Inductive Fixpoints in Higher Order Logic
نویسنده
چکیده
We show that an analogue of the domain-theoretic least fixpoint operator can be defined in a purely set-theoretic framework. It can be formalized in classical higher order logic, serving as a solid foundation for proving termination of (possibly nested) recursive programs in a variety of mechanized proof systems.
منابع مشابه
Inductive Invariants for Nested Recursion
We show that certain input-output relations, termed inductive invariants are of central importance for termination proofs of algorithms defined by nested recursion. Inductive invariants can be used to enhance the standard recdef definition package in Isabelle/HOL. We also offer a formalized theory in higher-order logic that incorporates inductive invariants and that can be used as an alternativ...
متن کاملFixpoints and Bounded Fixpoints for Complex Objects
We investigate a query language for complex-object databases, which is designed to (1) express only tractable queries, and (2) be as expressive over flat relations as first order logic with fixpoints. The language is obtained by extending the nested relational algebra NRA with a "bounded fixpoint" operator. As in the flat case, all PTime computable queries over ordered databases are expressible...
متن کاملOrder theoretic Correspondence theory for Intuitionistic mu-calculus
Sahlqvist correspondence theory [3], [4] is one of the most important and useful results of classical modal logic. It gives a syntactic identification of a class of modal formulas whose associated normal modal logics are strongly complete with respect to elementary (i.e. first-order definable) classes of frames. Every Sahlqvist formula is both canonical and corresponds to some elementary frame ...
متن کاملCompleteness and Definability of a Modal Logic Interpreted over Iterated Strict Partial Orders
Any strict partial order R on a nonempty set X defines a function θR which associates to each strict partial order S ⊆ R on X the strict partial order θR(S) = R ◦ S on X. Owing to the strong relationships between Alexandroff TD derivative operators and strict partial orders, this paper firstly calls forth the links between the CantorBendixson ranks of Alexandroff TD topological spaces and the g...
متن کاملUltimate Approximations in Nonmonotonic Knowledge Representation Systems
We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or ultimate approximation. We demonstrate that fixpoints of this ultimate approximation provide useful insights into fixpoints of the operator O. We apply our ...
متن کامل