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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 a category with a terminal object 1, binary coproducts (denoted by +), and binary products (denoted by ×), a list object over A can be defined as the initial algebra of the endofunctor that acts on objects by X ↦ 1 + (A × X) and on arrows by f ↦ [id 1,〈id A, f〉].
A singly-linked list structure, implementing a list with three integer elements. The term list is also used for several concrete data structures that can be used to implement abstract lists, especially linked lists and arrays. In some contexts, such as in Lisp programming, the term list may refer specifically to a linked list rather than an array.
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
However, a generator is an object with persistent state, which can repeatedly enter and leave the same scope. A generator call can then be used in place of a list, or other structure whose elements will be iterated over. Whenever the for loop in the example requires the next item, the generator is called, and yields the next item.
Python uses an English-based syntax. Haskell replaces the set-builder's braces with square brackets and uses symbols, including the standard set-builder vertical bar. The same can be achieved in Scala using Sequence Comprehensions, where the "for" keyword returns a list of the yielded variables using the "yield" keyword. [6]
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.