Sample Specifications by Examples and Properties

Let s illustrate the notion of specifications by examples and properties by a few sample specifications (others may be found in Section 14.4.2). The chosen language for properties is, strictly for the sake of illustration, non-recursive normal clauses that have a head with the predicate of the examples. Universal quantifiers are usually dropped for convenience. Also, negative examples are not allowed. Note that most of this Part II is independent of such choices. Our claim is that such properties and examples, if carefully chosen, embody the minimal knowledge that doesn t give away the solution, but is sufficient for successful algorithm design. 

Note that, for ease of syntax, we have changed the format of compact lists to lists whose elements alternately are values and counters. 

Note that properties P to generalize examples to 4, respectively. Example E can t be generalized. So what about generalizing examples 5 to g The clause  

But one could also think about writing properties that generalize more than the given examples, say with the first parameter being a list of any length. Rather than only generalizing the problem-specific constants a, fi. of the examples into variables X, y,. .., this consists in also generalizing the predefined constant nil into a variable, say T. The clauses  

Properties Pj to P3 generalize examples to 3, respectively. As in the preceding sample specification, there is no real motivation to explicitly generalize the other examples. But, this time, it is possible to generalize the nil constant into a variable without always having to introduce recursion. The resulting allowed properties are  

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