26,482 research outputs found
Computable decision making on the reals and other spaces via partiality and nondeterminism
Though many safety-critical software systems use floating point to represent
real-world input and output, programmers usually have idealized versions in
mind that compute with real numbers. Significant deviations from the ideal can
cause errors and jeopardize safety. Some programming systems implement exact
real arithmetic, which resolves this matter but complicates others, such as
decision making. In these systems, it is impossible to compute (total and
deterministic) discrete decisions based on connected spaces such as
. We present programming-language semantics based on constructive
topology with variants allowing nondeterminism and/or partiality. Either
nondeterminism or partiality suffices to allow computable decision making on
connected spaces such as . We then introduce pattern matching on
spaces, a language construct for creating programs on spaces, generalizing
pattern matching in functional programming, where patterns need not represent
decidable predicates and also may overlap or be inexhaustive, giving rise to
nondeterminism or partiality, respectively. Nondeterminism and/or partiality
also yield formal logics for constructing approximate decision procedures. We
implemented these constructs in the Marshall language for exact real
arithmetic.Comment: This is an extended version of a paper due to appear in the
proceedings of the ACM/IEEE Symposium on Logic in Computer Science (LICS) in
July 201
A General Framework for Sound and Complete Floyd-Hoare Logics
This paper presents an abstraction of Hoare logic to traced symmetric
monoidal categories, a very general framework for the theory of systems. Our
abstraction is based on a traced monoidal functor from an arbitrary traced
monoidal category into the category of pre-orders and monotone relations. We
give several examples of how our theory generalises usual Hoare logics (partial
correctness of while programs, partial correctness of pointer programs), and
provide some case studies on how it can be used to develop new Hoare logics
(run-time analysis of while programs and stream circuits).Comment: 27 page
A Declarative Semantics for CLP with Qualification and Proximity
Uncertainty in Logic Programming has been investigated during the last
decades, dealing with various extensions of the classical LP paradigm and
different applications. Existing proposals rely on different approaches, such
as clause annotations based on uncertain truth values, qualification values as
a generalization of uncertain truth values, and unification based on proximity
relations. On the other hand, the CLP scheme has established itself as a
powerful extension of LP that supports efficient computation over specialized
domains while keeping a clean declarative semantics. In this paper we propose a
new scheme SQCLP designed as an extension of CLP that supports qualification
values and proximity relations. We show that several previous proposals can be
viewed as particular cases of the new scheme, obtained by partial
instantiation. We present a declarative semantics for SQCLP that is based on
observables, providing fixpoint and proof-theoretical characterizations of
least program models as well as an implementation-independent notion of goal
solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
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