fg or Application[f,g]
represents the formal application of f to g.
- Application is a binary operator. fgh parses as Application[Application[f,g],h].
- Application[f,g] has no built-in meaning.
- Application[f,g] can be input as fg. The character is entered as ap or \[Application].
- Application can be used to build terms with combinators.
Examplesopen allclose all
Basic Examples (2)
Properties & Relations (3)
Possible Issues (1)
Neat Examples (2)
The reduction rule for the Turing combinator:
Prove that is a fixed-point combinator:
Eliminate variables to convert arbitrary terms into combinator form:
Find the combinator that doubles its argument:
Find the combinator for a function application:
Verify the result by applying the standard combinatory reductions for and :
Wolfram Research (2020), Application, Wolfram Language function, https://reference.wolfram.com/language/ref/Application.html.
Wolfram Language. 2020. "Application." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Application.html.
Wolfram Language. (2020). Application. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Application.html