One useful distinction I make is between types and datatypes. Types are a mathematical theory in which you are able to prove things about the terms of you progr

One useful distinction I make is between types and datatypes. Types are a mathematical theory in which you are able to prove things about the terms of you program. Datatypes are like types but without the structure or logic. They don't prove anything and are basically just sets. You have to bring your own rules. Dynamic languages are unityped, you can see this by noting working only on just a top type shares many properties (not all, e.g. flexibility) of being in a dynamic language. Dynamic languages however can have datatypes, which make sure operations on the collections a particular object inhabits makes sense according to rules the language designer defines. For your example, in a dynamic language I can state that r,a and b all belong to the same type but their datatypes may vary from moment to moment. In a statically typed language I cannot. Without types a ST language will assume that a and b are the same universal type. But I could give just a a top type and then your example would work. But I lose type safety. To get it back I could use interfaces, inheritance or algebraic datatypes each with their own pros and cons.