Unification

Unification may refer to:

See also

Unification (Star Trek: The Next Generation)

"Unification" is the title of a two-part episode of the syndicated American science fiction television series Star Trek: The Next Generation, from the fifth season, which features Leonard Nimoy as Spock. It earned a 15.4 household Nielsen rating, drawing over 25 million viewers, making it one of the most watched episodes in all seven seasons of The Next Generation's run.

Hearing that legendary Starfleet officer Spock may have defected to the Romulan Empire, Picard travels to Vulcan to talk to Spock's father, former ambassador Sarek, who is near death from the ravages of Bendi Syndrome. In a rare lucid moment, Sarek discloses that Spock has long harbored hopes of peacefully reuniting the Vulcan and Romulan peoples, who once were part of the same civilization. Rather than committing treason, Spock actually may be initiating steps to achieve that peaceful goal. Determined to find the truth, Picard and Data, disguised as Romulans, set out for the Romulan homeworld. Upon finding Spock, Picard learns that the Vulcan is indeed on an unauthorized mission to reunify his people with the Romulans. Spock counts among his allies a Romulan senator named Pardek and the Romulan proconsul Neral.

Unification (computer science)

Unification, in computer science and logic, is an algorithmic process of solving equations between symbolic expressions.

Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactical unification, otherwise semantical, or equational unification, or E-unification, or unification modulo theory.

A solution of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a complete, and minimal substitution set, that is, a set covering all its solutions, and containing no redundant members. Depending on the framework, a complete and minimal substitution set may have at most one, at most finitely many, or possibly infinitely many members, or may not exist at all. In some frameworks it is generally impossible to decide whether any solution exists. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.