Mappings and inductive invariants

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...

Bounded Quantifier Instantiation for Checking Inductive Invariants

We consider the problem of checking whether a proposed invariant φ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can sometimes solve it automatically. However they employ powerful quantifier instantiation methods that may diverge, especially when φ is not preserved. A notable diffi...