[Haskell-beginners] Are these statements about Haskell correct?

Hi Folks, Are these statements accurate: 1. The Haskell language is a layer of abstraction on top of Lambda Calculus. 2. Haskell programs may be expressed entirely using Lambda expressions. 3. The non-Lambda stuff in Haskell is syntactic sugar to make Haskell programs easier to write. 4. The field of Lambda Calculus is formal and rich and enables powerful properties of Lambda expressions to be proven. 5. A Haskell program may be translated to consist entirely of Lambda expressions. Then, Lambda Calculus may be employed to prove powerful properties about the program. /Roger