Transformationslogik

Transformationslogik, or transformation logic, is a formal framework for specifying and reasoning about transformations of structured data, software, and models. It integrates ideas from term rewriting, graph transformation, and dynamic logic to describe how sources are transformed into targets via rule applications. The goal is to support precise specifications, verification of transformation properties, and systematic derivations of results.

A transformation system consists of a set of rules. Each rule has a left-hand pattern identifying a substructure and a right-hand side describing the replacement. Rules may have preconditions, side conditions, and strategies that control application. Semantics define a derivation as a sequence of rule applications that yields a well-formed target.

Key properties studied include termination and confluence. Termination ensures every transformation sequence ends; confluence guarantees that different orders of rule application yield the same final result up to isomorphism. Invariants and correctness specifications are expressed as preconditions and postconditions or as logical formulas preserved across transformations.

Formalizations use signatures, rules, and interpretation structures. The framework relates to dynamic logic for reasoning about program-like transformations and to algebraic or category-theoretic models that capture composition. It can be implemented in reasoning tools and transformation engines to verify properties or generate correct transformations.

Applications include software refactoring, model-driven engineering, data migration, and compiler optimization, where correctness guarantees are important. Variants exist for term-based, graph-based, and hybrid transformations, with constraints and typing to ensure well-formed results.