Concept
Fold (higher-order function)
Related concepts (16)
Corecursion
In computer science, corecursion is a type of operation that is to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data.
Clojure
Clojure (ˈkloʊʒər, like closure) is a dynamic and functional dialect of the Lisp programming language on the Java platform. Like most other Lisps, Clojure's syntax is built on S-expressions that are first parsed into data structures by a reader before being compiled. Clojure's reader supports literal syntax for maps, sets and vectors along with lists, and these are compiled to the mentioned structures directly. Clojure treats code as data and has a Lisp macro system.
Map (higher-order function)
In many programming languages, map is the name of a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning the results in a collection of the same type. It is often called apply-to-all when considered in functional form. The concept of a map is not limited to lists: it works for sequential containers, tree-like containers, or even abstract containers such as futures and promises. Suppose we have a list of integers [1, 2, 3, 4, 5] and would like to calculate the square of each integer.
Initial algebra
In mathematics, an initial algebra is an initial object in the of F-algebras for a given endofunctor F. This initiality provides a general framework for induction and recursion. Consider the endofunctor F : Set → Set sending X to 1 + X, where 1 is the one-point (singleton) set, the terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a function f : (1 + X) → X. Defining such a function amounts to defining a point and a function X → X.
Catamorphism
In , the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra. In functional programming, catamorphisms provide generalizations of folds of lists to arbitrary algebraic data types, which can be described as initial algebras. The dual concept is that of anamorphism that generalize unfolds. A hylomorphism is the composition of an anamorphism followed by a catamorphism.
Elixir (programming language)
Elixir is a functional, concurrent, high-level general-purpose programming language that runs on the BEAM virtual machine, which is also used to implement the Erlang programming language. Elixir builds on top of Erlang and shares the same abstractions for building distributed, fault-tolerant applications. Elixir also provides tooling and an extensible design. The latter is supported by compile-time metaprogramming with macros and polymorphism via protocols.
Anamorphism
In computer programming, an anamorphism is a function that generates a sequence by repeated application of the function to its previous result. You begin with some value A and apply a function f to it to get B. Then you apply f to B to get C, and so on until some terminating condition is reached. The anamorphism is the function that generates the list of A, B, C, etc. You can think of the anamorphism as unfolding the initial value into a sequence.
Kotlin (programming language)
Kotlin (ˈkɒtlɪn) is a cross-platform, statically typed, general-purpose high-level programming language with type inference. Kotlin is designed to interoperate fully with Java, and the JVM version of Kotlin's standard library depends on the Java Class Library, but type inference allows its syntax to be more concise. Kotlin mainly targets the JVM, but also compiles to JavaScript (e.g., for frontend web applications using React) or native code via LLVM (e.g., for native iOS apps sharing business logic with Android apps).
Set (abstract data type)
In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
Function object
In computer programming, a function object is a construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same syntax (a function parameter that can also be a function). In some languages, particularly C++, function objects are often called functors (not related to the functional programming concept). A typical use of a function object is in writing callback functions. A callback in procedural languages, such as C, may be performed by using function pointers.