - A Practical Approach to Programming

Prentice-Hall, inc., Engelwood Cliffs, New Jersey 1985

J. Bentley: Associative Arrays

CACM, Vol. 28, No. 6 (June 1985),

F. Clarke: Words, words, words...

The RexxLA Newsletter, October 1998, Issue 199810

Helps from Personal REXX for Windows (TM)

Version 3.50, Quercus System

H. F. Ledgard, M. Marcotty: A Genealogy of Control Structures

CACM, Vol. 18,
No. 11 (November 1975), 629-639

The Article is a part of Vladimir Zabrodsky´s great website