In mathematics, Church encoding is a way of representing various data types in the lambda calculus. In the untyped lambda calculus the only primitive...
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Gödel numbering (redirect from Gödel encoding)
structure of sets. Gödel sets can also be used to encode formulas in infinitary languages. Church encoding Description number Gödel numbering for sequences...
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functional programming languages in general. The Church encoding is named in his honor. In his honor the Alonzo Church Award for Outstanding Contributions to Logic...
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lambda calculus. Whereas Church encoding starts with representations of the basic data types, and builds up from it, Scott encoding starts from the simplest...
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computability theory, natural numbers are represented by Church encoding as functions, where the Church numeral for 1 is represented by the function f {\displaystyle...
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apply the fixed-point combinator to may be expressed using an encoding, like Church encoding. In this case particular lambda terms (which define functions)...
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it may even turn out to be more efficient than other kinds of encoding. This encoding also has the advantage of being implementable in a statically typed...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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input syntactic representations of terms under a suitable encoding (e.g., Church encoding). One may also consider a toy trivial computation model where...
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projections. In 1936, Alonzo Church created a method for defining functions called the λ-calculus. Within λ-calculus, he defined an encoding of the natural numbers...
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Lambda calculus (section Encoding datatypes)
(2-tuple) can be defined in terms of TRUE and FALSE, by using the Church encoding for pairs. For example, PAIR encapsulates the pair (x,y), FIRST returns...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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in the article on quantification (logic). The existential quantifier is encoded as U+2203 ∃ THERE EXISTS in Unicode, and as \exists in LaTeX and related...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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Note that Booleans and Naturals are defined in the same way as in Church encoding. However, additional problems arise from propositional extensionality...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
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