Extensions to the Estimation Calculus

Walther’s estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules. However, there are certain features of the goal formulae which are more common to the problem of induction rule well-foundedness than the problem of termination, and which the calculus cannot handle. We present a sound extension of the calculus that is capable of dealing with these features. The extension develops Walther’s concept of an argument bounded function in two ways: firstly, so that the function may be bounded below by its argument, and secondly, so that a bound may exist between two arguments of a predicate. Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captured by the original calculus.