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CATAMORPHISM

Catamorphism

Homomorphism from an initial algebra into another algebra

In functional programming, the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism

Catamorphism

Hylomorphism (computer science)

Recursive function

and the catamorphism the summation of these leaf nodes. Morphism Morphisms of F-algebras From an initial algebra to an algebra: Catamorphism From a coalgebra

Hylomorphism (computer science)

Hylomorphism_(computer_science)

Fold (higher-order function)

Family of higher-order functions

function at each node on its terminal values and the recursive results (catamorphism, versus anamorphism of unfolds). Folds can be regarded as consistently

Fold (higher-order function)

Fold_(higher-order_function)

Paramorphism

algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension

Paramorphism

Anamorphism

Programming function applied recursively to its previous result

algebra to an algebra: Catamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension of the idea of catamorphisms: Paramorphism Extension

Anamorphism

Functional programming

Programming paradigm based on applying and composing functions

higher-order function, and the visitor pattern roughly corresponds to a catamorphism, or fold. Similarly, the idea of immutable data from functional programming

Functional programming

Functional_programming

Apomorphism

algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism Extension

Apomorphism

Tree accumulation

Computer science process

nodes according to their tree structure. Formally, this operation is a catamorphism. Upward accumulation refers to accumulating on each node information

Tree accumulation

Tree_accumulation

MapReduce

Parallel programming model

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

MapReduce

List of Greek and Latin roots in English/H–O

anamorphosis, anthropomorphism, apomorphy, autapomorphy, automorphism, catamorphism, dimorphic, dimorphism, dysmorphic, dysmorphophobia, ectomorph, ectomorphic

List of Greek and Latin roots in English/H–O

List_of_Greek_and_Latin_roots_in_English/H–O

Bird–Meertens formalism

Calculus for deriving computer programs

parallelisation are considerable. This is the basis of the map-reduce approach. Catamorphism Anamorphism Paramorphism Hylomorphism Ursula Martin; Tobias Nipkow (Apr

Bird–Meertens formalism

Bird–Meertens_formalism

F-algebra

Function type in category theory

like the Ackermann function. Algebras for a monad Algebraic data type Catamorphism Dialgebra The vertical arrows without labels in the second diagram must

F-algebra

List of Greek and Latin roots in English/M

List of Greek and Latin roots in English starting with the letter M

anamorphosis, anthropomorphism, apomorphy, autapomorphy, automorphism, catamorphism, dimorphic, dimorphism, dysmorphic, dysmorphophobia, ectomorph, ectomorphic

List of Greek and Latin roots in English/M

List_of_Greek_and_Latin_roots_in_English/M

Initial algebra

Mathematical object

“strong” functions like the Ackermann function. Algebraic data type Catamorphism Anamorphism Philip Wadler: Recursive types for free! University of Glasgow

Initial algebra

Initial_algebra

Attribute grammar

Type of formal grammar

aspect-oriented programming to functional programming by helping writing catamorphisms compositionally. It refers to the Utrecht University Attribute Grammar

Attribute grammar

Attribute_grammar