APL programming language

APL (for A Programming Language, or sometimes Array Processing Language) is a programming language invented in 1962 by Kenneth E. Iverson while at Harvard University. Iverson received the Turing Award in 1979 for his work.

"APL, in which you can write a program to simulate shuffling a deck of cards and then dealing them out to several players in four characters, none of which appear on a standard keyboard."

— David Given

Within its chosen domain, APL is an extremely powerful, expressive and concise programming language. It was originally created as a way to express mathematical notation in a rigorous way that could be interpreted by a computer. It is easy to learn but APL programs can take some time to understand. Unlike traditional structured programming languages, code in APL is typically structured as chains of monadic or dyadic operators acting on arrays. Because APL has so many nonstandard operators, APL does not have operator precedence. The original APL did not have control structuress (loops, if-then-else), but the array operations it included could simulate structured programming constructs. For example, the iota operator (which yields an array from 1 to N) can simulate for-loop iteration. APL systems are typically interactive.

The APL environment is called a workspace. In a workspace the user can define programs and data, i.e. the data values exists also outside the programs, and the user can manipulate the data without the necessity to define a program, for example:

N  .leftarrow  4 5 6 7

Assign the vector values 4 5 6 7 to N.

N+4  

Print the values 8 9 10 11

+/N

Print the sum of N, i.e. 22

The user can save the workspace with all values and programs. In any case, the programs are not compiled but interpreted.

APL is notorious for its use of a set of non-ASCII symbols that are an extension of traditional arithmetic and algebraic notation. These cryptic symbols, some have joked, make it possible to construct an entire air traffic control system in two lines of code. Because of its condensed nature and non-standard characters, APL has sometimes been termed a "write-only language", and reading an APL program can feel like decoding an alien tongue. Because of the unusual character set, many programmers used special APL keyboards in the production of APL code. Nowadays there are various ways to write APL code using only ASCII characters.

Iverson designed a successor to APL called J which uses ASCII "natively". So far there is a sole single source of J implementations: http://www.jsoftware.com/ Other programming languages offer functionality similar to APL. A+ is an open source programming language with many commands identical to APL.

Here's a "Hello World" program in APL:

'Hello World'

Here's how you would write a program that would sort a word list stored in vector X according to word length:

X[X+.¬' ';] 

Here's a program that find all prime numbers from 1 to N:

(.tilde N .contains N .circle . .product N)/N .leftarrow 1 .downarrow .iota N

Here's how to read it, from right to left:

1. .iota N creates a vector containing integers from 1 to N (if N = 6 at the beginning of the program, .iota N is {1, 2, 3, 4, 5, 6}
2. Drop first element of this vector (.downarrow function), i.e. 1. So 1 .downarrow .iota N is {2, 3, 4, 5, 6}
3. Set N to the vector (.leftarrow, assignment operator)
4. Generate outer product of R multiplied by R, i.e. a matrix which is the multiplication table of R by R (.circle . .product function)
5. Build a vector the same length as N with 1 in each place where the corresponding number in N is in the outer product matrix (.contains, set inclusion function), i.e. {0, 0, 1, 0, 1}
6. Logically negate the values in the vector (change zeros to ones and ones to zeros) (.tilde, negation function), i.e. {1, 1, 0, 1, 0}
7. Select the items in N for which the corresponding element is 1 (slash function), i.e. {2, 3, 5}

Here's the equivalent in Perl (another "write-only" language):

perl -le '$_ = 1; (1 x $_) !~ /^(11+)\\1+$/ && print while $_++'

References

• A Programming Language (1962), by Kenneth E. Iverson
• History of Programming Languages, chapter 14

External links: [http://www.bath.ac.uk/~ma1flfs/cm20168/ - APL - A Programming Language], Free APL Compiler