Unifier

A unifier is a term used to describe something that brings together different elements into a coherent whole. In general, a unifier resolves differences by aligning components so that they can be treated as a single, compatible entity.

In logic and computer science, a unifier is a substitution that makes two expressions identical. A most general unifier (MGU) is a substitution that unifies two terms and is more general than any other unifier. Robinson's unification algorithm computes MGUs for first-order terms, and unification underpins logic programming languages such as Prolog, as well as type inference and automated reasoning. Unification problems are decidable for first-order terms, though adding higher-order features or certain extensions increases complexity and may require an occurs-check to avoid self-reference.

In linguistics, especially in unification-based grammars and feature structures, a unifier is the operation that merges feature descriptions. It resolves constraints such as grammatical agreement and subcategorization by computing the most general unifier of two feature structures, ensuring compatibility in syntactic analysis and parsing.

In software engineering and data integration, the term unifier can refer to a component or process that reconciles divergent schemas or data models, producing a common representation suitable for processing or analysis.

In broader usage, a unifier may refer to a person, idea, or process intended to bring groups, theories, or systems into alignment. The concept emphasizes compatibility and coherent synthesis, identifying how elements can be merged with minimal, consistent changes.