By Hein J. L.

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**Extra info for Prolog Experiments in Discrete Mathematics, Logic, and Computability**

**Example text**

P(X) :- c(X). q(X) :- \+ c(X). - p(a). - q(a). - p(b). - q(b). What does this experiment have to do with logical if-then-else? 3. (If-then-else) For each of the following experiments enter the given data in the program and then ask the following questions. - s(a). - s(b). - s(c). - s(X). Use backtracking whenever possible to find alternative answers. ” Compare the two tests and discuss whether one definition is preferable to the other. a. p(a). p(b). q(a). r(b). s(X):- p(X), q(X). s(X):- \+ p(X), r(X).

A predicate) that the elements of the set must satisfy. For example, if we let p(a, b) mean that “a is a parent of b,” then the set S of all people who are parents can be described as S = {x | p(x, y) for some y} In terms of formal logic, the statement “p(x, y) for some y” can be written as $y p(x, y). So we can describe S as S = {x | $y p(x, y)}. Prolog provides a useful tool called the “setof” predicate that can be quite useful in calculating sets. We’ll introduce it with some examples. Suppose we put the following four facts in the program.

Recursive Techniques 37 d. - nospy seq, spy nat, seq(3). ) e. - trace, seq(3). ) 2. Make each of the following modifications to the definition of the seq predicate. a. Interchange the two seq clauses so that the basis case comes after the recursive case. Test the new definition to see whether anything happens. Why or why not? b. Starting with the modification to the seq predicate made in part (a), delete the call to nat(N) in the recursive clause. Test the new definition to see whether anything happens.

### Prolog Experiments in Discrete Mathematics, Logic, and Computability by Hein J. L.

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