Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, Apply is a function that applies functions to arguments. It is central to programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
A lisp is a speech impediment, historically also known as sigmatism. Stereotypically, people with a lisp are unable to pronounce sibilants , and replace them with interdentals , though there are actually several kinds of lisp...
and Scheme, and also in functional languages. In particular, it has a role in the study of the denotational semantics
Denotational semantics
In computer science, denotational semantics is an approach to formalizing the meanings of programming languages by constructing mathematical objects which describe the meanings of expressions from the languages...
of computer programs, by virtue of the fact that it is a continuous function
Scott continuity
In mathematics, given two partially ordered sets P and Q a function f : P \rightarrow Q between them is Scott-continuous if it preserves all directed suprema, i.e...
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, Apply is important in Cartesian closed categories, (and thus, also in Topos theory), where it is a universal morphism, right adjoint to currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
.
Programming
In computer programming, apply applies a function to a list of arguments. Eval
Eval
In some programming languages, eval is a function which evaluates a string as though it were an expression and returns a result; in others, it executes multiple lines of code as though they had been included instead of the line including the eval...
and apply are the two interdependent components of the eval-apply cycle, which is the essence of evaluating Lisp, described in SICP
Structure and Interpretation of Computer Programs
Structure and Interpretation of Computer Programs is a textbook published in 1984 about general computer programming concepts from MIT Press written by Massachusetts Institute of Technology professors Harold Abelson and Gerald Jay Sussman, with Julie Sussman...
.
Apply function
Apply is also the name of a special function in many languages, which takes a function and a list, and uses the list as the function's own argument list, as if the function were called with the elements of the list as the arguments. This is important in languages with variadic function
Variadic function
In computer programming, a variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments. Support for variadic functions differs widely among programming languages....
s, because this is the only way to call a function with an indeterminate (at compile time) number of arguments.
Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
apply is a function that applies a function to a list of arguments (note here that "+" is a variadic function that takes any number of arguments):(apply #'+ (list 1 2))
Similarly in Scheme:(apply + (list 1 2))
In C# and Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
, variadic arguments are simply collected in an array. Caller can explicitly pass in an array in place of the variadic arguments. This can only be done for a variadic parameter. It is not possible to apply an array of arguments to non-variadic parameter without using reflection
Reflection (computer science)
In computer science, reflection is the process by which a computer program can observe and modify its own structure and behavior at runtime....
. An ambiguous case arises should the caller want to pass an array itself as one of the arguments rather than using the array as a list of arguments. In this case, the caller should cast the array to Object to prevent the compiler from using the apply interpretation.variadicFunc(arrayOfArgs);
In Go
Go (programming language)
Go is a compiled, garbage-collected, concurrent programming language developed by Google Inc.The initial design of Go was started in September 2007 by Robert Griesemer, Rob Pike, and Ken Thompson. Go was officially announced in November 2009. In May 2010, Rob Pike publicly stated that Go was being...
, typed variadic arguments are simply collected in a slice. The caller can explicitly pass in a slice in place of the variadic arguments, by appending a ... to the slice argument. This can only be done for a variadic parameter. The caller can not apply an array of arguments to non-variadic parameters, without using reflection..
JavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
, function objects have an apply method, the first argument is the value of the this keyword inside the function; the second is the list of arguments:func.apply(null, args);
In Perl
Perl
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
, arrays, hashes and expressions are automatically "flattened" into a single list when evaluated in a list context, such as in the argument list of a function:
PHP is a general-purpose server-side scripting language originally designed for web development to produce dynamic web pages. For this purpose, PHP code is embedded into the HTML source document and interpreted by a web server with a PHP processor module, which generates the web page document...
, apply is called call_user_func_array:call_user_func_array('func_name', $args);
In Python
Python (programming language)
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
Ruby is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...
In computer programming, a variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments. Support for variadic functions differs widely among programming languages....
s is used to call a function on a sequence and array respectively:func(*args)
In Lua, apply can be written as follows: function apply(f,l)
return f(unpack(l))
end
In Smalltalk
Smalltalk
Smalltalk is an object-oriented, dynamically typed, reflective programming language. Smalltalk was created as the language to underpin the "new world" of computing exemplified by "human–computer symbiosis." It was designed and created in part for educational use, more so for constructionist...
, block (function) objects have a valueWithArguments: method which takes an array of arguments: aBlock valueWithArguments: args
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
, that is, where the bracket notation denotes the space of functions from A to B. By means of currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
, there is a unique function
.
Then Apply provides the universal morphism ,
so that
or, equivalently one has the commuting diagram
The notation for the space of functions from A to B occurs more commonly in computer science. In category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories...
, and is written as . There are other common notational differences as well; for example Apply is often called Eval, even though in computer science, these are not the same thing, with eval
Eval
In some programming languages, eval is a function which evaluates a string as though it were an expression and returns a result; in others, it executes multiple lines of code as though they had been included instead of the line including the eval...
distinguished from Apply, as being the evaluation of the quoted string form of a function with its arguments, rather than the application of a function to some arguments.
Also, in category theory, curry is commonly denoted by , so that is written for curry(g). This notation is in conflict with the use of in lambda calculus
Lambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
, where lambda is used to denote free variables. With all of these notational changes accounted for, the adjointness of Apply and curry is then expressed in the commuting diagram
In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories...
In category theory, a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming, in...
provide a more precise discussion of the category-theoretic formulation of this idea. Thus use of lambda here is not accidental; Cartesian-closed categories provide the general, natural setting for lambda calculus.
Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and gives some basic definitions...
In mathematics, directed complete partial orders and ω-complete partial orders are special classes of partially ordered sets, characterized by particular completeness properties...
s endowed with the Scott topology, both curry and apply are continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
s (that is, they are Scott continuous). This property helps establish the foundational validity of the study of the denotational semantics
Denotational semantics
In computer science, denotational semantics is an approach to formalizing the meanings of programming languages by constructing mathematical objects which describe the meanings of expressions from the languages...
of computer programs.
The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.
, that is, 
where the bracket notation 
denotes the space of functions from A to B. By means of currying
,
for the space of functions from A to B occurs more commonly in computer science. In category theory
is known as the exponential object
. There are other common notational differences as well; for example Apply is often called Eval, even though in computer science, these are not the same thing, with eval
, so that 
is written for curry(g). This notation is in conflict with the use of 
in lambda calculus
The articles on exponential object