A combinator, in the context of computer science and mathematics, is a function or an expression that combines or manipulates other functions or expressions to produce new functions or expressions. Combinators are used in fields like functional programming, lambda calculus, and logic.
Combinators are unique in that they do not rely on any external input, but rather operate solely on the functions or expressions they are given. They can take functions as arguments and return functions as results, effectively transforming or recomposing them in various ways.
Combinators are widely known for their ability to express complex computations by composing, applying, or transforming simpler functions. They can be thought of as building blocks that allow for the construction of more intricate computational processes by linking simpler components together.
In lambda calculus, a branch of mathematical logic, combinators have a fundamental role in representing and manipulating functions as objects. They are used to build function compositions, abstractions, and applications, enabling the formulation of calculations and proofs.
Combinators are often classified into different types or families, such as combinators for function composition, combinators for function application, or combinators for function abstraction. Each type of combinator follows specific rules and principles, providing a structured framework for combining and manipulating functions.
Overall, the concept of a combinator encapsulates the idea of using functions or expressions as inputs and outputs to create new computational structures, allowing for the powerful composition and transformation of functions in various fields of study.
