compl

Compl, short for complement, is a term used across mathematics, logic, and computer science to denote the operation of forming a complement relative to a specified universal set or domain. It is not a single software project but a general concept that often appears as a symbol, a superscript c, a bar, or a function name in documentation and code.

In set theory, the complement of a subset A of a universal set U is the set of elements in U not in A, commonly written A^c or compl(A). The notion is essential for expressing De Morgan's laws and for describing relationships between sets and their opposites.

In logic and probability, the complement of a proposition P is its negation, and the complement of an event A has probability P(A^c) = 1 − P(A) when the probability of the universal set is 1. The concept underpins many logical inferences and probabilistic calculations.

In computer science, the bitwise complement or logical negation inverts bits or truth values. Language-specific operators or function names vary; some libraries refer to it as compl, while others use ~, not, or an explicit complement function, depending on the language and context.

In formal language theory, the complement of a language L over alphabet Σ consists of all strings over Σ not in L. The complement is used with automata and regular expressions, with considerations tied to determinism and the chosen alphabet.

Usage and notation vary by field; the term “compl” is most commonly encountered as shorthand for the complement operation in mathematical writing and in some programming contexts.