Wiki: K

K is like APL with fewer built-ins. The syntax is ASCII-only, and most built-in functions are heavily overloaded single bytes of ASCII punctuation.

There are several implementations with subtly varying behavior. code.golf uses ngn/k, which is documented with the reference card found under "help" at the online interpreter. If you're new to K (and J, APL, etc...), this style of documentation might not be very helpful, but other learning material is available:

Razetime has put together an extensive tutorial which introduces the language in multiple chapters, and then spends some time on solving larger tasks (including a Sudoku solver!).
If you're looking for something in between the ref-card and a full blown tutorial, Stefan Kruger's kbook might be a good a fit.
Another implementation of a similar K version is oK which comes with a more extensive manual

Example

Let's look at a program that outputs all of the input arguments with their length appended to them: `0:{x,$#x}'x

(Try it on United States: it outputs Nebraska8 Rhode Island12…)

`0:{x,$#x}'x
           x    Get the list of inputs.
   {     }'     Apply some lambda function to each input.
                ({} makes a lambda, and the adverb ' means each.)
    x   x       Inside a monad lambda, "x" refers to the single argument.
       #        Monad # means "length"
      $         Monad $ means "convert to string"
     ,          Dyad , means "concatenate"
`0:             Output the list of strings line by line.
                0: is a dyadic writing-lines-to-a-file verb,
                and the left argument ` (the empty symbol) means "write to STDOUT".

You can see that K is essentially read and written "right-to-left", much like J and APL. x,$#x means (x,($(#x))). There's no operator precedence.

Golf tips

\ preceded by a space is "trace" (an identity function for debugging that prints its argument to STDOUT). This can be shorter than using `0:. Trace however passes its argument through the K formatter before printing, so this may only be useful for numbers.
$[x;T;F] can become x{T}/F when x is a non-negative integer, or (F;T)x if x is 0/1 and lazy evaluation is not needed.
x in the global scope is a list of the command line args.
Folds can take an optional left argument to use as a seed value. This can often save a byte: 1-+/x → 1-/x, "1.",,/$x → "1.",/$x, ...
Calling primitives with brackets can sometimes save a byte on parentheses: ((A)+B),C -> +[A;B],C (assume A, B and C are longer expressions).
Strings are sequences of (signed) bytes and can be used in place of a list of small integers in many cases.
Each type has its own null value which indicates a missing value, for example not found in the result of find, or out-of-bounds indexing:

Type	Null	Meaning
int	`0N`	$-2^{63}$
float	`0n`	NaN
char	`" "`	space
function	`::`	identity function
symbols	`	empty symbol

Base Conversion

These come up a lot, almost in every other problem. A few ideas can be found on the APL tips and J tips page on StackExchange, so here is a quick translation table:

	K	J	APL
Convert from base	`/`	`#.`	`⊥`
Convert to base	`\`	`#:` or `#.inv`	`⊤` or `⊥⍣¯1`

n\ combined with strings is very effective at compressing sequences of integers. Example:

28+,/4\">>/"  / days in a month (the string is `c$62 11 62 47)

0/x gets the last value of x. Compared to *|x, it can be combined with other adverbs, e.g. 0/' (last of each), and it returns 0 instead of 0N for an empty x.
n/"..." is a good starting point for a string hash.

Undocumented Features

The reference card included with ngn/K skips on a few later additions to the language.

Case

This overload of ' combines multiple vectors using a selection list. The operand is a list of integers in $[0,n)$, the derived function takes $n$ lists of the same length. For each index, Case picks a value from the list specified by the selection. This function is taken from K4, see the KX documentation.

  0 2 1 1 0'["ABCDE"; "abcde"; "01234"]
"A1cdE"
  / with n=2 case can be called infix:
  0 1 2 3 4(0 0 1 1 1)'100 101 102 103 104
0 1 102 103 104

Recurrence

An extension to \ and / (both n-do and while). Instead of operating on just the last value, an operand function with $n$ arguments accesses the $n$ previous values. Instead of passing a single seed value, you'll have to pass $n$ seed values. As an example, we use a recurrence relation to compute triangular numbers:

$$ T_n = 3T_{n-1}-3T_{n-2}+T_{n-3} \qquad T_0=0, T_1=1, T_2=3. $$

  / T_0 to T_10
  {(3*z-y)+x}\[10;0;1;3]
0 1 3 6 10 15 21 28 36 45 55
  / first triangular number larger than 1000
  {(3*z-y)+x}/[~1000<;0;1;3]
1035

Internal Functions

0: and 1: are used for input and output, and 2: for loading shared libraries. But 3: to 5: can also be called, even though they are intended to be internal representation of combinations the interpreter automatically optimizes.

3: gets the last value, equivalent to *|:
4: finds the index of the minimum (*<:)
5: finds the index of the maximum (*>:)

Using these over the two-primitive combinations saves bytes if you combine them with adverbs, e.g. 4:'x, 5:/x, ...

`.x`

Monadic . does something for all types, not everything documented. I'd recommend just trying it for different inputs to see what happens. Relevant for golfing could be (.x) ~ x for numbers and simple lists of numbers, and (.x) ~ (*x).1_x for nested and mixed type lists.

External resources

Matrix chat room specifically for ngn/k,
The APL Farm has a room for K discussion,
The K tree, a StackExchange chatroom about K. (inactive)
Tips for golfing in K,
A gist implementing the arithmetic operations required to solve the constant holes.