Return-Path: <kfoury@cs.bu.edu> Received: from cs.bu.edu (cs [128.197.12.2]) by cs3.bu.edu (8.12.11/8.12.11) with ESMTP id iAJLWvZd030645; Fri, 19 Nov 2004 16:32:57 -0500 Received: from cs.bu.edu (kfoury@fiddle [128.197.10.114]) (authenticated bits=0) by cs.bu.edu (8.12.2/8.12.2) with ESMTP id iAJLWw0g027176; Fri, 19 Nov 2004 16:32:58 -0500 (EST) Sender: kfoury@cs.bu.edu Message-ID: <419E6686.24EF4568@cs.bu.edu> Date: Fri, 19 Nov 2004 16:32:54 -0500 From: "Assaf J. Kfoury" <kfoury@cs.bu.edu> Organization: Boston University X-Mailer: Mozilla 4.78 [en] (X11; U; SunOS 5.8 sun4u) X-Accept-Language: en To: cs520@cs.bu.edu Subject: advice for the homework assignments Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Spam-HitLevel: X-Spam-DCC: dmv.com: cs3.bu.edu 1181; Body=1 Fuz1=1 Fuz2=1 X-Spam-Checker-Version: SpamAssassin 3.0.1 (2004-10-22) on cs3.bu.edu X-Spam-Level: X-Spam-Status: No, score=-4.6 required=10.0 tests=ALL_TRUSTED,AWL,BAYES_00 autolearn=ham version=3.0.1 X-Spam-Pyzor: Reported 0 times. Status: X-Mozilla-Status: 8001 X-Mozilla-Status2: 00000000 X-UIDL: 4192ca74000003eb
A couple of people in the class mentioned that
formatting derivations in LaTeX can be very
time-consuming. Yes, it can, especially if you
write them in the form of derivation trees, as
in my handouts.
To save time and avoid the many complications
of formatting in LaTeX (or in your preferred
text editor), you can write a derivation as a
sequence of numbered judgments. For example,
you can write the following derivation to show
that (lambda f. lambda x. f x) can be assigned the
type (Nat -> Nat) -> (Nat -> Nat):
(1) f: Nat -> Nat, x: Nat |- f: Nat -> Nat (T-Var)
(2) f: Nat -> Nat, x: Nat |- x: Nat (T-Var)
(3) f: Nat -> Nat, x: Nat |- f x: Nat (T-App + (1,2))
(4) f: Nat -> Nat |- (lam x. f x): Nat -> Nat (T-Abs + (3))
(5) |- (lam f. lam x. f x): (Nat -> Nat) -> Nat -> Nat (T-Abs +
(4))
Assaf
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