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Application, projection, and indexing


Everything in q is a value, and almost all values can be applied.

  • A list can be applied to its indexes to get its items.
  • A list with an elided item or items can be applied to a fill item or list of items
  • A dictionary can be applied to its keys to get its values.
  • A matrix can be applied its row indexes to get its rows; or to its row and column indexes to get its items.
  • A table can be applied to its row indexes to get its tuples; to its column names to get its columns; or to its row indexes and column names to get its items.
  • A function (operator, keyword, or lambda) can be applied to its argument/s to get a result.
  • A file or process handle can be applied to a string or parse tree

The domain of a function is all valid values of its argument/s; its range is all its possible results. For example, the domain of Add is numeric and temporal values, as is its range. By extension,

  • the domain of a list is its indexes; its range, its items
  • the domains of a matrix are its row and column indexes
  • the domain of a dictionary is its keys; its range is its values
  • the domains of a table are its row indexes and column names

Atoms need not apply

The only values that cannot be applied are atoms that are not file or process handles, nor the name of a variable or lambda.

In what follows, value means applicable value.

Application and indexing

Most programming languages treat the indexing of arrays and the application of functions as separate. Q conflates them. This is deliberate, and fundamental to the design of the language.

It also provides useful alternatives to control structures. See Application and indexing below.

Q for Mortals §6.5 Everything Is a Map


To apply a value means

  • to evaluate a function on its arguments
  • to select items from a list or dictionary
  • to write to a file or process handle

The syntax provides several ways to apply a value.

Bracket application

All values can be applied with bracket notation.

q)"abcdef"[1 4 3]
q)count[1 4 3]
q)ssr["Hello word!";"rd";"rld"]
"Hello world!"
q)m:("abc";"def";"ghi";"jkl")       / a matrix
q)m[3 1]                            / m is a list (unary)
q)m[0;2 0 1]                        / and also a matrix (binary)
q)main[]                            / nullary lambda

Infix application

Operators, and some binary keywords and derived functions can also be applied infix.

q)2+3                           / operator
q)2 3 4 5 mod 2                 / keyword
0 1 0 1
q)1000+\2 3 4                   / derived function
1002 1005 1009

Apply operator

Any applicable value can be applied by the Apply operator to a list of its arguments: one item per argument.

q)(+) . 2 3                         / apply + to a list of its 2 arguments
q).[+;2 3]                          / apply + to a list of its 2 arguments
q)ssr . ("Hello word!";"rd";"rld")  / apply ssr to a list of its 3 arguments
"Hello world!"
q)count . enlist 1 4 3              / apply count to a list of its 1 argument

Apply At operator

Lists, dictionaries and unary functions can be applied more conveniently with the Apply At operator.

q)"abcdef"@1 4 3
q)@[count;1 4 3]
q)d @ `cow`sheep                    / dictionary to its keys
q)@[d;`cow`sheep]                   / dictionary to its keys

Apply At is syntactic sugar: x@y is equivalent to x . enlist y.

Prefix application

Lists, dictionaries and unary keywords and lambdas can also be applied prefix. As this is equivalent to simply omitting the Apply At operator, the @ is mostly redundant.

q)"abcdef" 1 4 3
q)count 1 4 3

Postfix application

Iterators are unary operators that can be (and almost always are) applied postfix. They derive functions from their value arguments.

Some derived functions are variadic: they can be applied either unary or binary.

q)+\[2 3 4]                             / derived fn applied unary
2 5 9
q)+\[1000;2 3 4]                        / derived fn applied binary
1002 1005 1009
q)count'[("the";"quick";"brown";"fox")] / derived fn applied unary
3 5 5 3

Postfix yields infix.

Functions derived by applying an iterator postfix have infix syntax – no matter how many arguments they take.

Derived functions +\ and count' have infix syntax. They can be applied unary by parenthesizing them.

q)(+\)2 3 4
100 1005 1009
3 5 5 3

Application syntax

rank   bracket                                     other
of f   notation       Apply             Apply At   syntax        note 
0      f[]            f . enlist(::)    f@(::)               
1      f[x]           f . enlist x      f@x        f x,  x f     prefix, postfix
2      f[x;y]         f . (x;y)                    x f y         infix
3-8    f[x;y;z;…]     f . (x;y;z;…)                           

Long right scope

Values applied prefix or infix have long right scope. In other words:

When a unary value is applied prefix, its argument is everything to its right.

q)sqrt count "It's about time!"
When a binary value is applied infix, its right argument is everything to its right.
q)7 * 2 + 4

Republic of values

There is no precedence among values. In 7*2+4 the right argument of * is the result of evaluating the expression on its right.

This rule applies without exception.


The iterators are almost invariably applied postfix.

q)+/[17 13 12]

In the above, the Over iterator / is applied postfix to its single argument + to derive the function +/ (sum).

An iterator applied postfix has short left scope. That is, its argument is the value immediately to its left. For the Case iterator that value is an int vector. An iterator’s argument may itself be a derived function.

"Now" "is"  "the"  "time"
"for" "all" "good" "folk"
4 4
3 2 3 4
3 3 4 4

In the last example, the derived function count' is the argument of the second ' (Each).

Only iterators can be applied postfix.

Apply/Index and Apply/Index At for how to apply functions and index lists

Rank and syntax

The rank of a value is the number of

  • arguments it evaluates, if it is a function
  • indexes required to select an atom, if it is a list or dictionary

A value is variadic if it can be used with more than one rank. All matrixes and some derived functions are variadic.

q)+/[til 5]           / unary
q)+/[1000000;til 5]   / binary

Rank is a semantic property, and is independent of syntax. This is a ripe source of confusion.

Postfix yields infix

The syntax of a derived function is determined by the application that produced it.

The derived function +/ is variadic but has infix syntax. Applying it infix is straightforward.

q)1000000+/til 5

How then to apply it as a unary? Bracket notation ‘overrides’ infix syntax.

q)+/[til 5]           / unary
q)+/[1000000;til 5]   / binary

Or isolate it with parentheses. It remains variadic.

q)(+/)til 5           / unary
q)(+/)[1000000;til 5] / binary

The potential for confusion is even greater when the argument of a unary operator is a unary function. Here the derived function is unary – but it is still an infix! Parentheses or brackets can save us.

4 4
4 4

Or a keyword.

q)count each txt
4 4

Conversely, if the unary operator is applied not postfix but with bracket notation, the derived function is not an infix. But it can still be variadic.

q)'[count]txt             / unary derived function, applied prefix
4 4
q)/[+]til 5               / oops, a comment
q);/[+]til 5              / unary derived function, applied prefix
q);\[+][til 5]            / variadic derived function: applied unary
0 1 3 6 10
q);\[+][1000;til 5]       / variadic derived function: applied binary
1000 1001 1003 1006 1010
q)1000/[+]til 5           / but not infix
  [0]  1000/[+]til 5

Applying a unary operator with bracket notation is unusual and discouraged.


When a value of rank \(n\) is applied to \(m\) arguments and \(m<n\), the result is a projection of the value onto the supplied arguments (indexes), now known as the projected arguments or indexes.

In the projection, the values of projected arguments (or indexes) are fixed.

The rank of the projection is \(n-m\).

q)double 5                         / unary
q)halve[10]                        / unary
q)f:{x+y*z}                        / ternary
q)g 3                              / unary
q)(f . 2 3) 4
q)l:("Buddy can you spare";;"?")
q)l "a dime"                       / unary
"Buddy can you spare"
"a dime"
q)m["quick";"brown"]               / binary

The function definition in a projection is set at the time of projection. If the function is subsequently redefined, the projection is unaffected.

q)g:f[3;]   / triple
q)g 5
q)g 5       / still triple
Make projections explicit

When projecting a function onto an argument list, make the argument list full-length. This is not always necessary but it is good style, because it makes it clear the value is being projected, not applied.

q)goo:foo[2]    / discouraged
q)goo:foo[2;;]  / recommended

You could reasonably make an exception for operators and keywords, where the rank is well known.

q)f "fox"
5 2 5
q)g "\*ow\*"

When projecting a variadic function the argument list must always be full-length.

Since 4.1t 2021.12.07 projection creation from a lambda/foreign results in a rank error if too many parameters are defined, e.g.


Q for Mortals §6.4 Projection

Applying a list with elided items

A list with elided items can be applied as if it were a function of the same rank as the number of elided items.


q)("the";"quick";;"fox") @ "brown"

q)("the";;;"fox") . ("quick";"brown")

This is subject to the same limitation as function notation. If there are more than eight elided items, a rank error is signalled.


Indexing a list employs the same syntax as applying a function to arguments and works similarly.

q)show m:4 3#.Q.a



q)m[3 1;1]

q)m[3 1;]       / eliding an index means all positions

q)m[3 1]        / trailing indexes can be elided

q)m 3 1         / brackets can be elided for a single index

q)m @ 3 1       / Index At (top level)

q)m . 3 1       / Index (at depth)

q)m . (3 1;1)   / Index (at depth)

Indexing out of bounds

Indexing a list at a non-existent position returns a null of the type of the first item/s.

q)(til 5) 99
q)(`a`b`c!1.414214 2.718282 3.141593) `x

name dob        sex
dick 1980.05.24 m
jane 1990.09.03 f
q)t 2
name| `
dob | 0Nd
sex | `

name city | eye   sex
----------| ---------
Tom  NYC  | green m
Jo   LA   | blue  f
Tom  Lagos| brown m
q)kt `Jack`London

The thing and the name of the thing

What’s in a name? That which we call a rose
By any other name would smell as sweet;
Romeo and Juliet

In all of the above you can use the name of a value (as a symbol) as an alternative.

q)f[5;3]              / the rose
q)`f[5;3]             / the name of the rose
q)`f . 5 3
q)`g 3

This applies to values you define in the default or other namespaces. It does not apply to system names, nor to names local to lambdas.

Application and indexing

The conflation of application and indexing is deliberate and useful.

q)(sum;dev;var)[1;til 5]

Above, the list of three keywords is applied to (indexed by) the first argument, selecting dev, which is then applied to the second argument, til 5.

Q for Mortals §6.8 General Application