Continuous Lattices Proc. conf. Bremen, 1979 by B. Banaschewski, R.-E. Hoffmann

By B. Banaschewski, R.-E. Hoffmann

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For each of the following cases, use setof, bagof, or findall to construct the indicated set or bag. a. The set of all facts of the form p(0, X, Y, Z) for some X, Y, and Z. b. The bag of all numbers N such that p(X, Y, 0, N) for some X and Y. c. The bag of all numbers N such that p(X, Y, Z, N) for some X, Y, and Z. d. The bag of all pairs [Y, Z] such that p(X, Y, Z, N) for some X and N. e. The set of all facts of the form p(X, Y, Z, N) where N < 100. 3 List Membership and Set Operations Most versions of Prolog have a predicate to test whether an element is a member of a list.

Then we are given the opportunity to switch our choice from x to z. What should we do? We should switch. To see this, notice that once we pick a number, the probability that we did not pick the winner is 2/3. In other words, it is more likely that one of the other two numbers is a winner. So when we are given one of the other numbers and told that it is not the winner, it follows that the remaining other number has probability 2/3 of being the winner. So go ahead and switch. We can write an experiment to test the claim by using a random number generator.

1. 2. 3. 4. 5. 6. t=u u=v u = vŸt = uÆ t = v u = vŸt = u t=v t = uŸu = vÆ t = v QED. P P EE Axiom 1, 2, Conj 3, 4, MP 1, 2, 5, CP a. Construct a Prolog experiment to verify this proof. b. Explain how your Prolog experiment verifies the transitivity proof. 5 SLD-Resolution Let’s introduce some terminology regarding computations of logic programs. “SLD-resolution” is name of the inference rule—which is a special case of the resolution inference rule—that is used to perform computation in logic programs.

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