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- Church_encoding abstract "In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The data and operators form a mathematical structure which is embedded in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way.Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function. The Church encoding is not intended as a practical implementation of primitive data types. Its use is to show that other primitives data types are not required to represent any calculation. The completeness is representational. Additional functions are needed to translate the representation into common data types, for display to people. It is not possible in general to decide if two functions are extensionally equal due to the undecidability of equivalence from Church's theorem. The translation may apply the function in some way to retrieve the value it represents, or look up its value as a literal lambda term.Lambda calculus is usually interpreted as using intensional equality. There are potential problems with the interpretation of results because of the difference between the intensional and extensional definition of equality.".
- Church_encoding wikiPageExternalLink 33429551_PHD_totalthesis.pdf.
- Church_encoding wikiPageExternalLink supplemental.pdf.
- Church_encoding wikiPageExternalLink archon.pdf.
- Church_encoding wikiPageExternalLink const-int.
- Church_encoding wikiPageID "2989409".
- Church_encoding wikiPageLength "33911".
- Church_encoding wikiPageOutDegree "46".
- Church_encoding wikiPageRevisionID "671877914".
- Church_encoding wikiPageWikiLink Addition.
- Church_encoding wikiPageWikiLink Alonzo_Church.
- Church_encoding wikiPageWikiLink Arithmetic.
- Church_encoding wikiPageWikiLink Beta_reduction.
- Church_encoding wikiPageWikiLink Category:Lambda_calculus.
- Church_encoding wikiPageWikiLink Church-Turing_thesis.
- Church_encoding wikiPageWikiLink Churchs_theorem.
- Church_encoding wikiPageWikiLink Church–Turing_thesis.
- Church_encoding wikiPageWikiLink Cons.
- Church_encoding wikiPageWikiLink Deductive_lambda_calculus.
- Church_encoding wikiPageWikiLink Division_(mathematics).
- Church_encoding wikiPageWikiLink Embedding.
- Church_encoding wikiPageWikiLink Entscheidungsproblem.
- Church_encoding wikiPageWikiLink Exponentiation.
- Church_encoding wikiPageWikiLink Extensionality.
- Church_encoding wikiPageWikiLink Fixed-point_combinator.
- Church_encoding wikiPageWikiLink Fold_(higher-order_function).
- Church_encoding wikiPageWikiLink Function_composition.
- Church_encoding wikiPageWikiLink Haskell_(programming_language).
- Church_encoding wikiPageWikiLink Higher-order_function.
- Church_encoding wikiPageWikiLink Immutable_object.
- Church_encoding wikiPageWikiLink Integer.
- Church_encoding wikiPageWikiLink Lambda_calculus.
- Church_encoding wikiPageWikiLink Lambda_lifting.
- Church_encoding wikiPageWikiLink List_(abstract_data_type).
- Church_encoding wikiPageWikiLink List_(computing).
- Church_encoding wikiPageWikiLink Mathematics.
- Church_encoding wikiPageWikiLink Mogensen–Scott_encoding.
- Church_encoding wikiPageWikiLink Multiplication.
- Church_encoding wikiPageWikiLink Natural_number.
- Church_encoding wikiPageWikiLink Ordinal_number.
- Church_encoding wikiPageWikiLink Ostensive_definition.
- Church_encoding wikiPageWikiLink Pico_(programming_language).
- Church_encoding wikiPageWikiLink Rice_University.
- Church_encoding wikiPageWikiLink Smalltalk.
- Church_encoding wikiPageWikiLink Subtraction.
- Church_encoding wikiPageWikiLink Successor_function.
- Church_encoding wikiPageWikiLink System_F.
- Church_encoding wikiPageWikiLink Truth_value.
- Church_encoding wikiPageWikiLinkText "Church booleans".
- Church_encoding wikiPageWikiLinkText "Church encoding for pairs".
- Church_encoding wikiPageWikiLinkText "Church encoding of numerals".
- Church_encoding wikiPageWikiLinkText "Church encoding".
- Church_encoding wikiPageWikiLinkText "Church encoding#Church Booleans".
- Church_encoding wikiPageWikiLinkText "Church numeral".
- Church_encoding wikiPageWikiLinkText "Division".
- Church_encoding wikiPageWikiLinkText "Signed numbers".
- Church_encoding wikiPageWikiLinkText "divide".
- Church_encoding wikiPageWikiLinkText "division".
- Church_encoding wikiPageWikiLinkText "signed numbers".
- Church_encoding hasPhotoCollection Church_encoding.
- Church_encoding wikiPageUsesTemplate Template:See_also.
- Church_encoding subject Category:Lambda_calculus.
- Church_encoding hypernym Means.
- Church_encoding type Model.
- Church_encoding type Person.
- Church_encoding type Model.
- Church_encoding type Thing.
- Church_encoding comment "In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The data and operators form a mathematical structure which is embedded in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation.".
- Church_encoding label "Church encoding".
- Church_encoding seeAlso Cons.
- Church_encoding sameAs Church-Kodierung.
- Church_encoding sameAs Κωδικοποίηση_Τσερτς.
- Church_encoding sameAs Booleano_di_Church.
- Church_encoding sameAs Liczby_naturalne_Churcha.
- Church_encoding sameAs Codificação_de_Church.
- Church_encoding sameAs m.08j2bb.
- Church_encoding sameAs Q1089708.
- Church_encoding sameAs Q1089708.
- Church_encoding sameAs 邱奇数.
- Church_encoding wasDerivedFrom Church_encoding?oldid=671877914.
- Church_encoding isPrimaryTopicOf Church_encoding.