In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program.
In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner.
Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming which treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called with some given arguments, it will always return the same result, and cannot be affected by any mutable state or other side effects. This is in contrast with impure procedures, common in imperative programming, which can have side effects (such as modifying the program's state or taking input from a user). Proponents of purely functional programming claim that by restricting side effects, programs can have fewer bugs, be easier to debug and test, and be more suited to formal verification.Functional programming has its roots in academia, evolving from the lambda calculus, a formal system of computation based only on functions. Functional programming has historically been less popular than imperative programming, but many functional languages are seeing use today in industry and education, including Common Lisp, Scheme, Clojure, Wolfram Language, Racket, Erlang, Elixir, OCaml, Haskell, and F#. Functional programming is also key to some languages that have found success in specific domains, like JavaScript in the Web, R in statistics, J, K and Q in financial analysis, and XQuery/XSLT for XML. Domain-specific declarative languages like SQL and Lex/Yacc use some elements of functional programming, such as not allowing mutable values. In addition, many other programming languages support programming in a functional style or have implemented features from functional programming, such as C++11, Kotlin, Perl, PHP, Python, Go, Rust, Raku, Scala, and Java (since Java 8).
Question 1
Prove that if (V, \|\cdot\|) is a normed vector space, then
\left| \|x\| - \|y\| \right| \leq \|x-y\|
for every x,y \in V. Then deduce that the norm is a continuous function from V to \mathbb{R}.
I saw this video today and I believe it is a presentation from SUN's "Project Looking Glass". Now this is the desktop of my dreams!
http://abum.com/files/Movies/3d_desktop.wmv
http://www.sun.com/software/looking_glass/
Given a set of m real functions of n variables, what is a necessary and sufficient condition for the functions to be functionally independent ?
A set a functions f_i(x_1,...x_n)\quad i=1,...m are functionally independent, if the only function \phi(u_1,...u_m) such that \phi(f_1,...f_m)=0 is...
Let be F the functional given by
J(y)=J(x,y,dy/dx)
my question is,apart from the usual definition of functional derivative and Lagrange equation,..does a numerical method exist to calculate it,i mean am looking for a recursive method,you introduce an initial function y0(x) from this you...
Hi,
Does anyone of you have some links or references to books on Functional Density Theory ? I know the basics but i would like to learn a whole lot more.
Thanks in advance
marlon
This is about amines:
The functional groups present are: C=O and NH2
Why does the N get protonated always but not C=O, since the oxygen has more lone pairs and more electronegative than N so shouldn't the oxygen be protonated more easily? I can't think of any good reasons... please help...
Lets say for example a hydrocarbon skeleton has two diff functional groups branched to the skeleton.. Let's say one of the functional groups pH is less than 9 to 10, and the other functional group's pH is greater than 2 to 4
that means that molecule to be electrically charged, the pH of the...
Does anyone know good online references about functional derivatives? Most of the documents contain only the definition, but I would like some more complete material containing, for example, rules for differentiate composite functionals and other details.
I'm trying to learn density functional theory by myself, but I'm a bit confused as to how to use it. Is the following methodology correct (I think it'd take forever to use LaTex to write the equations, so I have a link to small webpage that already has the equations laid out and numbered)...
Hi All,
I have a problem, and it is so confusing to me. I put it here in the hope of getting some helps to make it clear.
Thank you,
the problem is given below.
What is the greatest value of b for which any real valued function f that satisfies the following properties mus also...
schröder's equation is a functional equation. let's assume A is a subset of the real numbers and g maps A to itself. the goal is to find a nonzero (invertible, if possible) function f and a real number r such that f\circ g=rf.
motivation: if there is an invertible f, then the nth iterate...
Is it possible for us to make a functional model of the human brain?
I'm not interested in the phylosophical implications, but more in the resources, techonolgies we can use (that's why I posted here... )
where could i find in internet a course of functinal derivation and integration for physicist?...
a explanation or introduction to functional integration
let be the equation f(g(t))=g(t) where f is known but g(t) not... i think that perhaps we could solve it by iteration so g(t) would be
g(t)=fofofofofofofo... where fof means the composition of f with itself...is that solution right? i do not even konw if my process to solve the functional...