Re: question about ch. 5

From: Assaf J. Kfoury (kfoury@cs.bu.edu)
Date: Mon Sep 20 2004 - 16:46:33 EDT 

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Date: Mon, 20 Sep 2004 16:46:33 -0400
From: "Assaf J. Kfoury" <kfoury@cs.bu.edu>
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To: Hany Morcos <hmorcos@cs.bu.edu>, cs520@cs.bu.edu
Subject: Re: question about ch. 5
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I think you are referring to the *parentheses*. There
are no *braces*, i.e., "{" and "}", in the definitions of
scc, plus and times.

Look at the definition of scc:

lambda n. lambda s. lambda z. s (n s z)

If you omit the parentheses, then you will get a new
definition, equivalent to the following -- call it scc'

scc' = lambda n. lambda s. lambda z. (((s n) s) z)

If you apply scc' to a Church numeral c_k and evaluate
the application (scc' c_k), you will *not* get c_{k+1}.
So, without the parentheses in the definition of scc,
you will not get the desired behavior.

(See also page 6 in my Handout 4.)

I hope this answers your question.

Assaf

Hany Morcos wrote:

> Prof. Kfoury,
>
> I have a question in ch. 5. In the definition of the functions scc, plus and
> times ... (p 61)
> What is the meaning of the braces around some arguments ? how does that
> affect the evaluation of the function ?
>
> Thanks,
> Hany

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