[Haskell-cafe] Lambda Calculus: Bound and Free formal definitions

[Mark Spezzano]

Hi,

Presently I am going through AJT Davie's text "An Introduction to Functional Programming Systems Using Haskell".

On page 84, regarding formal definitions of FREE and BOUND variables he gives Defn 5.2 as 

The variable X is free in the expression E in the following cases

a) <omitted>

b) If E is a combination E1 E2 then X is free in E if and only if X is free in E1 or X is free in E2

c) <omitted>

Then in Defn 5.3 he states

The variable X is bound in the expression E in the following cases

a) <omitted>

b) If E is a combination E1 E2 then X is free in E if and only if X is free in E1 or X is free in E2.

c) <omitted>

Now, are these definitions correct? They seem to contradict each other....and they don't make much sense on their own either (try every combination of E1 and E2 for bound and free and you'll see what I mean). If it is correct then please give some examples of E1 and E2 showing exactly why. Personally I think that there's an error in the book.

You can see the full text on Google Books (page 84)

Thanks for reading!

Mark Spezzano