6,290 research outputs found
Gradual Liquid Type Inference
Liquid typing provides a decidable refinement inference mechanism that is
convenient but subject to two major issues: (1) inference is global and
requires top-level annotations, making it unsuitable for inference of modular
code components and prohibiting its applicability to library code, and (2)
inference failure results in obscure error messages. These difficulties
seriously hamper the migration of existing code to use refinements. This paper
shows that gradual liquid type inference---a novel combination of liquid
inference and gradual refinement types---addresses both issues. Gradual
refinement types, which support imprecise predicates that are optimistically
interpreted, can be used in argument positions to constrain liquid inference so
that the global inference process e effectively infers modular specifications
usable for library components. Dually, when gradual refinements appear as the
result of inference, they signal an inconsistency in the use of static
refinements. Because liquid refinements are drawn from a nite set of
predicates, in gradual liquid type inference we can enumerate the safe
concretizations of each imprecise refinement, i.e. the static refinements that
justify why a program is gradually well-typed. This enumeration is useful for
static liquid type error explanation, since the safe concretizations exhibit
all the potential inconsistencies that lead to static type errors. We develop
the theory of gradual liquid type inference and explore its pragmatics in the
setting of Liquid Haskell.Comment: To appear at OOPSLA 201
Dynamics of Bound Magnon Pairs in the Quasi-One-Dimensional Frustrated Magnet LiCuVO_4
We report on the dynamics of the spin-1/2 quasi-one-dimensional frustrated
magnet LiCuVO measured by nuclear spin relaxation in high magnetic
fields 10--34 T, in which the ground state has spin-density-wave order. The
spin fluctuations in the paramagnetic phase exhibit striking anisotropy with
respect to the magnetic field. The transverse excitation spectrum probed by
V nuclei has an excitation gap, which increases with field. On the other
hand, the gapless longitudinal fluctuations sensed by Li nuclei grow with
lowering temperature, but tend to be suppressed with increasing field. Such
anisotropic spin dynamics and its field dependence agree with the theoretical
predictions and are ascribed to the formation of bound magnon pairs, a
remarkable consequence of the frustration between ferromagnetic nearest
neighbor and antiferromagnetic next-nearest-neighbor interactions.Comment: 7 pages, 6 figure
Causal Slingshots
Causal slingshots are formal arguments advanced by proponents of an event ontology of token-level causation which, in the end, are intended to show two things: (i) The logical form of statements expressing causal dependencies on token level features a binary predicate " causes ...” and (ii) that predicate takes events as arguments. Even though formalisms are only revealing with respect to the logical form of natural language statements, if the latter are shown to be adequately captured within a corresponding formalism, proponents of slingshots usually take the adequacy of their formalizations for granted without justifying it. The first part of this paper argues that the most discussed version of a causal slingshot, viz. the one e.g. presented by Davidson (Essays on actions and events. Oxford, Clarendon Press, 1980), can indeed be refuted for relying on an inadequate formal apparatus. In contrast, the formal means of Gödel's (The philosophy of Betrand Russell. New York, Tudor, 1944) often neglected slingshot are shown to stand on solid ground in the second part of the paper. Nonetheless, I contend that Gödel's slingshot does only half the work friends of event causation would like it to do. It provides good reasons for (i) but not for (ii
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