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In Haskell, the polymorphic function map :: (a -> b) -> [a] -> [b] is generalized to a polytypic function fmap :: Functor f => (a -> b) -> f a -> f b, which applies to any type belonging the Functor type class. The type constructor of lists [] can be defined as an instance of the Functor type class using the map function from the previous example:
Note that in order to use Map, you have to provide the functor Map.Make with a module which defines the key type and the comparison function. The third-party library ExtLib provides a polymorphic version of functional maps, called PMap , [ 12 ] which is given a comparison function upon creation.
A function is bijective if it is both injective and surjective. A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection). A function is bijective if and only if every possible image is mapped to by exactly one argument. [1]
An internal iterator is a higher order function (often taking anonymous functions) that traverses a collection while applying a function to each element. For example, Python's map function applies a caller-defined function to each element:
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert ...
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. [1] The values returned by a hash function are called hash values , hash codes , hash digests , digests , or simply hashes . [ 2 ]
A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a hash map.
The r = 4 case of the logistic map is a nonlinear transformation of both the bit-shift map and the μ = 2 case of the tent map. If r > 4 , this leads to negative population sizes. (This problem does not appear in the older Ricker model , which also exhibits chaotic dynamics.)