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This paper introduces Composable Attribute Grammars (CAGs), a formalism that extends classical attribute grammars to allow for the modular composition of translation specifications and of translators. CAGs bring to complex translator writing systems the same benefits of modularity found in modern programming languages, including comprehensibility, reusability, and incremental meta-compilation.A CAG is built from several smaller component AGs, each of which solves a particular subproblem, such as name analysis or register allocation. A component AG is based upon a simplified phrase-structure that reflects the properties of its subproblem rather than the phrase-structure of the source language. Different component phrase-structures for various subproblems are combined by mapping them into a phrase-structure for the source language. Both input and output attributes can be associated with the terminal symbols of a component AG. Output attributes enable the results of solving a subproblem to be distributed back to anywhere that originally contributed part of the subproblem, e.g. transparently distributing the results of global name analysis back to every symbolic reference in the source program.After introducing CAGs by way of an example, we provide a formal definition of CAGs and their semantics. We describe a subclass of CAGs and their semantics. We describe a subclass of CAGs, called separable CAGs, that have favorable implementation properties. We discuss the novel aspects of CAGs, compare them to other proposals for inserting modularity into attribute grammars, and relate our experience using CAGs in the Linguist translator-writing system.