In functional programming, the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra.
Catamorphisms provide generalizations of folds of lists to arbitrary algebraic data types, which can be described as initial algebras.
The dual concept is that of anamorphism that generalize unfolds. A hylomorphism is the composition of an anamorphism followed by a catamorphism.
In functional programming, the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism...
algebra to an algebra: Catamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension of the idea of catamorphisms: Paramorphism Extension...
algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension...
algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension...
higher-order function, and the visitor pattern roughly corresponds to a catamorphism, or fold. Similarly, the idea of immutable data from functional programming...
function A → B can be used for the Map operation. This means that we have a catamorphism A* → (B, •, e). Here A* denotes a Kleene star, also known as the type...
nodes according to their tree structure. Formally, this operation is a catamorphism. Upward accumulation refers to accumulating on each node information...
aspect-oriented programming to functional programming by helping writing catamorphisms compositionally. It refers to the Utrecht University Attribute Grammar...
a form of corecursion in the same way that a paramorphism (such as a catamorphism, such as fold) is a form of recursion. The Coq proof assistant supports...
“strong” functions like the Ackermann function. Algebraic data type Catamorphism Anamorphism Philip Wadler: Recursive types for free! University of Glasgow...
illustrated by David 'Hyperdave' Richardson. His graphic story "The Catamorph" featuring the eponymous hero created with Jan Scherpenhuizen appeared...
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