Abstract

When providing a collection of constructors to define an inductive type, we actually also define a dual operation: a destructor. This destructor is always defined using the same structure of pattern-matching, so that we have a tendency to forget that we do extend the “pattern-matching ” capability with a new destructor at each definition. Constructors and destructors play a dual role in the definition of inductive types. Constructors produce elements of the inductive type, destructors consume elements of the inductive type. The inductive type itself is defined as the smallest collection of elements that is stable with respect to the constructors: it must contain all constants that are declared to be in the inductive type and all results of the constructors when the arguments of these constructors are already found to be in the inductive type. When considering structural recursion, recursive definitions are functions that consume elements of the inductive type. The discipline of structural recursion imposes that recursive calls consume data that is obtained through the destructor. The inductive type uses the constructors and destructors in a specific way. Co-inductive

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