68,872 research outputs found
A Graphical Language for Proof Strategies
Complex automated proof strategies are often difficult to extract, visualise,
modify, and debug. Traditional tactic languages, often based on stack-based
goal propagation, make it easy to write proofs that obscure the flow of goals
between tactics and are fragile to minor changes in input, proof structure or
changes to tactics themselves. Here, we address this by introducing a graphical
language called PSGraph for writing proof strategies. Strategies are
constructed visually by "wiring together" collections of tactics and evaluated
by propagating goal nodes through the diagram via graph rewriting. Tactic nodes
can have many output wires, and use a filtering procedure based on goal-types
(predicates describing the features of a goal) to decide where best to send
newly-generated sub-goals.
In addition to making the flow of goal information explicit, the graphical
language can fulfil the role of many tacticals using visual idioms like
branching, merging, and feedback loops. We argue that this language enables
development of more robust proof strategies and provide several examples, along
with a prototype implementation in Isabelle
Collaborative Verification-Driven Engineering of Hybrid Systems
Hybrid systems with both discrete and continuous dynamics are an important
model for real-world cyber-physical systems. The key challenge is to ensure
their correct functioning w.r.t. safety requirements. Promising techniques to
ensure safety seem to be model-driven engineering to develop hybrid systems in
a well-defined and traceable manner, and formal verification to prove their
correctness. Their combination forms the vision of verification-driven
engineering. Often, hybrid systems are rather complex in that they require
expertise from many domains (e.g., robotics, control systems, computer science,
software engineering, and mechanical engineering). Moreover, despite the
remarkable progress in automating formal verification of hybrid systems, the
construction of proofs of complex systems often requires nontrivial human
guidance, since hybrid systems verification tools solve undecidable problems.
It is, thus, not uncommon for development and verification teams to consist of
many players with diverse expertise. This paper introduces a
verification-driven engineering toolset that extends our previous work on
hybrid and arithmetic verification with tools for (i) graphical (UML) and
textual modeling of hybrid systems, (ii) exchanging and comparing models and
proofs, and (iii) managing verification tasks. This toolset makes it easier to
tackle large-scale verification tasks
A Vision of Collaborative Verification-Driven Engineering of Hybrid Systems
Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for real-world physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires significant human guidance, since hybrid systems verification tools solve undecidable problems. It is thus not uncommon for verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) modeling hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks.
Understanding and maintaining tactics graphically OR how we are learning that a diagram can be worth more than 10K LoC
The use of a functional language to implement proof strategies as proof tactics in interactive theorem provers, often provides short, concise and elegant implementations. Whilst being elegant, the use of higher order features and combinator languages often results in a very procedural view of a strategy, which may deviate significantly from the high-level ideas behind it. This can make a tactic hard to understand and hence difficult to to debug and maintain for experts and non-experts alike: one often has to tear apart complex combinations of lower level tactics manually in order to analyse a failure in the overall strategy.In an industrial technology transfer project, we have been working on porting a very large and complex proof tactic into PSGraph, a graphical language for representing proof strategies. The goal of this work is to improve understandability and maintainability of tactics. Motivated by some initial successes with this, we here extend PSGraph with additional features for development and debugging. Through the re-implementation and refactoring of several existing tactics, we demonstrates the advantages of PSGraph compared with a typical sentential tactic language with respect to debugging, readability and maintenance. In order to act as guidance for others, we give a fairly detailed comparison of the user experience with the two approaches. The paper is supported by a web page providing further details about the implementation as well as interactive illustrations of the examples
Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview
We consider the problem of learning about and comparing the consequences of
dynamic treatment strategies on the basis of observational data. We formulate
this within a probabilistic decision-theoretic framework. Our approach is
compared with related work by Robins and others: in particular, we show how
Robins's 'G-computation' algorithm arises naturally from this
decision-theoretic perspective. Careful attention is paid to the mathematical
and substantive conditions required to justify the use of this formula. These
conditions revolve around a property we term stability, which relates the
probabilistic behaviours of observational and interventional regimes. We show
how an assumption of 'sequential randomization' (or 'no unmeasured
confounders'), or an alternative assumption of 'sequential irrelevance', can be
used to infer stability. Probabilistic influence diagrams are used to simplify
manipulations, and their power and limitations are discussed. We compare our
approach with alternative formulations based on causal DAGs or potential
response models. We aim to show that formulating the problem of assessing
dynamic treatment strategies as a problem of decision analysis brings clarity,
simplicity and generality.Comment: 49 pages, 15 figure
A Diagrammatic Axiomatisation for Qubit Entanglement
Diagrammatic techniques for reasoning about monoidal categories provide an
intuitive understanding of the symmetries and connections of interacting
computational processes. In the context of categorical quantum mechanics,
Coecke and Kissinger suggested that two 3-qubit states, GHZ and W, may be used
as the building blocks of a new graphical calculus, aimed at a diagrammatic
classification of multipartite qubit entanglement that would highlight the
communicational properties of quantum states, and their potential uses in
cryptographic schemes.
In this paper, we present a full graphical axiomatisation of the relations
between GHZ and W: the ZW calculus. This refines a version of the preexisting
ZX calculus, while keeping its most desirable characteristics: undirectedness,
a large degree of symmetry, and an algebraic underpinning. We prove that the ZW
calculus is complete for the category of free abelian groups on a power of two
generators - "qubits with integer coefficients" - and provide an explicit
normalisation procedure.Comment: 12 page
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