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nLab > Latest Changes: recursion scheme

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  1.  
    • CommentRowNumber1.
    • CommentAuthormaxsnew
    • CommentTimeAug 13th 2022

    Init page and try to describe why some computer scientists have wacky names like catamorphism for a homomorphism out of an initial algebra.

    Not sure what “context” sidebar to put here. Do we have one for just “computer science” or more specifically here “functional programming”?

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 13th 2022

    We have no dedicated context menu for computer science yet (you could start one!). I would typically use either or both of these two pointers:

      #### Constructivism, Realizability, Computability
  +-- {: .hide}
  [[!include constructivism - contents]]
  =--

  #### Type theory
  +-- {: .hide}
  [[!include type theory - contents]]
  =--
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 13th 2022

    changed page name to singular, to comply with house style

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorm4rk1x
    • CommentTimeNov 25th 2022
    This page is good, but incomplete.

    Hinze, Wu and Gibbons showed that every recursion scheme results from an hylomorphism (a (co)recursive (co)algebra) and an adjunction.
    My feeling is that this result is not very well-known in mathematics since it has been invented by functional programmers, but it is nonetheless mathematically sound and not exclusive to the functional world.

    I suggest adding a new page called "Adjoint Recursion Schemes" .
    • CommentRowNumber5.
    • CommentAuthorm4rk1x
    • CommentTimeNov 25th 2022
    • recursion schemes as a tool for termination/productivity in languages with general recursion
    • recursion schemes via adjunctions
    • the mother of all recursion schemes is a conjugate hylo
    • comprehensive list of recursion schemes in YangW22

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2022
    • (edited Nov 26th 2022)

    added some more hyperlinks

    By the way:

    In rev 3 you added that:

    …allows the user to write functions that are not-well defined mathematically.

    Could you give an example for what this is referring to?

    diff, v4, current

1 to 6 of 6

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