under Church encoding. The Church–Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding.[dubious...
40 KB (6,538 words) - 22:51, 23 July 2024
lambda calculus. Whereas Church encoding starts with representations of the basic data types, and builds up from it, Scott encoding starts from the simplest...
10 KB (1,781 words) - 02:54, 7 July 2024
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...
23 KB (2,189 words) - 19:06, 31 July 2024
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...
11 KB (1,530 words) - 00:00, 24 August 2024
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...
57 KB (6,728 words) - 14:28, 6 June 2024
computability theory, natural numbers are represented by Church encoding as functions, where the Church numeral for 1 is represented by the function f {\displaystyle...
33 KB (3,305 words) - 23:50, 3 September 2024
apply the fixed-point combinator to may be expressed using an encoding, like Church encoding. In this case particular lambda terms (which define functions)...
32 KB (4,392 words) - 21:51, 2 September 2024
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...
8 KB (901 words) - 17:00, 15 April 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
4 KB (402 words) - 00:58, 1 September 2024
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...
86 KB (11,552 words) - 04:59, 28 August 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
11 KB (1,474 words) - 03:24, 7 September 2024
Entscheidungsproblem (redirect from Church's Theorem)
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...
19 KB (2,620 words) - 06:57, 20 August 2024
input syntactic representations of terms under a suitable encoding (e.g., Church encoding). One may also consider a toy trivial computation model where...
41 KB (5,243 words) - 13:58, 25 August 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
4 KB (421 words) - 18:30, 15 May 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
6 KB (835 words) - 22:17, 19 December 2023
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
6 KB (617 words) - 15:11, 17 April 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
16 KB (2,493 words) - 13:11, 1 June 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
8 KB (958 words) - 16:16, 13 June 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
3 KB (434 words) - 15:39, 18 October 2023
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
6 KB (708 words) - 22:05, 28 July 2024
Union (set theory) (section Notation encoding)
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
9 KB (1,262 words) - 02:59, 23 February 2024
Note that Booleans and Naturals are defined in the same way as in Church encoding. However, additional problems arise from propositional extensionality...
9 KB (1,344 words) - 21:04, 30 May 2024
New York: Raven Press, ISBN 9780486432281. Papers include those by Gödel, Church, Rosser, Kleene, and Post. Dummett, Michael (1991), The Logical Basis of...
17 KB (1,896 words) - 00:32, 16 May 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
16 KB (1,960 words) - 12:52, 27 August 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
7 KB (796 words) - 08:53, 30 June 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
11 KB (1,725 words) - 04:27, 24 August 2024
Turing machine (section Church's thesis)
"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...
74 KB (9,526 words) - 14:50, 20 August 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
21 KB (2,821 words) - 15:28, 14 June 2024
OCaml (section Church numerals)
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...
37 KB (4,007 words) - 12:41, 6 September 2024
predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable function Computable...
8 KB (1,141 words) - 20:15, 8 October 2023