under Church encoding. The Church–Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding.[dubious...

lambda calculus. Whereas Church encoding starts with representations of the basic data types, and builds up from it, Scott encoding starts from the simplest...

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...

structure of sets. Gödel sets can also be used to encode formulas in infinitary languages. Church encoding Description number Gödel numbering for sequences...

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...

computability theory, natural numbers are represented by Church encoding as functions, where the Church numeral for 1 is represented by the function f {\displaystyle...

apply the fixed-point combinator to may be expressed using an encoding, like Church encoding. In this case particular lambda terms (which define functions)...

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...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

(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...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

a given statement is provable using the rules of logic. In 1936, Alonzo Church and Alan Turing published independent papers showing that a general solution...

input syntactic representations of terms under a suitable encoding (e.g., Church encoding). One may also consider a toy trivial computation model where...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

Note that Booleans and Naturals are defined in the same way as in Church encoding. However, additional problems arise from propositional extensionality...

New York: Raven Press, ISBN 9780486432281. Papers include those by Gödel, Church, Rosser, Kleene, and Post. Dummett, Michael (1991), The Logical Basis of...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

"universal" nature was introduced by Alonzo Church. Church's work intertwined with Turing's to form the basis for the Church–Turing thesis. This thesis states that...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...

1 The following code defines a Church encoding of natural numbers, with successor (succ) and addition (add). A Church numeral n is a higher-order function...

predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...