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Church encoding - Church booleans | | Church encoding - Church booleans: Encyclopedia II - Church encoding - Church booleans | | Church booleans are the Church encoding of the boolean values true and false. Some programming languages use these as implementation model for boolean arithmetic; examples are Smalltalk and Pico. The boolean values are represented as functions of two values that evaluate to one or the other of their arguments.
Formal definition in lambda calculus:
true ≡ λa.λb. a
...
See also:Church encoding, Church encoding - Church numerals, Church encoding - Definition, Church encoding - Computation with Church numerals, Church encoding - Translation with other representations, Church encoding - Church booleans | | | Church encoding, Church encoding - Church booleans, Church encoding - Church numerals, Church encoding - Computation with Church numerals, Church encoding - Definition, Church encoding - Translation with other representations, Lambda calculus | | |
| | | Church encoding: Encyclopedia II - Church encoding - Church booleans
Church encoding - Church booleans
Church booleans are the Church encoding of the boolean values true and false. Some programming languages use these as implementation model for boolean arithmetic; examples are Smalltalk and Pico. The boolean values are represented as functions of two values that evaluate to one or the other of their arguments.
Formal definition in lambda calculus:
true ≡ λa.λb. a
false ≡ λa.λb. b
Functions of boolean arithmetic can be derived for Church booleans:
and ≡ λm.λn.λa.λb. m (n a b) b
or ≡ λm.λn.λa.λb. m a (n a b)
not ≡ λm.λa.λb. m b a
Other related archives=β, Alonzo Church, Church booleans, Gödel numbering, Haskell, Lambda calculus, Pico, Smalltalk, composition, higher-order function, lambda abstractions, lambda calculus, natural numbers, β-equivalent
 Adapted from the Wikipedia article "Church booleans", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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