Apply

In mathematics and computer science, apply is a function that applies a function 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 , where it is right adjoint to currying in . A special case of this are the Cartesian closed categories, whose internal language is simply typed lambda calculus. In computer programming, apply applies a function to a list of arguments. Eval and apply are the two interdependent components of the eval-apply cycle, which is the essence of evaluating Lisp, described in SICP. Function application corresponds to beta reduction in lambda calculus. Apply is also the name of a special function in many languages, which takes a function and a list, and uses the list as the function's own argument list, as if the function were called with the elements of the list as the arguments. This is important in languages with variadic functions, because this is the only way to call a function with an indeterminate (at compile time) number of arguments. In Common Lisp apply is a function that applies a function to a list of arguments (note here that "+" is a variadic function that takes any number of arguments): (apply #'+ (list 1 2)) Similarly in Scheme: (apply + (list 1 2)) In C++, Bind is used either via the std namespace or via the boost namespace. In C# and Java, variadic arguments are simply collected in an array. Caller can explicitly pass in an array in place of the variadic arguments. This can only be done for a variadic parameter.

Reducibility bounds of objective functions over the integers

Friedrich Eisenbrand, Kim-Manuel Klein

We study the settings where we are given a separable objective function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our results appl ...

Amsterdam2023

Reducibility bounds of objective functions over the integers

Python module for finite rate of innovation (FRI) sampling

Reducibility bounds of objective functions over the integers

Python module for finite rate of innovation (FRI) sampling