Chinese mathematics competitions and olympiads: 1993-2001 by Andy Liu

By Andy Liu

This publication is a continuation of the sooner quantity (1981-1993) and covers the years 1993 to 2001.China has an excellent list within the foreign Mathematical Olympiad, and the ebook comprises the issues which have been used to spot the workforce applicants and choose the chinese language groups. the issues are meticulously built, many with detailed flavour. they arrive in all degrees of hassle, from the rather uncomplicated to the main tough.

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This goal returns S = [a, b, c]. For another example, suppose that we want to calculate the set of second arguments that have the letter a as a first argument of p. In other words, we 60 Prolog Experiments want to calculate the set S = {x | p(a, x)} = {b, c}. We can compute the set S with the following goal. - setof(X, p(a, X), S). This goal returns S = [b, c]. For another example, suppose that we want to construct the set of “grandparent” relationships from p. If we let g(x, y) mean that x is a grandparent of y, then we can describe the set S of these relations as the following set.

Abcd = X. - abcd = [H|T]. - a+b = X. - ‘a+b’ = X. - ‘a+b’ = [H|T]. Although atoms can’t be manipulated, there is a Prolog predicate that transforms between atoms and strings. The predicate “name” does the job. Try out the following goals to get the idea. - name(abc, X). - name(X, [97, 98, 99]). - name(abc, [97, 98, 99]). - name(a+b, X). - name('a+b',X). Experiments to Perform 1. Try out a few more examples to get used to the notation for lists. For example, try out the following goals. - [A, B | C] = [1, 2, 3, 4, 5].

7. 8. 9. -p(b, Y) P P P P P P (the goal) 5, 6, R, q1 = {X/a, W/Y}. 1, 7, R, q2 = {Z/b} 3, 8, R, q3 = {Y/d}. Applying the composition of the three unifiers to the given goal atom, we obtain g(a, W)q1q2q3 = g(a, d), which is a logical consequence of the program P. Experiments to Perform 1. For the given program, trace the execution of the goal G. Then observe the relationships between the calls of the trace and the clauses on lines 6, 7, 8, and 9 of the SLD-refutation. 2. For the given example there is another SLD-refutation.

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