The continuing controversy over the esoteric functions and difficult
readability of APL is caused by a failure to realize the unique combination of
(1) a concise notation,
(2) an interpreter rather than a compiler, and
(3) restricted workspaces has resulted in advantages and disadvantages
that cannot be foreseen by considering each characteristic separately.
Using an interpreter means that each time a line is encountered it must
be translated into machine language.
If algorithms are written in the standard looping fashion,
a lot of CPU time is generated just for interpretation.
Concise APL notation, however, often permits
one to write expressions that eliminate
this looping for the interpreter.
But the result is an unorthodox expression which is not readily
When this situation is combined with a workspace limitation
of 30K or 60K, and perhaps pressure to get results quickly,
it is not hard to realize why documenting a function that takes
less than 15 characters to express in APL is resisted by APL programmers.
This is especially true when the documentation may require over 10 lines
of comment within the function,
as well as auxiliary explanations.
The enclosed function acc is a perfect example.
acc expresses in less than 15 characters what is required.
But even 16 comment lines and 25 lines of auxiliary explanation do not
give a full appreciation of the power of acc . acc
can be used anywhere that you derive an expression of
the form f[t]←(f[t-1]×i[t])+d[t] for t
taking the values 2, 3, 4,
and f given. d and i
can be vectors derived in very complex ways.
Furthermore, acc will also give all
values f[t] of the
form f[t]←(f[t-1]+d[t])×i[t] simply by
writing (d×i) acc i instead
of d acc i .
acc was timed on an IBM 370/168 and
used less than 15% of the CPU that the standard
looping method required for vectors 31 elements long.
This saving results from the fact that APL has a concise
notation and an interpreter.
The saving increases with the length of vectors used
and is enough to warrant use by APL programmers.
A programmer must be concerned about three things:
(1) base programming time,
(2) CPU time, and
(3) documentation time.
By base programming time I mean the time taken to write
and debug programs with no documentation.
Base programming in APL is at least 2½ times
faster than in any other language and significantly
faster still when done by an expert in APL.
This is APL’s great advantage and is widely publicized.
CPU time is a concern if you want to maximize resources,
have a lot of users,
or have a relatively slow computer,
and compact functions like acc
should be used.
Documentation is APL’s biggest and most vexing problem.
There is a greater need for documentation in APL than in languages
such as Fortran, simply because functions like acc
do not occur in Fortran.
Since more documentation is required,
more time is required if programs are to be properly
However, the limited workspace size deters
most programmers from making adequate documentation.
I believe that this documentation problem can be greatly
lessened, if not eliminated,
by implementing three practices.
First, document functions in one workspace while
using an undocumented version to execute.
Second, have a public library of programming techniques,
standards, and gems like acc which are fully
documented and can therefore be referred to concisely.
This will save duplication of effort.
Third, when documenting functions like acc ,
always show the looping version since this is what is easiest to grasp.
|Systems Development Department|
|Sun Life Assurance Company of Canada|
|P.O. Box 6075, Montreal, Canada|
|29 December 1976|
∇ z←d acc i
 ⍝accumulated∆values ← deposits accumulation
 ⍝ does the same thing as
 ⍝ n←⍴d
 ⍝ z←,d[t←1]
 ⍝ z←z,d[t]+i[t]×z[t-1]
 ⍝ →(t<n)/over
 ⍝ a general function which gives every value f[t] of
 ⍝ where
 ⍝ d is a vector
 ⍝ i is a vector that cannot have any element
equal to zero except the last
 ⍝ element since ×\i would make every following
element equal to zero.
Let d d d d
be a vector of savings account deposits at various
times t t t t and
let i i i i be one plus the interest
earned between deposit times.
For example, if interest is 3 percent between t
and t ,
then i is 1.03 .
We also need a dummy value for i in order
to make i and d of equal length. i
can be any value except zero.
The following shows how acc calculates the answers.
which is the accumulated amount just after each deposit.
If d is 2 1 3 4
and i is 1.01 1.02 1.03 1.04
then d acc i
gives 2 3.04 6.1312 10.376448
Originally appeared in the APL Quote Quad, Volume 7, Number 4, Winter 1977.
|created: ||2015-01-20 17:10|
|updated: ||2015-01-20 20:40|