15317 Constructive Logic
Recitation 8: G4ip review and Prolog tutorial
Today in recitation, we reviewed some of the rules of the G4ip calculus
by constructing a proof of the doublenegation of Peirce's Law:
¬ ¬ (((P ⊃ Q) ⊃ P) ⊃ P). In constructing the
proof, we discussed the importance of remembering choice points when we
apply noninvertible rules like ⊃⊃L, although we never
found ourselves needing to backtrack while proving this particular theorem.
We also discussed the importance of never throwing a hypothesis away without
good reason, in case it might be needed later in the proof.
After that, we played around with GNU Prolog a bit, writing the
plus and times examples from class. We saw how
plus could be used to compute subtraction, but
times could not necessarily be used to compute (even exact)
division. The intuitive reason is that times cannot be given an
appropriate mode (i.e. specification of inputs and outputs) to be
interpreted as division unless we rewrote it with a different subgoal order,
in which case it could no longer be interpreted as multiplication. In
both cases, the failure was to backtrack infinitely after finding one
correct answer.
References:
 Plus and Times code in Prolog, with discussion of modes:
plustimes.pl
(Recall that to load a file file.pl into Prolog, you give the
query ['file.pl']. at the ? prompt.)
[ Home
 Schedule
 Assignments
 Handouts
 Software
]
fp@cs
Frank Pfenning
