687 research outputs found
Self-Formalisation of Higher-Order Logic: Semantics, Soundness, and a Verified Implementation
This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10817-015-9357-xWe present a mechanised semantics for higher-order logic (HOL), and a proof of soundness for the inference system, including the rules for making definitions, implemented by the kernel of the HOL Light theorem prover. Our work extends Harrison’s verification of the inference system without definitions. Soundness of the logic extends to soundness of a theorem prover, because we also show that a synthesised implementation of the kernel in CakeML refines the inference system. Apart from adding support for definitions and synthesising an implementation, we improve on Harrison’s work by making our model of HOL parametric on the universe of sets, and we prove soundness for an improved principle of constant specification in the hope of encouraging its adoption. Our semantics supports defined constants directly via a context, and we find this approach cleaner than our previous work formalising Wiedijk’s Stateless HOL.The first author was supported by the Gates Cambridge Trust. The second author was funded in part by the EPSRC (grant number EP/K503769/1). The third author was partially supported by the Royal Society UK and the Swedish Research Council
Towards Practical Graph-Based Verification for an Object-Oriented Concurrency Model
To harness the power of multi-core and distributed platforms, and to make the
development of concurrent software more accessible to software engineers,
different object-oriented concurrency models such as SCOOP have been proposed.
Despite the practical importance of analysing SCOOP programs, there are
currently no general verification approaches that operate directly on program
code without additional annotations. One reason for this is the multitude of
partially conflicting semantic formalisations for SCOOP (either in theory or
by-implementation). Here, we propose a simple graph transformation system (GTS)
based run-time semantics for SCOOP that grasps the most common features of all
known semantics of the language. This run-time model is implemented in the
state-of-the-art GTS tool GROOVE, which allows us to simulate, analyse, and
verify a subset of SCOOP programs with respect to deadlocks and other
behavioural properties. Besides proposing the first approach to verify SCOOP
programs by automatic translation to GTS, we also highlight our experiences of
applying GTS (and especially GROOVE) for specifying semantics in the form of a
run-time model, which should be transferable to GTS models for other concurrent
languages and libraries.Comment: In Proceedings GaM 2015, arXiv:1504.0244
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Permission-Based Separation Logic for Multithreaded Java Programs
This paper presents a program logic for reasoning about multithreaded
Java-like programs with dynamic thread creation, thread joining and reentrant
object monitors. The logic is based on concurrent separation logic. It is the
first detailed adaptation of concurrent separation logic to a multithreaded
Java-like language. The program logic associates a unique static access
permission with each heap location, ensuring exclusive write accesses and
ruling out data races. Concurrent reads are supported through fractional
permissions. Permissions can be transferred between threads upon thread
starting, thread joining, initial monitor entrancies and final monitor exits.
In order to distinguish between initial monitor entrancies and monitor
reentrancies, auxiliary variables keep track of multisets of currently held
monitors. Data abstraction and behavioral subtyping are facilitated through
abstract predicates, which are also used to represent monitor invariants,
preconditions for thread starting and postconditions for thread joining.
Value-parametrized types allow to conveniently capture common strong global
invariants, like static object ownership relations. The program logic is
presented for a model language with Java-like classes and interfaces, the
soundness of the program logic is proven, and a number of illustrative examples
are presented
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