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Ontology asks, What exists?,
to which the answer is Everything.
— W.V.O. Quine, Word and Object

Aggregate function

A function that reduces its argument, typically a list to an atom, e.g. sum


As in apply a function to its arguments: evaluate a function on values corresponding to its arguments.


In the expression 10%4 the operator % is evaluated on the arguments 10 and 4. 10 is the left argument and 4 is the right argument.

By extension, the first and second arguments of a binary function are called its left argument and right argument regardless of whether it is applied infix. In the expression %[10;4] 10 and 4 are still referred to as the left and right arguments.

By extension, where a function has rank >2, its left argument is its first argument, and its right arguments are the remaining arguments.

Correspondingly, the left domain and right domain of a binary function are the domains of its first and second arguments, regardless of whether or not the function may be applied infix.

By extension, where a function has rank >2, its left domain is the domain of its first argument, and its right domains are the domains of the remaining arguments.

The terminology generalizes to iterables.

  • The left domain of a matrix m is til count m.
  • The right domain of a matrix is til count first m.
  • The right domains of a list m of depth n are 1_n{til count first x}\m.

Although unary functions may be applied prefix, the single argument of a unary function is sometimes referred to as its right argument.

Argument list

A pair of square brackets enclosing zero or more items separated by semicolons.

%[10;4]  / % applied to argument list [10;4]


A single instance of a datatype, eg 42, "a", 1b, 2012.09.15. The type of an atom is always negative.

Atomic function

An atomic function is a uniform function such that for r:f[x] r[i]~f x[i] is true for all i, e.g. signum. A function f is atomic if f is identical to f'.

Atomic functions


Attributes are metadata that apply to lists of special form. They are often used on a dictionary domain or a table column to reduce storage requirements or to speed retrieval.

# Set Attribute


An iterable of rank 2, i.e. a function that takes 2 arguments, or a list of depth ≥2. (The terms dyad and dyadic are now deprecated.)

Bracket notation

Applying an iterable to its argument/s or indexes by writing it to the left of an argument list, e.g. +[2;3] or count["zero"].


Character constant

A character constant is defined by entering the characters between double-quotes, as in "abcdefg". If only one character is entered the constant is an atom, otherwise the constant is a list. For example, "a" is an atom. The expression enlist "a" is required to indicate a one character list.

Escape sequences for entering non-graphic characters in character constants.

Character vector

A character vector is a simple list whose items are all character atoms. When displayed in a session, it appears as a string of characters surrounded by double-quotes, as in: "abcdefg", not as individual characters separated by semicolons and surrounded by parentheses (that is, not in list notation).

When a character vector contains only one character, the display is distinguished from the atomic character by prepending a comma, as in ,"x".

String is another name for character vector.


Characters ignored by the interpreter.

Comment syntax

Comparison tolerance

Because floating-point values resulting from computations are usually only approximations to the true mathematical values, the Equal operator is defined so that x = y is 1b (true) for two floating-point values that are either near one another or identical.



Lists, dictionaries and tables conform if they are either atoms or have the same count.



Console refers to the source of messages to q and their responses that are typed in a q session.

Control word

Control words do, if, and while interrupt the usual evaluation rules, e.g. by omitting expressions, terminating evaluation.

Evaluation control


The number of items in a list, keys in a dictionary or rows in a table. The count of an atom is 1.


The depth of a list is the number of levels of nesting. For example, an atom has depth 0, a list of atoms has depth 1, a list of lists of atoms has depth 2, and so on.

The following function computes the depth of any data object:

q)depth:{$[0>type x; 0; 1 + max depth'[x]]}

That is, an atom has depth 0 and a list has depth equal to 1 plus the maximum depth of its items.

q)depth 10             / atom
q)depth 10 20          / vector
q)depth (10 20;30)     / list


A dictionary is a mapping from a list of keys to a list of values. (The keys should be unique, though q does not enforce this.) The values of a dictionary can be any data structure.

q)/4 keys and 4 atomic values
q)`bob`carol`ted`alice!42 39 51 44
bob  | 42
carol| 39
ted  | 51
alice| 44
q)/2 keys and 2 list values
q)show kids:`names`ages!(`bob`carol`ted`alice;42 39 51 44)
names| bob carol ted alice
ages | 42  39    51  44

! Dict


The domain of a function is all the possible values of its argument. Domain and range

Functions with multiple arguments have multiple domains. A function’s first domain is known as its left domain. Its second domain is its right domain. For example, the left domain of rotate is integer atoms and its right domain is lists.

q)3 rotate "abcde"

If a function has more than two arguments, all but the first domain are its right arguments and their corresponding domains its right domains. For example, the left domain of ssr is char lists, and its right domains are char lists or atoms.

q)ssr["advance";"adv";"a d"]
"a dance"
q)ssr["a";"a";"-"]   / left domain doesn't include atoms
  [0]  ssr["a";"a";"-"]

All iterables have domains. The domain of a dictionary is its keys. The domain of a list is its indexes. The left domain of a matrix is its row numbers. Its right domain is its column numbers. The left domain of a table is its row numbers. Its right domain is its column names.

All iterables are mappings from their domains to their ranges

Empty list

The generic empty list has no items, has count 0, and is denoted by (). The empty character vector may be written "", the empty integer vector 0#0, the empty floating-point vector 0#0.0, and the empty symbol vector 0#` or `$().

The distinction between () and the typed empty lists is relevant to certain operators (e.g. Match) and also to formatting data on the screen.


A representation of a list as indexes of the items in its nub or another list.


The items of a dictionary are its entries. Each entry consists of a key and a corresponding value.

Escape sequence

An escape sequence is a special sequence of characters representing a character atom. An escape sequence usually has some non-graphic meaning, for example the tab character. An escape sequence can be entered in a character constant and displayed in character data.

Expression block, expression list

A pair of square brackets enclosing zero or more expressions separated by semicolons.

Finite-state machine

A dictionary or list represents a finite-state machine when its values (dictionary) or items (list) can be used to index it. For example:

q)show l:-10?10
1 8 5 7 0 3 6 4 2 9             / all items are also indexes
q)yrp                           / a European tour
from   to     wp
London Paris  0
Paris  Genoa  1
Genoa  Milan  1
Milan  Vienna 1
Vienna Berlin 1
Berlin London 0
q)show route:(!/)yrp`from`to    / finite-state machine
London| Paris
Paris | Genoa
Genoa | Milan
Milan | Vienna
Vienna| Berlin
Berlin| London


A mapping from input/s to result defined by an algorithm.

Operators, keywords, compositions, projections and lambdas are all functions.

.Q.res returns a list of keywords

Function atom

A function can appear in an expression as data, and not be subject to immediate evaluation when the expression is executed, in which case it is an atom. For example:

q)f: +            / f is assigned Add 
q)(f;102)         / an item in a list


A handle is a symbol holding the name of a global variable, which is a node in the K-tree. For example, the handle of the name a_c is `a_c. The term handle is used to point out that a global variable is directly accessed. Both of the following expressions amend x:

x: .[ x; i; f; y]
   .[`x; i; f; y]

In the first, referencing x as the first argument causes its entire value to be constructed, even though only a small part may be needed. In the second, the symbol `x is used as the first argument. In this case, only the parts of x referred to by the index i will be referenced and reassigned. The second case is usually more efficient than the first, sometimes significantly so.

Where x is a directory, referencing the global variable x causes the entire dictionary value to be constructed, even though only a small part of it may be needed. Consequently, in the description of Amend, the symbol atoms holding global variable names are referred to as handles.

Identity element

For function f the value x such that y~f[x;y] for any y.

Q knows the identity elements of some functions, e.g. + (zero), but not others, e.g. {x+y} (also zero).

Variadic syntax


Applying an operator by writing it between its arguments, e.g.
2+3 applies + to 2 and 3

Item, list item

A member of a list: can be any function or data structure.


A function, handle, list, or dictionary: an object that can be applied to its argument/s.


An iterator is a higher-order operator. It takes an iterable as its argument and returns a derived function that iterates it.

All the iterators are unary operators. They are the only operators that can be applied postfix. They almost invariably are.

Reference: Iterators
Wikipedia: Iterator pattern, Iterator
StackOverflow: What exactly are iterator, iterable, and iteration?
Dictionaries: Wiktionary, Oxford


The K-tree is the hierarchical name space containing all global variables created in a session. The initial state of the K-tree when kdb+ is started is a working directory whose absolute path name is `. together with a set of other top-level directories containing various utilities. The working directory is for interactive use and is the default active, or current, directory.

An application should define its own top-level directory that serves as its logical root, using a name which will not conflict with any other top-level application or utility directories present. Every subdirectory in the K-tree is a dictionary that can be accessed like any other variable, simply by its name.

Keyed table

See Table.


Functions are defined in the lambda notation: an optional signature followed by a list of expressions, separated by semicolons, and all embraced by curly braces, e.g.

A defined function is also known as a lambda.

Lambda notation

Left argument

See Argument

Left-atomic function

A left-atomic function f is a binary f that is atomic in its left, or first, argument. That is, for every valid right argument y, the unary f[;y] is atomic.

Left domain

See Argument


An array, its items indexed by position.

List notation


A list in which all items are lists of the same count.

Name, namespace

A namespace is a container or context within which a name resolves to a unique value. Namespaces are children of the default namespace and are designated by a dot prefix. Names in the default namespace have no prefix. The default namespace of a q session is parent to multiple namespaces, e.g. .h, .Q and .z. (Namespaces with 1-character names – of either case – are reserved for use by Kx.)

q).z.p                         / UTC timestamp

Namespaces are dictionaries.

q)`.[`v]      / value of v in root namespace
q)`.ns[`v]    / value of v in ns
q)`. `v       / indexed by juxtaposition
q)`.ns `v`v
6 6
5 6


A synonym for primitive.


The unique items of a list.

Reference: distinct


Null is the value of an unspecified item in a list formed with parentheses and semicolons. For example, null is the item at index position 2 of (1 2;"abc";;`xyz).

Null is an atom; its value is :: . Nulls have special meaning in the right argument of the operator Index and in the bracket form of function application.


A function of rank 0, i.e. that takes no arguments.


A primitive binary function that may be applied infix as well as prefix, e.g. +, &.



Applying an iterator to its argument by writing it to the right, e.g. +/ applies iterator / to +. (Not to be confused with projecting an operator on its left argument.)


Prefix notation applies a unary iterable m to its argument or indices x; i.e. m x is equivalent to m[x].



Defined in the q language.

Project, projection

A function passed fewer arguments than its rank projects those arguments and returns a projection: a function of the unspecified argument/s.



An iterable with rank 4.


The range of a function is the complete set of all its possible results.

All iterables are mappings from their domains to their ranges. Domain and range


Of a function, the number of arguments it takes.

rank adjective example
0 nullary {42}
1 unary til
2 binary + Add
3 ternary ssr string search and replace
4 quaternary .[d;i;m;my] Amend

Function notation

Of a list, the depth to which it is nested. A vector has rank 1; a matrix, rank 2.

Reference, pass by

Pass by reference means passing the name of an object (as a symbol atom) as an argument to a function, e.g. key `.q.

Right argument/s

See Argument

Right-atomic function

A right-atomic function f is a binary that is atomic in its right, or second, argument. That is, for every valid left argument x, the unary function f[x;] is an atomic function.

Right domain/s

See Argument


A script is a text file; its lines a list of expressions and/or system commands, to be executed in sequence. By convention, a script file has the extension q.

Within a script

  • function definitions may extend over multiple lines
  • an empty comment begins a multiline comment.


The argument list that (optionally) begins a lambda, e.g. in {[a;b](a*a)+(b*b)+2*a*b}, the signature is [a;b].

Simple table

See Table.


There is no string datatype in q. String in q means a char vector, e.g. "abc".


A symbol is an atom which holds a string of characters, much as an integer holds a string of digits. For example, `abc denotes a symbol atom. This method of forming symbols can only be used when the characters are those that can appear in names. To form symbols containing other characters, put the contents between double quotes, as in `$"abc-345".

A symbol is an atom, and as such has count 1; its count is not related to the number of characters that appear in its display. The individual characters in a symbol are not directly accessible, but symbols can be sorted and compared with other symbols. Symbols are analogous to integers and floating-point numbers, in that they are atoms but their displays may require more than one character. (If they are needed, the characters in a symbol can be accessed by converting it to a character string.)

System command

Expressions beginning with \ are system commands. (Or multiline comments).

q)/ load the script in file my_app.q
q)\l my_app.q


A simple table is a list of named lists of equal count.

q)show t:([]names:`bob`carol`ted`alice; ages:42 39 51 44)
names ages
bob   42
carol 39
ted   51
alice 44

It is also a list of dictionaries with the same keys.

q)first t
names| `bob
ages | 42

Table syntax can declare one or more columns of a table as a key. The values of the key column/s of a table are unique.

q)show kt:([names:`bob`carol`bob`alice;city:`NYC`CHI`SFO`SFO]; ages:42 39 51 44)
names city| ages
----------| ----
bob   NYC | 42
carol CHI | 39
bob   SFO | 51
alice SFO | 44

A keyed table is a table of which one or more columns have been defined as its key. A table’s key/s (if any) are supposed to be distinct: updating the table with rows with existing keys overwrites the previous records with those keys. A table without keys is a simple table.

A keyed table is a dictionary. Its key is a table.

q)key kt
names city
bob   NYC
carol CHI
bob   SFO
alice SFO


An iterable of rank 3, i.e. a function wiith three arguments; or a list of depth ≥3.

Unary form

Most binary operators have unary forms that take a single argument. Q provides more legible covers for these functions.

Exposed infrastructure

Unary function

An iterable of rank 1, i.e. a function with 1 argument, or a list of depth ≥1.

Unary operator

See Iterator.

Reference: Iterators

Uniform function

A uniform function f such that count[x]~count f x, e.g. deltas

Uniform list

A list in which all items are of the same datatype. See also vector.

Unsigned function

A lambda without a signature, e.g. {x*x}.

Value, pass by

Pass by value means passing an object (not its name) as an argument to a function, e.g. key .q.


An iterable that may be applied to a variable number arguments is variadic. For example, a matrix, the operator @, or the derived function +/.


A uniform list of basic types that has a special shorthand notation. A char vector is known as a string.


Default name of the first or only argument of an unsigned function.


Default name of the second argument of an unsigned function.


Default name of the third argument of an unsigned function.


A view is a calculation that is re-evaluated only if the values of the underlying dependencies have changed since its last evaluation. Views can help avoid expensive calculations by delaying propagation of change until a result is demanded.

The syntax for the definition is


The act of defining a view does not trigger its evaluation.

A view should not have side effects, i.e. should not update global variables.

view, views
.Q.view (subview) Tutorial: Views tutorial