Paramorphism

In formal methods of computer science, a paramorphism (from Greek παρά, meaning "close together") is an extension of the concept of catamorphism first introduced by Lambert Meertens[1] to deal with a form which “eats its argument and keeps it too”,[2][3] as exemplified by the factorial function. Its categorical dual is the apomorphism.

It is a more convenient version of catamorphism in that it gives the combining step function immediate access not only to the result value recursively computed from each recursive subobject, but the original subobject itself as well.

Example Haskell implementation, for lists: 

cata :: (a ->       b  -> b) -> b -> [a] ->  b
para :: (a -> ([a], b) -> b) -> b -> [a] ->  b
ana  :: (b -> (a,            b))  ->  b  -> [a]
apo  :: (b -> (a, Either [a] b))  ->  b  -> [a]

cata f b (a:as) = f a     (cata f b as)
cata _ b []     = b

para f b (a:as) = f a (as, para f b as)
para _ b []     = b

ana  u b = case u b of (a,       b') -> a : ana u b'

apo  u b = case u b of (a, Right b') -> a : apo u b'
                       (a, Left  as) -> a : as

See also

References

  1. ^ "Paramorphisms" (PDF). 1990. p. 44. CiteSeerX 10.1.1.19.4825. {{cite web}}: Cite uses deprecated parameter |citeseerx= (help)
  2. ^ Philip Wadler.Views: A way for pattern matching to cohabit with data abstraction. Technical Report 34, Programming Methodology Group, University of Gothenburg and Chalmers University of Technology, March 1987.
  3. ^ Meijer, Erik; Fokkinga, Maarten; Paterson, Ross (1991). "Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire". CiteSeerX 10.1.1.41.125. {{cite web}}: Cite uses deprecated parameter |citeseerx= (help); Missing or empty |url= (help)


Stub icon

This formal methods-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.