In mathematics and computer science, apply is a function that applies functions to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a continuous function on complete partial orders. Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology.
The most general setting for apply is in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose internal language is simply typed lambda calculus.
ARE YOU INTERESTED?
If You Feel You Can Help Our Members, Maintain And Improve Our Site.. Then Here Is The Opportunity For You..
Request Here To Become A Moderator
Post here your request for Moderator after reading the Rules. Remember no posting for request before 50...