Paramorphism
Encyclopedia
A paramorphism is an extension of the concept of catamorphism
to deal with a form which “eats its argument and keeps it too”, as exemplified by the factorial
function. Its categorical dual is the apomorphism
Catamorphism
In category theory, the concept of catamorphism denotes the unique homomorphism from an initial algebra into some other algebra. The concept has been applied to functional programming as folds.The dual concept is that of anamorphism...
to deal with a form which “eats its argument and keeps it too”, as exemplified by the factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
function. Its categorical dual is the apomorphism
Apomorphism
An apomorphism is the categorical dual of a paramorphism and an extension of the concept of anamorphism...
See also
- AnamorphismAnamorphismAnamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image...
- ApomorphismApomorphismAn apomorphism is the categorical dual of a paramorphism and an extension of the concept of anamorphism...
- CatamorphismCatamorphismIn category theory, the concept of catamorphism denotes the unique homomorphism from an initial algebra into some other algebra. The concept has been applied to functional programming as folds.The dual concept is that of anamorphism...
- HylomorphismHylomorphism (computer science)In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism and a catamorphism...