Attribute grammars and mathematical semantics are rival language definition methods. We show that any attribute grammar G has a reformulation MS (G) within mathematical semantics. Most attribute grammars have properties that discipline the sets of equations the grammar gives to derivation trees. We list six such properties, and show that for a grammar G with one of these properties both MS (G) and the compiler for G can be simplified. Because these compiler-friendly properties are of independent interest, the paper is written in such a way that the first and last sections do not depend on the other sections.