[plt-scheme] redex is great

From: Robby Findler (robby at eecs.northwestern.edu)
Date: Sat Feb 21 10:07:36 EST 2009

Yes, that's what I meant with the comments at the end. The example was
just in response to your comments about T and (T T), etc. The final
paragraph suggests how to make your example work.


On Sat, Feb 21, 2009 at 8:55 AM, Jos Koot <jos.koot at telefonica.net> wrote:
> This does not reduce T in (x T) and (λ x T), I think
> You probably get a head normal form, but not a normal form, I think
> Jos
> ----- Original Message ----- From: "Robby Findler"
> <robby at eecs.northwestern.edu>
> To: "Jos Koot" <jos.koot at telefonica.net>
> Cc: <plt-scheme at list.cs.brown.edu>
> Sent: Saturday, February 21, 2009 3:41 PM
> Subject: Re: [plt-scheme] redex is great
> On Sat, Feb 21, 2009 at 8:22 AM, Jos Koot <jos.koot at telefonica.net> wrote:
>> Suppose we have a language and a reductor that uses in-hole. Then if term
>> T
>> matches the in-hole clause, the term (T T) has two matches. As far as I
>> can
>> see both matches are returned by apply-reduction-relation (which in
>> general
>> is nice, of course, but here I am talking about leftmost reduction). Hence
>> this reductor does not limit itself to leftmost redices only.
> I'm not completely sure I'm getting your meaning above, but consider
> this grammar:
>  T = (λ x T) | (T T) | x
>  E = hole | ((λ x T) E) | (E T)
>  x = variables
> with this rule:
> (--> (in-hole E ((λ x T_1) (λ x T_2)))
>     (in-hole E (subst x T_1 T_2)))
> and this example input:
>  (((λ x x) (λ y y))
>  ((λ p p) (λ q q)))
> It reduces to this:
>  ((λ y y)
>  ((λ p p) (λ q q)))
> but it does not reduce to this:
>  (((λ x x) (λ y y))
>  (λ q q))
> because the decomposition of the term does not allow the hole to be on
> the second application. That is, the context is restricting
> applicability of the rule to only a subset of the places where it
> might otherwise apply.
> I didn't go thru the exercise and try it out myself, but reading over
> your definition of nf? and reduction-step, you should be able to
> formulate them as contexts. nf? could clearly be formulated as a
> non-terminal in the grammar that matches only things that nf? returns
> true for, and then reduction-step can be turned into a definition of a
> context that has the hole at the point where (in the definition of
> reduction-step) you call subst (ie, case 3).
> Robby

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