APL Idioms
In this article, I raise ten APL problems; each problem has a simple one line solution which does not involve the creation of any intermediate variable. The objective in solving such problems, for novices and experts alike, is to acquire new APL skills; if you can solve the problem without struggle, find an alternative to the first solution. In short, the solution to the problems should be an idiom: these idioms may be compiled into a Vector idiom dictionary. The solutions will be posted on the Vector website a week or so before the publication of the next issue.
1. How many elements does a given variable have?
If the monadic function CE provides the solution, it should yield the following answers:
Syntax  Answer 
CE 90  1 
CE 0 8 9/9  0 
CE 'ABC' 'DEF  2 

2 
CE ''  0 
Restriction: assume that the keyboard does not have the comma (,) symbol.
2. Is a value within a given range?
For any numeric value and a given range, return a result corresponding to the following table:
2 Value is below the minimum value.
1 Value is equal to the minimum value.
0 Value is between the minimum and maximum value.
¯1 Value is equal to the maximum value.
¯1 Value exceeds maximum value.
Result  Description 
2  Value is below the minimum value. 
1  1 Value is equal to the minimum value. 
0  Value is between the minimum and maximum value. 
¯1  ¯1 Value is equal to the maximum value. 
¯1  ¯1 Value exceeds maximum value. 
Restriction: assume that the keyboard does not have any relational operators.
3. Sort a numeric array of integers in ascending order of the number of digits.
For a character array, the solution is simple.
CA←⊃'Sun' 'Mon' 'Tuesday' 'Wed' 'Thursday' 'Fri' 'Sat' CA[⍋CA+.=' ';] Thursday Tuesday Sun Mon Wed Fri Sat
Note that the array is sorted in ascending order of the number of spaces in each row and not in any particular alphabetical order. Is this a clue or a red herring? For practice, devise a solution that ignores embedded spaces. For a numeric array, the monadic function SN provides the solution as follows:
SN 8 1⍴89 ¯78 1229 32 129 11 90232 1 1 89 ¯78 32 11 129 1229 90232
Restriction: assume that the keyboard does not have the format (⍕) or quad (⎕) symbol.
4. Return the element(s) of a numeric array indexed by its first dimension.
If the monadic function LD provides the solution, it should yield the following answers:
Syntax  Answer 
LD 6  6 
LD 98 878 332 2.3 44  44 
LD 2 3 4⍴+\24/1  13 14 15 16 17 18 19 20 21 22 23 24 
Restriction: assume that the keyboard does not have the shape of (⍴) symbol.
5. Return the sum of element(s) of a numeric array on its first dimension.
If the monadic function LS provides the solution, it should yield the following answers:
Syntax  Answer 
LD 6  6 
LS 98 878 332 2.3 44  1354.3 
LD 2 3 4⍴+\24/1  14 16 18 20 22 24 26 28 30 32 34 36 
Restriction: assume that the keyboard does not have the plus (+) symbol. I have used +\24/1 in order to ensure that I get the first 24 numbers in index origin 1: you can set ⎕io ←1 and use ⍳24 instead.
6. Convert the string representation of integers to numbers.
If the monadic function CN provides the solution, it should work as follows:
CN '898' 898 
10 ×CN '898' 8980 
CN ¨'898' '34' 898 34 
10 ×CN ¨'898' '34' 8980 340 
Restriction: assume that the keyboard does not have the execute (⍎) symbol.
7. Return a numeric array as zeros, increasing the last dimension by 1
If the monadic function ZM provides the solution, it should work as follows:
ZM 2 3 4 0 0 0 0 ZM 2 3⍴⍳6 0 0 0 0 0 0 0 0 ZM 2 3 4⍴⍳24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Restriction: assume that the keyboard does not have the times (×), take (↑), minus (), or comma (,) symbols and it does not end with ⍴0.
8. Return the first ones from a Boolean vector.
If the monadic function FO provides the solution, it should work as follows:
FO 288 68 45 67 77 90 100 13 27 0 0 0 1 0 0 0 0 1 0 0 FO 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1
Restriction: assume that the keyboard does not have the not (~) or rotate (⌽) symbols.
9. Return the last ones from a Boolean vector.
If the monadic function LO provides the solution, it should work as follows:
LO 288 68 45 67 77 90 100 13 27 0 0 0 0 0 1 0 0 0 1 0 LO 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1
Restriction: assume that the keyboard does not have the not (~) or rotate (⌽) symbols.
10. Return the elements of a numeric array found at given coordinates.
If the dyadic function RE provides the solution, it should work as follows:
⎕←A←3 4⍴78 90 22 2.3 43.9 92 12 67 23 33 88 9.34 78 90 22 2.3 43.9 92 12 67 23 33 88 9.34 ⎕←B←2 2⍴1 3 2 4 1 3 2 4 A RE B 22 67 ⎕←C←2 5 6⍴60⊢1000 554 684 485 119 559 530 193 631 783 1 838 366 380 987 986 224 269 670 572 312 314 779 160 285 168 883 895 230 361 764 763 891 592 47 51 589 705 297 689 215 208 1000 688 772 946 957 16 721 172 822 982 379 781 163 797 12 702 723 847 735 D←⊃(1 3 4) (1 5 5) (2 1 6) C RE D 224 361 589
Restrictions: assume that a looping solution is not allowed nor one involving semicolon and that index origin is 1.
If you are a developer working with APL, you should be able to propose at least three solutions or idioms in respect of the problems above. The restrictions imposed in formulating the solution should help in determining an idiom.
Subject to readers’ active participation – via correspondence with the editor – the responses will be analysed in a regular feature in future editions of Vector.