1,008 research outputs found
An Open Challenge Problem Repository for Systems Supporting Binders
A variety of logical frameworks support the use of higher-order abstract
syntax in representing formal systems; however, each system has its own set of
benchmarks. Even worse, general proof assistants that provide special libraries
for dealing with binders offer a very limited evaluation of such libraries, and
the examples given often do not exercise and stress-test key aspects that arise
in the presence of binders. In this paper we design an open repository ORBI
(Open challenge problem Repository for systems supporting reasoning with
BInders). We believe the field of reasoning about languages with binders has
matured, and a common set of benchmarks provides an important basis for
evaluation and qualitative comparison of different systems and libraries that
support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
Toward Structured Proofs for Dynamic Logics
We present Kaisar, a structured interactive proof language for differential
dynamic logic (dL), for safety-critical cyber-physical systems (CPS). The
defining feature of Kaisar is *nominal terms*, which simplify CPS proofs by
making the frequently needed historical references to past program states
first-class. To support nominals, we extend the notion of structured proof with
a first-class notion of *structured symbolic execution* of CPS models. We
implement Kaisar in the theorem prover KeYmaera X and reproduce an example on
the safe operation of a parachute and a case study on ground robot control. We
show how nominals simplify common CPS reasoning tasks when combined with other
features of structured proof. We develop an extensive metatheory for Kaisar. In
addition to soundness and completeness, we show a formal specification for
Kaisar's nominals and relate Kaisar to a nominal variant of dL
The âTheoretical Lensâ Concept: We All Know What it Means, but do We All Know the Same Thing?
The term theoretical lens has grown in usage in business and social science research and particularly in the information systems (IS) discipline. In this paper, we question what the term really means by examining it on several dimensions in the context of its actual use. In particular, we consider 1) where the term appears in each paper, 2) how many conceptualizations of theoretical lens each paper uses, 3) the research method the paper uses, 4) the IS domain the paper considers, and 5) which underlying conceptualizations the paper actually uses. To do so, we examine the full set of actual uses in the IS journal that uses the term most frequently, the European Journal of Information Systems. We conclude by discussing several further questions that these observations raise, which suggest deeper issues about better and less advantageous uses of theoretical lenses in IS research and what these issues might imply for the IS discipline
The use of proof plans in tactic synthesis
We undertake a programme of tactic synthesis. We first formalize the notion of
a tactic as a rewrite rule, then give a correctness criterion for this by means of a
reflection mechanism in the constructive type theory OYSTER. We further formalize
the notion of a tactic specification, given as a synthesis goal and a decidability
goal. We use a proof planner. CIAM. to guide the search for inductive proofs
of these, and are able to successfully synthesize several tactics in this fashion.
This involves two extensions to existing methods: context-sensitive rewriting and
higher-order wave rules. Further, we show that from a proof of the decidability
goal one may compile to a Prolog program a pseudo- tactic which may be run to
efficiently simulate the input/output behaviour of the synthetic tacti
A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality
International audienceWe developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL. Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants. Compared with earlier SAT solver verifications, the main novelties are the inclusion of rules for forget, restart, and incremental solving and the application of refinement
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