Technological importance of traceability mappings for model transformations is well-known, but they have often been considered as an auxiliary element generated during the transformation execution and providing accessory information. This paper argues that traceability mappings should instead be regarded as a core aspect of the transformation definition, and a key instrument in the transformation management. We will show how a transformation can be represented as the result of execution of a metamodel mapping, which acts as a special encoding of the transformation definition. Since mappings enjoy Boolean operations (as sets of links) and sequential composition (as sets of directed links), encoding transformations by mappings makes it possible to define these operations for transformations as well, which can be useful for model transformation reuse, compositional design, and chaining.