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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-Turing thesis is that lambda calculus is Turing complete.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 wikiPageRevisionID "604756291".
- Church_encoding hasPhotoCollection Church_encoding.
- Church_encoding subject Category:Lambda_calculus.
- 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 "Booleano di Church".
- Church_encoding label "Church encoding".
- Church_encoding label "Church-Kodierung".
- Church_encoding label "Codificação de Church".
- Church_encoding label "Liczby naturalne Churcha".
- Church_encoding label "邱奇数".
- Church_encoding sameAs Church-Kodierung.
- 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 wasDerivedFrom Church_encoding?oldid=604756291.
- Church_encoding isPrimaryTopicOf Church_encoding.