Vocabulary

The following page documents K related words. All definitions written here should be hence treated as such, and not as an extension of their English counterparts.

Noun

A noun is a basic value in K, which can be a:

• Number
• Character
• Symbol
• Function
• Dictionary
• Array
• Table

Verb

A verb is a primitive function in K. K has 20 primitive verbs which represent multiple overloads that form its base functionality.

Adverb

An adverb is a primitive syntactical form in K which takes 1 or 2 functions on the left and changes their functionality.

Dictionary

A K dictionary is a mapping from a set of K nouns as keys to a set of K nouns which constitute the values of the dictionary. Keys may not need to be unique, depending on the K version.

Function

A function can be a:

• Primitive verb
• Lambda
• Train
• Projection of any of the above.

Valence

The valence of a noun which supports application(function, array, dict) is the number of arguments it can take. K primitives are usually multi-valent and support different overloads for different valences.

Monad

A Monad is a function which has valence 1 (single argument function).

Dyad

A Dyad is a function which has valence 2 (two argument function).

Matrix

A matrix is a 2D array (a list of lists) where all elements have the same length.

Shape

The shape of an array is the length of each dimension in it.

Conform

Conforming is a rule that applies to arithmetic verbs in K. A conforming operation is one which can take two arrays with arbitrary shape and line up each atom with a corresponding atom, preserving the structure of one of the given arguments. Conforming operations can only be done on arrays which recursively conform in terms of element length.

Atomic

An atomic operation is one which can work on the lowest atoms of an array. Atoms can be one of:

• Integer
• Character
• Float
• Symbol

Vector

A vector is a simple list that contains no subarrays.

Scalar

A scalar is the smallest individual unit that can the added to an array, that is not an array. Otherwise this is See Atomic for the types of scalars.

Lambda

The basic universal syntax for defining functions is the K lambda. A lambda with no arguments defined has its first three arguments stored in variables x, y and z. A lambda also has a variable for self reference (recursion).