Functional Definition and 417 Threads

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).

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  1. nomadreid

    I Oddity of a functional equation for the R zeta function

    In https://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/fnleqn.htm the equation ζ(s)=ζ(1-s) is used, where ζ is the Riemann zeta function, which I find curious, for the following reasons this indicates a symmetry around Re(s)=1/2, which seems to be what the diagram at 20:27 of seems to...
  2. D

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  3. D

    Find an example of a linear functional with some properties

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  4. M

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  5. C

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  6. P

    Biology Which organs/parts of the body are only functional on glucose?

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  7. M

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  8. Y

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  9. Euge

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  10. MexChemE

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  11. M

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  12. P

    I Definition of functional derivative

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  13. chopnhack

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  14. M

    MHB How Do Derived Functional Dependencies Impact Key Candidate Identification?

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  15. G

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  16. T

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  17. anemone

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  18. J

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  19. JD_PM

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  20. anemone

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  21. LCSphysicist

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  22. LCSphysicist

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  24. dRic2

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  25. Mr Green T

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  26. Yellotherephysics

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  27. caffeinemachine

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  28. U

    I Proof involving functional graphs and the injective property

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  29. D

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  30. U

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  31. filip97

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  32. Arman777

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  33. P

    A Calculating Functional Derivatives: -1≤xₒ≤1 vs -1<xₒ<1

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  34. T

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  35. G

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  36. The black vegetable

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  37. T

    A Stuck on evaluating this functional determinant

    I am trying to show that given the following stochastic differential equation: ##\dot{x} = W(x(\tau))+\eta(\tau),## we have ##det|\frac{d\eta(\tau)}{dx(\tau')}| = exp^{\int_{0}^{T}d\tau \,Tr \ln([\frac{d}{d\tau}-W'(x(\tau))]\delta (\tau - \tau'))} = exp^{\frac{1}{2}\int_{0}^{T}d\tau...
  38. M

    What is the name of the C=N+=C functional group?

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  39. binbagsss

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  40. Q

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  41. Calculuser

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  42. M

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  43. J

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  44. chmodfree

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  45. M

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  48. MermaidWonders

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  49. C

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  50. fsonnichsen

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