Partial closures and semantics of while: Towards an iteration-based theory of data types

The present paper proposes first a generalization of closure theory and revisits Moore's theory in this framework. Afterwards closures of non cyclic functions are introduced and a method is given to transform cyclic into non cyclic functions. Eventually semantics of the while construct is found to be the closure of a function. Computability on inductive and non inductive data types is then studied with iterative means.