Inductive invariants and dimension theory

AN INDUCTIVE FUZZY DIMENSION

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

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...

Inductive Invariants for Nested Recursion

Formula Slicing: Inductive Invariants from Preconditions

We propose a “formula slicing” method for finding inductive invariants. It is based on the observation that many loops in the program affect only a small part of the memory, and many invariants which were valid before a loop are still valid after. Given a precondition of the loop, obtained from the preceding program fragment, we weaken it until it becomes inductive. The weakening procedure is g...

Inductive Reasoning for Shape Invariants pdfsubject

Automatic verification of imperative programs that destructively manipulate heap data structures is challenging. In this paper we propose an approach for verifying that such programs do not corrupt their data structures. We specify heap data structures such as lists, arrays of lists, and trees inductively as solutions of logic programs. We use off-the-shelf first-order theorem provers to reason...