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- Initial_algebra abstract "In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion. For instance, consider the endofunctor 1+(-) on the category of sets, where 1 is the one-point set, the terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a point x ∈ X and a function X→X. The set of natural numbers is the carrier of the initial such algebra: the point is zero and the function is the successor map. For a second example, consider the endofunctor 1+N×(-) on the category of sets, where N is the set of natural numbers. An algebra for this endofunctor is a set X together with a point x ∈ X and a function N×X → X. The set of finite lists of natural numbers is the initial such algebra. The point is the empty list, and the function is cons, taking a number and a finite list, and returning a new finite list with the number at the head.".
- Initial_algebra wikiPageExternalLink rutten94initial.html.
- Initial_algebra wikiPageExternalLink free-rectypes.txt.
- Initial_algebra wikiPageExternalLink initiality_20and_20finality.html.
- Initial_algebra wikiPageExternalLink thesis.pdf.
- Initial_algebra wikiPageID "4116488".
- Initial_algebra wikiPageLength "7952".
- Initial_algebra wikiPageOutDegree "58".
- Initial_algebra wikiPageRevisionID "619033352".
- Initial_algebra wikiPageWikiLink Ackermann_function.
- Initial_algebra wikiPageWikiLink Actual_infinity.
- Initial_algebra wikiPageWikiLink Algebraic_data_type.
- Initial_algebra wikiPageWikiLink Anamorphism.
- Initial_algebra wikiPageWikiLink Binary_tree.
- Initial_algebra wikiPageWikiLink Catamorphism.
- Initial_algebra wikiPageWikiLink Category:Category_theory.
- Initial_algebra wikiPageWikiLink Category:Functional_programming.
- Initial_algebra wikiPageWikiLink Category:Type_theory.
- Initial_algebra wikiPageWikiLink Charity_(programming_language).
- Initial_algebra wikiPageWikiLink Coinduction.
- Initial_algebra wikiPageWikiLink Coinductive.
- Initial_algebra wikiPageWikiLink Computability_theory.
- Initial_algebra wikiPageWikiLink Computability_theory_(computer_science).
- Initial_algebra wikiPageWikiLink Cons.
- Initial_algebra wikiPageWikiLink Corecursion.
- Initial_algebra wikiPageWikiLink Data_structure.
- Initial_algebra wikiPageWikiLink Data_structures.
- Initial_algebra wikiPageWikiLink Data_type.
- Initial_algebra wikiPageWikiLink Datatype.
- Initial_algebra wikiPageWikiLink Domain_of_a_function.
- Initial_algebra wikiPageWikiLink Duality_(mathematics).
- Initial_algebra wikiPageWikiLink Endofunctor.
- Initial_algebra wikiPageWikiLink F-algebra.
- Initial_algebra wikiPageWikiLink F-coalgebra.
- Initial_algebra wikiPageWikiLink Fold_(higher-order_function).
- Initial_algebra wikiPageWikiLink Function_(mathematics).
- Initial_algebra wikiPageWikiLink Functional_programming.
- Initial_algebra wikiPageWikiLink Functor.
- Initial_algebra wikiPageWikiLink Greatest_fixed_point.
- Initial_algebra wikiPageWikiLink Haskell_(programming_language).
- Initial_algebra wikiPageWikiLink Homomorphism.
- Initial_algebra wikiPageWikiLink Identity_function.
- Initial_algebra wikiPageWikiLink Infinite_list.
- Initial_algebra wikiPageWikiLink Initial_and_terminal_objects.
- Initial_algebra wikiPageWikiLink Initial_object.
- Initial_algebra wikiPageWikiLink Inverse_function.
- Initial_algebra wikiPageWikiLink Isomorphism.
- Initial_algebra wikiPageWikiLink Lazy_evaluation.
- Initial_algebra wikiPageWikiLink Least_fixed_point.
- Initial_algebra wikiPageWikiLink List_(abstract_data_type).
- Initial_algebra wikiPageWikiLink List_(computing).
- Initial_algebra wikiPageWikiLink Lookup_table.
- Initial_algebra wikiPageWikiLink ML_(programming_language).
- Initial_algebra wikiPageWikiLink ML_programming_language.
- Initial_algebra wikiPageWikiLink Mathematical_induction.
- Initial_algebra wikiPageWikiLink Mathematical_optimization.
- Initial_algebra wikiPageWikiLink Mathematical_programming.
- Initial_algebra wikiPageWikiLink Mathematics.
- Initial_algebra wikiPageWikiLink Natural_number.
- Initial_algebra wikiPageWikiLink Normalization_property_(abstract_rewriting).
- Initial_algebra wikiPageWikiLink Normalization_property_(lambda-calculus).
- Initial_algebra wikiPageWikiLink Parametricity.
- Initial_algebra wikiPageWikiLink Partial_function.
- Initial_algebra wikiPageWikiLink Programming_language.
- Initial_algebra wikiPageWikiLink Recursion.
- Initial_algebra wikiPageWikiLink Simple_algebra.
- Initial_algebra wikiPageWikiLink Terminal_object.
- Initial_algebra wikiPageWikiLink Tree.
- Initial_algebra wikiPageWikiLink Truth-value.
- Initial_algebra wikiPageWikiLink Truth_value.
- Initial_algebra wikiPageWikiLink Unique.
- Initial_algebra wikiPageWikiLink Uniqueness_quantification.
- Initial_algebra wikiPageWikiLink Universal_property.
- Initial_algebra wikiPageWikiLink Up_to.
- Initial_algebra wikiPageWikiLinkText "Initial algebra".
- Initial_algebra wikiPageWikiLinkText "final coalgebra".
- Initial_algebra wikiPageWikiLinkText "final".
- Initial_algebra wikiPageWikiLinkText "initial algebra".
- Initial_algebra wikiPageWikiLinkText "initial".
- Initial_algebra hasPhotoCollection Initial_algebra.
- Initial_algebra wikiPageUsesTemplate Template:Technical.
- Initial_algebra subject Category:Category_theory.
- Initial_algebra subject Category:Functional_programming.
- Initial_algebra subject Category:Type_theory.
- Initial_algebra type Function.
- Initial_algebra comment "In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion. For instance, consider the endofunctor 1+(-) on the category of sets, where 1 is the one-point set, the terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a point x ∈ X and a function X→X.".
- Initial_algebra label "Initial algebra".
- Initial_algebra sameAs 始代数.
- Initial_algebra sameAs m.0bjznt.
- Initial_algebra sameAs Q6034125.
- Initial_algebra sameAs Q6034125.
- Initial_algebra wasDerivedFrom Initial_algebra?oldid=619033352.
- Initial_algebra isPrimaryTopicOf Initial_algebra.