[Haskell-cafe] Type Synonyms

[Tom Davies]

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?