fulltext - 3 More Functional Programming The purpose of...

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Unformatted text preview: 3. More Functional Programming The purpose of this chapter is to deepen your understanding of the con- cepts encountered so far and to introduce advanced forms of datatypes and recursive functions. The first two sections give a structured presentation of theorem proving by simplification (Sect. 3.1) and discuss important heuris- tics for induction (Sect. 3.2). You can skip them if you are not planning to perform proofs yourself. We then present a case study: a compiler for ex- pressions (Sect. 3.3). Advanced datatypes, including those involving function spaces, are covered in Sect. 3.4; it closes with another case study, search trees (“tries”). Finally we introduce recdef , a general form of recursive function definition that goes well beyond primrec (Sect. 3.5). 3.1 Simplification So far we have proved our theorems by auto , which simplifies all subgoals. In fact, auto can do much more than that. To go beyond toy examples, you need to understand the ingredients of auto . This section covers the method....
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