In
formal methods
In computer science, formal methods are mathematically rigorous techniques for the specification, development, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the exp ...
of
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, an apomorphism (from ''
ἀπό'' —
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
for "apart") is the
categorical dual
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category ''C'' and the dual properties of the opposite category ''C''op. Given a statement regarding the category ''C'', by interchanging the sou ...
of a
paramorphism and an extension of the concept of
anamorphism (
coinduction
In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects.
Coinduction is the mathematical dual to structural induction. Coinductively defined types are known as codata and ...
). Whereas a paramorphism models
primitive recursion
In computability theory, a primitive recursive function is roughly speaking a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop can be determined ...
over an
inductive data type, an apomorphism models primitive
corecursion
In computer science, corecursion is a type of operation that is dual to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, ...
over a coinductive data type.
Origins
The term "apomorphism" was introduced in ''Functional Programming with Apomorphisms (Corecursion)''.
See also
*
Morphism
* Morphisms of
F-algebras
** From an initial algebra to an algebra:
Catamorphism
** From a coalgebra to a final coalgebra:
Anamorphism
** An anamorphism followed by an catamorphism:
Hylomorphism
Hylomorphism (also hylemorphism) is a philosophical theory developed by Aristotle, which conceives every physical entity or being (''ousia'') as a compound of matter (potency) and immaterial form (act), with the generic form as immanently real ...
** Extension of the idea of catamorphisms:
Paramorphism
References
Recursion schemes
{{formalmethods-stub