Fun with Letter Diamonds
A recent programming challenge appeared on The Social Programmer blog: http://www.craigmurphy.com/blog/?p=1417. The idea is to create a letter 'diamond' from any given starting letter. For example the diamonds for 'D' and 'E' are:
A B B C C D D C C B B A A B B C C D D E E D D C C B B A
So far there have been entries in a number of computer languages, some of which run to many lines of code. In APL, the solution can be done in a single line:
mat⍪1 0↓⊖mat←(⌽mat),0 1↓mat←⊃(-⍳⍴letters)↑¨letters←(⎕A⍳'E')↑⎕A A B B C C D D E E D D C C B B A
I'm hoping that programmers new to APL will be intrigued and will want to explore further. You may not have an APL font installed, so here is a screenshot. If the code above doesn't look like the blue line in this screenshot you need to install a Unicode APL font before you can read the rest of this Wiki page.
To see how this works, it might be clearer to re-cast the code as a function returning an explicit result R:
∇R←LetterDiamond A;letters  letters←(⎕A⍳A)↑⎕A ⍝ Get letters, e.g. A-E  R←⊃(-⍳⍴letters)↑¨letters ⍝ Form upper-right side  R←R⍪1 0↓⊖R←(⌽R),0 1↓R ⍝ Reflect to get whole diamond ∇ LetterDiamond 'E' A B B C C D D E E D D C C B B A
Line  just gets the letters from 'A' to 'E' (say):
letters←(⎕A⍳'E')↑⎕A letters ABCDE
⎕A is the alphabet, ⎕A⍳'E' finds the position of 'E' in the alphabet (5) and 5↑⎕A gives the first five letters of the alphabet.
Line  forms the top right quadrant of the diamond:
R←⊃(-⍳⍴letters)↑¨letters R A B C D E
To break this down further, the expression -⍳⍴letters just produces the following negative numbers:
-⍳⍴letters ¯1 ¯2 ¯3 ¯4 ¯5
These numbers are used to perform a take (↑) on the letters, producing a nested vector in which each element is a character padded at the left by 0 to 4 spaces:
(-⍳⍴letters)↑¨letters A B C D E ⎕DISPLAY (-⍳⍴letters)↑¨letters ┌→──────────────────────────────┐ │ ┌→┐ ┌→─┐ ┌→──┐ ┌→───┐ ┌→────┐ │ │ │A│ │ B│ │ C│ │ D│ │ E│ │ │ └─┘ └──┘ └───┘ └────┘ └─────┘ │ └∊──────────────────────────────┘ ⍝ This is the equivalent to doing: (¯1↑'A')(¯2↑'B')(¯3↑'C')(¯4↑'D')(¯5↑'E') A B C D E
Finally the disclose ⊃ function converts this into a matrix.
Line  is responsible for forming the final diamond. First we use the reverse ⌽ function to flip the array horizontally:
⌽R A B C D E (⌽R),R AA B B C C D D E E (⌽R),0 1↓R A B B C C D D E E
Finally we repeat the process to flip the array vertically using the first axis rotate ⊖ and form the final result:
R⍪1 0↓⊖R←(⌽R),0 1↓R A B B C C D D E E D D C C B B A
If you want to learn more about APL or try running the code in an APL interpreter, see the APL Tutorial on this Wiki.