Apply Definition and 508 Threads

In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a continuous function on complete partial orders. Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology.
The most general setting for apply is in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose internal language is simply typed lambda calculus.

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  1. E

    How does timedilation apply to things other than lightclocks?

    I'm studying special relativity and this does not make any sense to me: I understand the lightclock example of how time dilation works. But I don't understand how it applies to other things. This is probably a stupid question, but I can't figure it out.
  2. P

    Can we apply non-linear smoothing to a linear looking like data ?

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  3. S

    What are caustics as they apply to optics?

    I've searched the web for caustics and optics, but mostly see pictures of them. They seem to have some positive use. In some fashion they seem to magnify. They seem to be somehow related to critical curves, whatever they are. Both seem to be helpful in gravitational lensing. How?
  4. H

    When can you not apply the alternating series test?

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  5. D

    Schools Too late to apply for grad schools?

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  6. P

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  7. T

    What happens if i apply different AC frequencies into a motor?

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  8. S

    Physics Calculations That Apply to a Variety of Geometric Objects

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  9. P

    Schools What university should I apply to for a Physics undergraduate couse?

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  10. R

    Do properties associated with photons also apply to other bosons?

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  11. I

    Really understanding how to apply calculus.

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  12. T

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  13. K

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  14. D

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  15. M

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  16. W

    Change ODE system to Polar to apply Poincare-Bendixson

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  17. J

    Automotive How to apply more torque to increase speed from steady-state

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  18. U

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  19. P

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  20. J

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  21. S

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  22. S

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  23. M

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  24. P

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  25. S

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  29. L

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  30. S

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  31. E

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    Programs Where should I apply? PhD in Applied Mathematics

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  34. C

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  35. Y

    Poynting theory apply to both static and time varying fields?

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  36. G

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  39. B

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  40. stripes

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  41. V

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  42. U

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  43. L

    Schools Don't know what level of graduate school to apply too, help please

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  44. Spinnor

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  45. G

    Does the uncertainty relation apply to the past?

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  46. T

    Programs Should You Apply for a PhD Track to Secure a Master's Admission?

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  47. R

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  48. J

    Does water displacement theory apply to other liquids?

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  49. amylase

    How does Nyquist's theory apply to digital recording of opera music?

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  50. S

    Does Newton's third law apply to Atwood's machine?

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