Hi,
the definition in the book is a syntactic one, you are not allowed to
beta-reduce when applying the definition.
In particular
E = E1 E2 = (\x.xy)(\z.z)
The definition speaks about the term
(\x.xy)(\z.z) and not about (\z.z)y
and the definition does not speak about occurences of variables, it implicitely
defines
the _set_ of bound variables and the _set_ of free variables of term.
Both sets needn't be disjoint, for example
In (\x.x) x
x is a free as well as a bound variable.
Regards,
David
Am 30.12.2010 04:50, schrieb Mark Spezzano:
Hi all,
Thanks for your comments
Maybe I should clarify...
For example,
5.2 FREE:
========
If E1 = \y.xy then x is free
If E2 = \z.z then x is not even mentioned
So E = E1 E2 = x (\z.z) and x is free as expected
So E = E2 E1 = \y.xy and x is free as expected
5.3 BOUND:
=========
If E1 = \x.xy then x is bound
If E2 = \z.z then is not even mentioned
So E = E1 E2 = (\x.xy)(\z.z) = (\z.z)y -- Error: x is not bound but should be
by the rule of 5.3
So E = E2 E1 = (\z.z)(\x.xy) = (\x.xy) then x is bound.
Where's my mistake in the second-to-last example? Shouldn't x be bound
(somewhere/somehow)?
Thanks,
Mark
On 30/12/2010, at 1:52 PM, Mark Spezzano wrote:
Duh, Sorry. Yes, there was a typo
the second one should read
If E is a combination E1 E2 then X is bound in E if and only if X is bound in
E1 or is bound in E2.
Apologies for that oversight!
Mark
On 30/12/2010, at 1:21 PM, Antoine Latter wrote:
Was there a typo in your email? Because those two definitions appear
identical. I could be missing something - I haven't read that book.
Antoine
On Wed, Dec 29, 2010 at 9:05 PM, Mark Spezzano
<mark.spezz...@chariot.net.au> wrote:
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
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