[Haskell-cafe] Type Synonyms

Newbie question: I was wondering the other day if type synonyms might be more useful if they were more restricted, that is, with the definitions: type Foo = String type Bar = String foo :: Foo foo = "a foo" bar :: Bar bar = "a bar" x :: Foo -> ... x f b = ...only valid for Foo Strings... both 'x foo' and 'x bar' type check correctly. Wouldn't it be useful if Foo and Bar were both equivalent to String, but Foo and Bar were not equivalent themselves? For instance, if you are using Strings as properties of something and want to associate the type of the property with its value, without wrapping the String. Would this break a transitivity property of the type system? Am I just suffering from laziness?