3,988 research outputs found
A constructive modal semantics for contextual verification
This paper introduces a non-standard semantics for a modal version of constructive KT for contextual (assumptions-based) verification. The modal fragment expresses verifiability under extensions of contexts, enjoying adapted validity and (weak) monotonicity properties depending on satisfaction of the contextual data
A Logical Foundation for Environment Classifiers
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with
a sound type system using the notion of environment classifiers. They are
special identifiers, with which code fragments and variable declarations are
annotated, and their scoping mechanism is used to ensure statically that
certain code fragments are closed and safely runnable. In this paper, we
investigate the Curry-Howard isomorphism for environment classifiers by
developing a typed {\lambda}-calculus {\lambda}|>. It corresponds to
multi-modal logic that allows quantification by transition variables---a
counterpart of classifiers---which range over (possibly empty) sequences of
labeled transitions between possible worlds. This interpretation will reduce
the "run" construct---which has a special typing rule in
{\lambda}{\alpha}---and embedding of closed code into other code fragments of
different stages---which would be only realized by the cross-stage persistence
operator in {\lambda}{\alpha}---to merely a special case of classifier
application. {\lambda}|> enjoys not only basic properties including subject
reduction, confluence, and strong normalization but also an important property
as a multi-stage calculus: time-ordered normalization of full reduction. Then,
we develop a big-step evaluation semantics for an ML-like language based on
{\lambda}|> with its type system and prove that the evaluation of a well-typed
{\lambda}|> program is properly staged. We also identify a fragment of the
language, where erasure evaluation is possible. Finally, we show that the proof
system augmented with a classical axiom is sound and complete with respect to a
Kripke semantics of the logic
Multi-level Contextual Type Theory
Contextual type theory distinguishes between bound variables and
meta-variables to write potentially incomplete terms in the presence of
binders. It has found good use as a framework for concise explanations of
higher-order unification, characterize holes in proofs, and in developing a
foundation for programming with higher-order abstract syntax, as embodied by
the programming and reasoning environment Beluga. However, to reason about
these applications, we need to introduce meta^2-variables to characterize the
dependency on meta-variables and bound variables. In other words, we must go
beyond a two-level system granting only bound variables and meta-variables.
In this paper we generalize contextual type theory to n levels for arbitrary
n, so as to obtain a formal system offering bound variables, meta-variables and
so on all the way to meta^n-variables. We obtain a uniform account by
collapsing all these different kinds of variables into a single notion of
variabe indexed by some level k. We give a decidable bi-directional type system
which characterizes beta-eta-normal forms together with a generalized
substitution operation.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
The First-Order Hypothetical Logic of Proofs
The Propositional Logic of Proofs (LP) is a modal logic in which the modality â–¡A is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.Fil: Steren, Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y TecnologÃa; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Time-Staging Enhancement of Hybrid System Falsification
Optimization-based falsification employs stochastic optimization algorithms
to search for error input of hybrid systems. In this paper we introduce a
simple idea to enhance falsification, namely time staging, that allows the
time-causal structure of time-dependent signals to be exploited by the
optimizers. Time staging consists of running a falsification solver multiple
times, from one interval to another, incrementally constructing an input signal
candidate. Our experiments show that time staging can dramatically increase
performance in some realistic examples. We also present theoretical results
that suggest the kinds of models and specifications for which time staging is
likely to be effective
Modalities, Cohesion, and Information Flow
It is informally understood that the purpose of modal type constructors in
programming calculi is to control the flow of information between types. In
order to lend rigorous support to this idea, we study the category of
classified sets, a variant of a denotational semantics for information flow
proposed by Abadi et al. We use classified sets to prove multiple
noninterference theorems for modalities of a monadic and comonadic flavour. The
common machinery behind our theorems stems from the the fact that classified
sets are a (weak) model of Lawvere's theory of axiomatic cohesion. In the
process, we show how cohesion can be used for reasoning about multi-modal
settings. This leads to the conclusion that cohesion is a particularly useful
setting for the study of both information flow, but also modalities in type
theory and programming languages at large
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