Evaluation Logic

A new typed, higher-order logic is described which appears particularly well tted to reasoning about forms of computation whose operational behaviour can be speci ed using the Natural Semantics style of structural operational semantics [5]. The logic's underlying type system is Moggi's computational metalanguage [11], which enforces a distinction between computations and values via the categorical structure of a strong monad. This is extended to a (constructive) predicate logic with modal formulas about evaluation of computations to values, called evaluation modalities. The categorical structure corresponding to this kind of logic is explained and a couple of examples of categorical models given. As a rst example of the naturalness and applicability of this new logic to program semantics, we investigate the translation of a (tiny) fragment of Standard ML into a theory over the logic, which is proved computationally adequate for ML's Natural Semantics [10]. Whilst it is tiny, the ML fragment does however contain both higher-order functional and imperative features, about which the logic allows us to reason without having to mention global states explicitly

Normal Forms and Cut-Free Proofs as Natural Transformations

What equations can we guarantee that simple functional programs must satisfy, irrespective of their obvious defining equations? Equivalently, what non-trivial identifications must hold between lambda terms, thought-of as encoding appropriate natural deduction proofs ? We show that the usual syntax guarantees that certain naturality equations from category theory are necessarily provable. At the same time, our categorical approach addresses an equational meaning of cut-elimination and asymmetrical interpretations of cut-free proofs. This viewpoint is connected to Reynolds' relational interpretation of parametricity ([27], [2]), and to the Kelly-Lambek-Mac LaneMints approach to coherence problems in category theory. 1 Introduction In the past several years, there has been renewed interest and research into the interconnections of proof theory, typed lambda calculus (as a functional programming paradigm) and category theory. Some of these connections can be surprisingly subtle. Here we a..

A Topos-Based Approach to Building Language Ontologies

International audienceA common tendency in lexical semantics is to assume the existence of a hierarchy of types for fine-grained analyses of semantic phenomena. This paper provides a formal account of the existence of such a structure. A type system based on the categorical notion of topos is introduced, and is shown to be possibly adaptable to several existing formal approaches where such hierarchies are used. A refinement of the type hierarchy based on Fred Sommers' ontological theory is also proposed

EXPLORING CONFORMATION SELECTIVE FAR INFRARED ACTION SPECTROSCOPY OF ISOLATED MOLECULES AND SOLVATED CLUSTERS

begin{wrapfigure}{r}{0pt} includegraphics[scale=0.25]{abstractdrawing.eps} end{wrapfigure} Far-Infrared (IR) spectroscopy has been labeled as a promising method for identifying structural motifs in large molecules. However, several hurdles have kept this promising spectral region from breaking through to widespread use for gas phase experiments. Normal modes in the far-IR mostly have weak intensities, and high brightness sources of far-IR radiation are rare. Moreover, standard density functional theory - applied to identify the specific molecular structure responsible for the measured IR spectra - does not reproduce features in the far-IR well. This mismatch can be attributed to the high degree of anharmonicity of many of the normal modes present in the far-IR. We have overcome these hurdles by combining an advanced laser source with novel experiments and high-level dynamical calculations. We present far-IR spectra of a family of phenolic molecules and solvated clusters, obtained using the free electron laser FELIX. By employing IR-UV ion-dip spectroscopy in the gas phase, we are able to obtain conformer specific far-IR spectra of isolated molecules or solvated clusters. The studied systems display both intra- and intermolecular hydrogen bonding, enabling us to study the merits of far-IR action spectroscopy for direct probing of these weak interactions. Moreover, the combination of far-IR experiments with quantum chemical calculations allows us to test the limits of the harmonic approximation in DFT calculations, and to test the possibilities of employing a more sophisticated technique, namely Born-Oppenheimer molecular dynamics