structural recursion การใช้

• The examples in this section illustrate what is known as " structural recursion ".
• Structural recursion is usually proved correct by structural induction; in particularly easy cases, the inductive step is often left out.
• Since their introduction, inductive types have been extended to encode more and more structures, while still being predicative and supporting structural recursion.
• Structural recursion includes nearly all tree traversals, including XML processing, binary tree creation and search, etc . By considering the algebraic structure of the natural numbers ( that is, a natural number is either zero or the successor of a natural number ), functions such as factorial may also be regarded as structural recursion.
• Structural recursion includes nearly all tree traversals, including XML processing, binary tree creation and search, etc . By considering the algebraic structure of the natural numbers ( that is, a natural number is either zero or the successor of a natural number ), functions such as factorial may also be regarded as structural recursion.
• The paper then distinguishes between structural recursion, where the related data definition happens to be self-referential, requiring usually a straightforward design process, and generative recursion, where new problem data is generated in the middle of the problem-solving process and the problem solving method is re-used, often requiring " ad hoc " mathematical insight, and stresses how this distinction makes their approach scalable to the object-oriented ( OO ) world.