A programming language

What Hacker News says

1. adrian_bJul 2025
   The popularity of a convention has no relationship with its usability.

   Everybody learns in school the traditional convention for writing mathematical expressions.

   It appears that for most people it is difficult or impossible to unlearn later such a convention, even if they encounter a superior convention.

   On the other hand, I am among those fewer for which this is not true, so when I have first read the book "A Programming Language" of K. Iverson, on which the later APL language and its successors have been based, I have immediately recognized that the Iverson convention is much better than the school convention, and I have no trouble in using it.

   When reading a program written with the Iverson convention, you still read from left to right, but you typically do not read until the end of the line, but only as much of the left part as necessary to understand the purpose of the line. (Because the right operand of any operator is everything that follows it until the end of the line, and the details of that computation may be irrelevant. With school notation, when searching where a variable has been modified and how, you must jump between the beginning of the line and the end of the line, to find the last operations that have generated the stored value, when reading and understanding the complete expression would be a waste of time.)

   The original motivation of the Iverson convention, which remains very important, was to give a useful meaning for a sequence of identical non-commutative operators, e.g. subtraction and division. This is particularly desirable when the operators are used in vector reductions.

   (With school notation, a0 - a1 - a2 - ... - an is seldom a useful expression, but with the Iverson convention it becomes alternate sum, which is needed very frequently. Similarly for division.)

   Show morethread
2. 082349872349872Jan 2023
   Kenneth Iverson, "A Programming Language" (1962)
   thread
3. tmcbJan 2020
   Not a very original suggestion, but the original book (“A Programming Language”, by Ken Iverson) would probably fit in.
   thread
4. avmichMar 2019
   Read "A programming language", where APL came from - https://www.amazon.com/Programming-Language-Kenneth-Iverson/... - you might get more understanding why it is the way it is.

   It is the mathematical notation, put into, as Dijkstra expressed, "technologies of the past", completed (to be Turing-complete) and made executable.

   At least, I think, this is the basic idea.

   thread
5. ofalkaedDec 2025
   This submission popping back up from the second chance pool got me to do some digging for the formal description of system/360[0], this is not the APL we know today but the APL outlined in Iverson's A Programming Language[1].

   [0] https://www.cs.trinity.edu/~jhowland/class.files.cs2321.html...

   [1] https://www.jsoftware.com/papers/APL.htm

   thread
6. toshFeb 2024

     +/1 2 3 4 5
   

   meaning

     plus over 1 2 3 4 5
   

   meaning

     the plus reduction of 1 2 3 4 5
   

   meaning

     1+2+3+4+5
   

   meaning

     15
   

   "over" (/) is a higher order function that takes the function "+" and applies it to "1 2 3 4 5"

   over can also be used with *

     */1 2 3 4 5
   

   meaning

     the product reduction of 1 2 3 4 5
   

   meaning

     120 
   

   "/" as "over" comes from a mathematical notation by Ken Iverson: APL (A Programming Language) [0][1] which Ken names "reduction" (h/t mlochbaum)

   > An operation (such as summation) which is applied to all components of a vector to produce a result of a simpler structure is called a reduction.

   "/" is known as "insert" in J [2] and "over" in k dialects (like Goal)[3].

   [0] https://en.wikipedia.org/wiki/APL_(programming_language)#Mat...

   [1] https://www.softwarepreservation.org/projects/apl/Books/APRO...

   [2] https://code.jsoftware.com/wiki/Vocabulary/slash

   [3] https://k.miraheze.org/wiki/Primitives

   Show morethread