Induce-Statements and Induce-Expressions: Constructs for Inductive Programming

A for loop is somewhat similar to an inductive argument Just as the truth of a proposition P n depends on the truth of P n the correctness of iteration n of a for loop depends on iteration n having been completed correctly This paper presents the induce construct a new programming construct based on the form of inductive arguments It is more expressive than the for loop yet less expressive than the while loop Like the for loop it is always terminating Unlike the for loop it allows the convenient and concise expression of many algorithms The for loop traverses a set of consecutive natural numbers the induce construct generalizes to other data types The induce construct is presented in two forms one for imperative lan guages and one for functional languages The expressive power of lan guages in which this is the only recursion construct is greater than prim itive recursion namely it is the multiply recursive functions in the rst order case and the set of functions expressible in G odel s system T in the general case