arXiv subjects

Tjark Weber

Publications and source records attributed to Tjark Weber.

5 recordsLinked to original sources

arXiv2025

Sound and Complete Invariant-Based Heap Encodings (Technical Report)

Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel invariant-based heap encoding leveraging uninterpreted predicates and prophecy variables to reduce verification of heap-manipulating programs to verification of programs over integers only. Our encoding of heap is general and agnostic to specific data structures. To the best of our knowledge, our approach is the first heap invariant-based method that achieves both soundness and completeness. We provide formal proofs establishing the correctness of our encodings. Through an experimental evaluation, we demonstrate that time-indexed heap invariants significantly extend the capability of existing verification tools, allowing automatic verification of programs with heap that were previously out of reach for state-of-the-art tools.

cs.LO↗

arXiv2021

Modal Logics for Nominal Transition Systems

We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for these systems is introduced, and proved adequate and expressively complete for bisimulation equivalence. A main technical novelty is the use of finitely supported infinite conjunctions. We show how to treat different bisimulation variants such as early, late, open and weak in a systematic way, explore the folklore theorem that state predicates can be replaced by actions, and make substantial comparisons with related work. The main definitions and theorems have been formalised in Nominal Isabelle.

cs.LO↗

arXiv2021

Mechanisation of Model-theoretic Conservative Extension for HOL with Ad-hoc Overloading

Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The latter may be ad-hoc overloaded, i.e. have different definitions for non-overlapping types. We prove that symbols that are independent of a new definition may keep their interpretation in a model extension. This work revises our earlier notion of model-theoretic conservative extension and generalises an earlier model construction. We obtain consistency of theories of definitions in higher-order logic (HOL) with ad-hoc overloading as a corollary. Our results are mechanised in the HOL4 theorem prover.

cs.LO↗

arXiv2016

The Largest Respectful Function

Respectful functions were introduced by Sangiorgi as a compositional tool to formulate short and clear bisimulation proofs. Usually, the larger the respectful function, the easier the bisimulation proof. In particular the largest respectful function, defined as the pointwise union of all respectful functions, has been shown to be very useful. We here provide an explicit and constructive characterization of it.

cs.LO↗

arXiv2012

On the Use of Underspecified Data-Type Semantics for Type Safety in Low-Level Code

In recent projects on operating-system verification, C and C++ data types are often formalized using a semantics that does not fully specify the precise byte encoding of objects. It is well-known that such an underspecified data-type semantics can be used to detect certain kinds of type errors. In general, however, underspecified data-type semantics are unsound: they assign well-defined meaning to programs that have undefined behavior according to the C and C++ language standards. A precise characterization of the type-correctness properties that can be enforced with underspecified data-type semantics is still missing. In this paper, we identify strengths and weaknesses of underspecified data-type semantics for ensuring type safety of low-level systems code. We prove sufficient conditions to detect certain classes of type errors and, finally, identify a trade-off between the complexity of underspecified data-type semantics and their type-checking capabilities.

cs.LO↗