currying

A type signature defines the inputs and outputs for a function or method. A type signature includes at least the function name and the number of its parameters. In some programming languages, it may also specify the function's return type or the types of its parameters. Type signature - Haskell. A type signature in Haskell is written, generally, in the following format: functionName : ...

Including:

• Type signature - Haskell
• Type signature - Java

Read more here: » Type signature: Encyclopedia - Type signature

A curry is any of a great variety of distinctively spiced dishes, best-known in Indian and Thai cuisine, but curry has been adopted into all of the mainstream cuisines of the Asia-Pacific area, from Pakistan in the west and even eventually to Japan. Along with tea, curry is one of the few dishes or drinks that is truly "pan-Asian", although its roots are from India. Curry - Curries around the world. The term curry derives from kari, a Tamil word meaning sauce and referring to various kinds of ...

Including:

• Curry - Curries around the world
• Curry - Tamil cuisine
• Curry - Malayali cuisine
• Curry - Other Indian cuisine
• Curry - Thai cuisine
• Curry - British cuisine
• Curry - Malaysian cuisine
• Curry - Elsewhere
• Curry - Curry addiction
• Curry - Ingredients
• Curry - Thickeners
• Curry - Spices
• Curry - Sour ingredients
• Curry - Fresh herbs and spices
• Curry - Other
• Curry - Curry powder
• Curry - Curry leaves

Read more here: » Curry: Encyclopedia - Curry

The modern idea of a mathematical function was introduced by Leibniz, and the associated notation y = f(x) was invented by Leonhard Euler, in the 18th century. But the intuitive idea of a function as any rule or procedure that assigns an output to each given input proved to be naive. Joseph Fourier, for example, claimed that every function had a Fourier series, something no mathematician would claim today. The concept of a function was not put on a rigorous basis u ...

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Function mathematics, Function mathematics - Introduction, Function mathematics - Functions of more than one variable, Function mathematics - History, Function mathematics - Formal definition, Function mathematics - Domains codomains and ranges, Function mathematics - Injective surjective and bijective functions, Function mathematics - Images and preimages, Function mathematics - Graph of a function, Function mathematics - Examples of functions, Function mathematics - Properties of functions, Function mathematics - Ambiguous functions, Function mathematics - n-ary function: function of several variables, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Functions from the categorical viewpoint

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Introduction

Formally, we start with a countably infinite set of identifiers, say {a, b, c, ..., x, y, z, x1, x2, ...}. The set of all lambda expressions can then be described by the following context-free grammar in BNF: <expr> ::= <identifier> <expr> ::= (λ <identifier>. <expr>) <expr ...

See also:

Lambda calculus, Lambda calculus - History, Lambda calculus - Informal description, Lambda calculus - Formal definition, Lambda calculus - α-conversion, Lambda calculus - β-reduction, Lambda calculus - η-conversion, Lambda calculus - Arithmetic in lambda calculus, Lambda calculus - Logic and predicates, Lambda calculus - Recursion, Lambda calculus - Computable functions and lambda calculus, Lambda calculus - Undecidability of equivalence, Lambda calculus - Lambda calculus and programming languages

Read more here: » Lambda calculus: Encyclopedia II - Lambda calculus - Formal definition

The following examples are legal Haskell if included in a file that is then compiled in a command-line fashion using any Haskell compiler. To execute these definitions within a Haskell interpreter such as Hugs or GHCI, the "let" syntax must be used, as documented in the manuals for these interpreters. For example, the first definition would be expressed as let { fac 0 = 1; fac n | n > 0 = n * fac (n-1) } Haskell programming language - Anatomy of a Haskell function. The "Hello World" of functional langua ...

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Haskell programming language, Haskell programming language - Examples, Haskell programming language - Anatomy of a Haskell function, Haskell programming language - More complex examples, Haskell programming language - Implementations, Haskell programming language - Extensions

Read more here: » Haskell programming language: Encyclopedia II - Haskell programming language - Examples

Examples of cartesian closed categories include: The category Set of all sets, with functions as morphisms, is cartesian closed. The product X×Y is the cartesian product of X and Y, and ZY is the set of all functions from Y to Z. The adjointness is expressed by the following fact: the function f : X×Y → Z is naturally identified with the function g : X → ZY defined by gSee also:

Cartesian closed category, Cartesian closed category - Definition, Cartesian closed category - Examples, Cartesian closed category - Applications, Cartesian closed category - Equational theory

Read more here: » Cartesian closed category: Encyclopedia II - Cartesian closed category - Examples

Boo programming language - Hello world program. print "Hello, world!" Boo programming language - Fibonacci series generator function. def fib(): a, b = 0L, 1L while true: yield b a, b = b, a + b Boo programming language - Basic Windows Form example demonstrating classes closures and events. import System.Windows.Forms import System.Drawing class MyForm(Form): def constructor(): b = Button(Te ...

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Boo programming language, Boo programming language - Code samples, Boo programming language - Hello world program, Boo programming language - Fibonacci series generator function, Boo programming language - Basic Windows Form example demonstrating classes closures and events, Boo programming language - Asynchronous design pattern with a closure, Boo programming language - Currying

Read more here: » Boo programming language: Encyclopedia II - Boo programming language - Code samples

The term curry derives from kari, a Tamil word meaning sauce and referring to various kinds of dishes common in South India made with vegetables or meat and usually eaten with rice. The term is used more broadly, especially in the Western Hemisphere, to refer to almost any spiced, sauce-based dishes cooked in various south and southeast Asian styles. This imprecise umbrella term is largely a legacy of the British Raj. In India, the word curry actually refers to anything cooked and eaten with rice. Anything can be made into a cu ...

See also:

Curry, Curry - Curries around the world, Curry - Tamil cuisine, Curry - Malayali cuisine, Curry - Other Indian cuisine, Curry - Thai cuisine, Curry - British cuisine, Curry - Malaysian cuisine, Curry - Elsewhere, Curry - Curry addiction, Curry - Ingredients, Curry - Thickeners, Curry - Spices, Curry - Sour ingredients, Curry - Fresh herbs and spices, Curry - Other, Curry - Curry powder, Curry - Curry leaves

Read more here: » Curry: Encyclopedia II - Curry - Curries around the world

A precise definition is required for the purposes of mathematics. A function is a binary relation, f, with the property that for an element x there is no more than one element y such that x is related to y. This uniquely determined element y is denoted f(x). Because two definitions of binary relation are in use, there are actually two definitions of function, in ...

See also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - Domain codomain argument image, Function mathematics - Graph of a function, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Argument order and lambda notation, Function mathematics - Examples of functions, Function mathematics - Image of a set, Function mathematics - Range of a function, Function mathematics - Preimage of a set, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Classes of functions, Function mathematics - Injective surjective bijective, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Mathematical definition of a function

An input to a function is called argument of the function. For each argument x, the corresponding unique y in the codomain is called the function value at x, or the image of x under f. The image of x can be written as f(x) or as y. Written mathematics sometimes omits the parentheses around the argument, thus: sin x, but calculators and computers require parentheses around the argument. In some branches of mathematics, such as automata theory, th ...

See also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - The vocabulary of functions, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - The vocabulary of functions

Purely functional programs have no side-effects. Since functions do not modify state, no data may be changed by parallel function calls. For this reason, pure functions are always thread-safe, a fact which is exploited by languages that use call-by-future evaluation. Because ordering of side-effects does not have to be preserved in their absence, some languages (such as Haskell) use call-by-need evaluation for pure functions. "Pure" functional programming languages typically enforce referential transparency, which is the notion ...

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Functional programming, Functional programming - History, Functional programming - Higher-order functions, Functional programming - Comparison with imperative programming, Functional programming - Pure functions, Functional programming - Monads, Functional programming - Expansion of functional programming, Functional programming - Speed and space considerations, Functional programming - Functional languages

Read more here: » Functional programming: Encyclopedia II - Functional programming - Pure functions

The "Hello World" of functional languages is the factorial function. Expressed as pure Haskell: fac :: Integer -> Integer fac 0 = 1 fac n | n > 0 = n *fac (n-1) Or on a single line: let { fac 0 = 1; fac n | n > 0 = n *fac (n-1) } This describes the factorial as a recursive function, with a single terminating base case. It is similar to the descriptions of factorials found in mathematics textbooks. Much of Haske ...

See also:

Haskell programming language, Haskell programming language - Examples, Haskell programming language - More complex examples, Haskell programming language - Criticism, Haskell programming language - Implementations, Haskell programming language - Extensions

Read more here: » Haskell programming language: Encyclopedia II - Haskell programming language - Examples

Since version 3 the SuperCollider environment is split into a server, scsynth, and a client, sclang, that communicate using OpenSound Control. SC Language combines the object oriented structure of Smalltalk and features from functional programming languages with a C programming language family syntax. The SC Server application supports a simple C plugin API making it easy to write efficient sound algorithms (unit generators) which can then be combined into graphs of calculations. Due to the fact that ...

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SuperCollider programming language, SuperCollider programming language - Architecture, SuperCollider programming language - Language Features, SuperCollider programming language - Synthesis Server Features, SuperCollider programming language - Code examples, SuperCollider programming language - System requirements

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The category C is called cartesian closed iff it satisfies the following three properties: it has a terminal object any two objects X and Y of C have a product X×Y in C any two objects Y and Z of C have an exponential ZY in C For the first two conditions above, it is the same to require that any finite (possibly empty) family of objects of C admit a product in C, because of t ...

See also:

Cartesian closed category, Cartesian closed category - Definition, Cartesian closed category - Examples, Cartesian closed category - Applications, Cartesian closed category - Equational theory

Read more here: » Cartesian closed category: Encyclopedia II - Cartesian closed category - Definition

Informally, a restriction of a function f is the result of trimming its graph to a smaller domain. More precisely, if f is a function from a X to Y, and S is any subset of X, the restriction of f to S is the function f|S from S to Y such that f|S(s) = f(s) for all s in S. The restriction f|S can also be expressed as the composition f incS,X, where incSSee also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - Domain codomain argument image, Function mathematics - Graph of a function, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Argument order and lambda notation, Function mathematics - Examples of functions, Function mathematics - Image of a set, Function mathematics - Range of a function, Function mathematics - Preimage of a set, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Classes of functions, Function mathematics - Injective surjective bijective, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Restrictions and extensions

Functional languages have long been criticised as resource-hungry, both in terms of CPU resources and memory. This was mainly due to two factors: some early functional languages were implemented with little concern for efficiency non-functional languages achieved speed in part by leaving out features such as bounds checking and garbage collection which are considered by many to be important parts of modern computing fr ...

See also:

Functional programming, Functional programming - History, Functional programming - Higher-order functions, Functional programming - Comparison with imperative programming, Functional programming - Pure functions, Functional programming - Monads, Functional programming - Expansion of functional programming, Functional programming - Speed and space considerations, Functional programming - Functional languages

Read more here: » Functional programming: Encyclopedia II - Functional programming - Speed and space considerations

If f: X → R and g: X → R are functions with common domain X and codomain is a ring R, then one can define the sum function f + g: X → R and the product function f × g: X → R as follows: (f + g)(x) = f(x) + g(x) (f × g)(x) = f(x) × < ...

See also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - Domain codomain argument image, Function mathematics - Graph of a function, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Argument order and lambda notation, Function mathematics - Examples of functions, Function mathematics - Image of a set, Function mathematics - Range of a function, Function mathematics - Preimage of a set, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Classes of functions, Function mathematics - Injective surjective bijective, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Pointwise operations

Function mathematics - Injective surjective bijective. Three important properties that a function may have are: injective (or one-to-one, or an injection) if it associates different arguments to different values; i.e., if f(a) = f(b) implies a = b, for any arguments a and b; surjective (or onto, or a surjection) if its range is equal to its codomain; in other words, if for every y in the ...

See also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - Domain codomain argument image, Function mathematics - Graph of a function, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Argument order and lambda notation, Function mathematics - Examples of functions, Function mathematics - Image of a set, Function mathematics - Range of a function, Function mathematics - Preimage of a set, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Classes of functions, Function mathematics - Injective surjective bijective, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Classes of functions

The notion of function is generalizes to the notion of morphism in the context of category theory. A category is a collection of objects and morphisms, each morphism is an ordered triple (X, Y, f), where f is a rule connecting domain X and codomain Y, and X and Y are objects in the collection. Ordinary functions are sometimes referred to as morphisms in a concrete category. ...

See also:

Function mathematics, Function mathematics - Mathematical definition of a function, Function mathematics - First definition, Function mathematics - Second definition, Function mathematics - History of the concept, Function mathematics - Functions in other fields, Function mathematics - Domain codomain argument image, Function mathematics - Graph of a function, Function mathematics - Specifying a function, Function mathematics - Functions with multiple inputs and outputs, Function mathematics - Functions of two or more variables, Function mathematics - Functions with output in a product set, Function mathematics - Binary operations, Function mathematics - Argument order and lambda notation, Function mathematics - Examples of functions, Function mathematics - Image of a set, Function mathematics - Range of a function, Function mathematics - Preimage of a set, Function mathematics - Composing functions, Function mathematics - Inverse function, Function mathematics - Set of all functions, Function mathematics - Is a function more than its graph?, Function mathematics - Partial functions and multi-functions, Function mathematics - Classes of functions, Function mathematics - Injective surjective bijective, Function mathematics - Other properties, Function mathematics - Restrictions and extensions, Function mathematics - Pointwise operations, Function mathematics - Computable and non-computable functions, Function mathematics - Lambda calculus, Function mathematics - Functions in category theory

Read more here: » Function mathematics: Encyclopedia II - Function mathematics - Functions in category theory

The first computer-based functional programming language was Information Processing Language (IPL) from the RAND corporation. Another very old functional language is Lisp, though neither the original LISP nor modern Lisps such as Common Lisp are pure-functional. Some Lisp variants include Scheme, Dylan, and Logo (though Logo is an imperitive language). The modern canonical examples are Haskell and members of the ML family including SML and OCaml. Others include Erlang, Clean, and Miranda. A third type of a commonly used functional language is Xslt. Ano ...

See also:

Functional programming, Functional programming - History, Functional programming - Higher-order functions, Functional programming - Comparison with imperative programming, Functional programming - Pure functions, Functional programming - Monads, Functional programming - Expansion of functional programming, Functional programming - Speed and space considerations, Functional programming - Functional languages

Read more here: » Functional programming: Encyclopedia II - Functional programming - Functional languages