78,368 research outputs found
Towards a canonical classical natural deduction system
This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be
isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's -calculus with the idea
of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms.
This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction
system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of
the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics
of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned
isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third
problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format,
that affects mainly the recent proof-theoretic efforts of derivation of -calculi for call-by-value. An isomorphic counterpart
to the -subsystem of Curien-Herbelin's-calculus is derived, obtaining a new
-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT
Towards a canonical classical natural deduction system
Preprint submitted to Elsevier, 6 July 2012This paper studies a new classical natural deduction system, presented as a typed
calculus named lambda-mu- let. It is designed to be isomorphic to Curien and Herbelin's lambda-mu-mu~-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and
substitution (resp. elimination) in natural deduction. It is a combination of Parigot's lambda-mu -calculus with the idea of "coercion calculus" due to Cervesato and Pfenning, accommodating
let-expressions in a surprising way: they expand Parigot's syntactic class of named terms.
This calculus and the mentioned isomorphism Theta offer three missing components of
the proof theory of classical logic: a canonical natural deduction system; a robust process
of "read-back" of calculi in the sequent calculus format into natural deduction syntax;
a formalization of the usual semantics of the lambda-mu-mu~-calculus, that explains co-terms and cuts as, respectively, contexts and hole- filling instructions. lambda-mu-let is not yet another
classical calculus, but rather a canonical reflection in natural deduction of the impeccable
treatment of classical logic by sequent calculus; and provides the "read-back" map and
the formalized semantics, based on the precise notions of context and "hole-expression"
provided by lambda-mu-let.
We use "read-back" to achieve a precise connection with Parigot's lambda-mu , and to derive
lambda-calculi for call-by-value combining control and let-expressions in a logically founded
way. Finally, the semantics , when fully developed, can be inverted at each syntactic
category. This development gives us license to see sequent calculus as the semantics of
natural deduction; and uncovers a new syntactic concept in lambda-mu-mu~ ("co-context"), with
which one can give a new de nition of eta-reduction
A Caputo Boundary Value Problem in Nabla Fractional Calculus
Boundary value problems have long been of interest in the continuous differential equations context. However, with the advent of new areas like Nabla Fractional Calculus, we may consider such problems in new contexts. In this work, we will consider several right focal boundary value problems, involving a Caputo fractional difference operator, in the Nabla Fractional Calculus context. Properties of the Green\u27s functions for each of these boundary value problems will be investigated and, in the case of a particular boundary value problem, used to establish the existence of positive solutions to a nonlinear version of the boundary value problem.
Adviser: Allan C. Peterso
Realising nondeterministic I/O in the Glasgow Haskell Compiler
In this paper we demonstrate how to relate the semantics given by the nondeterministic call-by-need calculus FUNDIO [SS03] to Haskell. After introducing new correct program transformations for FUNDIO, we translate the core language used in the Glasgow Haskell Compiler into the FUNDIO language, where the IO construct of FUNDIO corresponds to direct-call IO-actions in Haskell. We sketch the investigations of [Sab03b] where a lot of program transformations performed by the compiler have been shown to be correct w.r.t. the FUNDIO semantics. This enabled us to achieve a FUNDIO-compatible Haskell-compiler, by turning o not yet investigated transformations and the small set of incompatible transformations. With this compiler, Haskell programs which use the extension unsafePerformIO in arbitrary contexts, can be compiled in a "safe" manner
Qualitative design and implementation of human-robot spatial interactions
Despite the large number of navigation algorithms available for mobile robots, in many social contexts they often exhibit inopportune motion behaviours in proximity of people, often with very "unnatural" movements due to the execution of segmented trajectories or the sudden activation of safety mechanisms (e.g., for obstacle avoidance). We argue that the reason of the problem is not only the difficulty of modelling human behaviours and generating opportune robot control policies, but also the way human-robot spatial interactions are represented and implemented.
In this paper we propose a new methodology based on a qualitative representation of spatial interactions, which is both flexible and compact, adopting the well-defined and coherent formalization of Qualitative Trajectory Calculus (QTC). We show the potential of a QTC-based approach to abstract and design complex robot behaviours, where the desired robot's behaviour is represented together with its actual performance in one coherent approach, focusing on spatial interactions rather than pure navigation problems
A Uniform presentation of chocs and p-calculus
Projet PROGRAISWe present a generic calculus of "mobile" processes intended as language, labelled transition system, and bisimulation. The distinctive feature of this presentation is an explicit treatment of contexts. Calculi having processes (CHOCS) or channels (p-calculus) as transmissible values are obtained as instances of the generic calculus. Our main tecnical contributions are : - a needed weakening of the notion of bisimulation for CHOCS and a new characterization of p-calculus bisimulation. - a sufficint condition for checking the bisimilarity of CHOCS processes via a standard translation into the p-calculus. - a uniform notion of bisimulation for the p-calculus
Lazy Evaluation and Delimited Control
The call-by-need lambda calculus provides an equational framework for
reasoning syntactically about lazy evaluation. This paper examines its
operational characteristics. By a series of reasoning steps, we systematically
unpack the standard-order reduction relation of the calculus and discover a
novel abstract machine definition which, like the calculus, goes "under
lambdas." We prove that machine evaluation is equivalent to standard-order
evaluation. Unlike traditional abstract machines, delimited control plays a
significant role in the machine's behavior. In particular, the machine replaces
the manipulation of a heap using store-based effects with disciplined
management of the evaluation stack using control-based effects. In short, state
is replaced with control. To further articulate this observation, we present a
simulation of call-by-need in a call-by-value language using delimited control
operations
Reconstruction of quantum theory on the basis of the formula of total probability
The notion of context (complex of physical conditions) is basic in this
paper. We show that the main structures of quantum theory (interference of
probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state
space, representation of observables by operators) are present in a latent form
in the classical Kolmogorov probability model. However, this model should be
considered as a calculus of contextual probabilities. In our approach it is
forbidden to consider abstract context independent probabilities: ``first
context and then probability.'' We start with the conventional formula of total
probability for contextual (conditional) probabilities and then we rewrite it
by eliminating combinations of incompatible contexts from consideration. In
this way we obtain interference of probabilities without to appeal to the
Hilbert space formalism or wave mechanics. However, we did not just reconstruct
the probabilistic formalism of conventional quantum mechanics. Our contextual
probabilistic model is essentially more general and, besides the projection to
the complex Hilbert space, it has other projections. The most important new
prediction is the possibility (at least theoretical) of appearance of
hyperbolic interference
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