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In languages which support first-class functions and currying, map may be partially applied to lift a function that works on only one value to an element-wise equivalent that works on an entire container; for example, map square is a Haskell function which squares each element of a list.
In computer programming, apply applies a function to a list of arguments. Eval and apply are the two interdependent components of the eval-apply cycle, which is the essence of evaluating Lisp, described in SICP. [1] Function application corresponds to beta reduction in lambda calculus.
A traditional imperative program might use a loop to traverse and modify a list. A functional program, on the other hand, would probably use a higher-order "map" function that takes a function and a list, generating and returning a new list by applying the function to each list item.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
The arrays are heterogeneous: a single array can have keys of different types. PHP's associative arrays can be used to represent trees, lists, stacks, queues, and other common data structures not built into PHP. An associative array can be declared using the following syntax:
Pandas also supports the syntax data.iloc[n], which always takes an integer n and returns the nth value, counting from 0. This allows a user to act as though the index is an array-like sequence of integers, regardless of how it's actually defined. [9]: 110–113 Pandas supports hierarchical indices with multiple values per data point.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...