Light affine logic (LAL) is a formal system derived from linear logic that is claimed to correspond, through the Curry-Howard Isomorphism, to the class PTIME of polytime functions. The completeness of the system with respect to PTIME has been proven by embedding different presentations of PTIME into LAL. The dual property of polytime soundness, on the other hand, has been stated and proven in a...

A promising line of research in the interaction between syntax and semantics has been open by the work on Continuation Semantics started by [1] and [5] and further explored by [8]. Work done within Curry Howard Correspondence to Classical Logic has brought to the attention the duality distinction holding between terms and contexts (or co-terms), and can help further shaping the syntax-semantics...

We construct a partially-ordered hierarchy of delimited control operators similar to those of the CPS hierarchy of Danvy and Filinski [6]. However, instead of relying on nested CPS translations, these operators give directly a Curry-Howard interpretation of a fragment of linear logic extended with subexponentials, i.e., multiple pairs of ! and ?. We show how the fundamental problem of delimited...

The spin-up and spin-down of a fluid in a rapidly-rotating, fluid-filled, closed half cone is studied both numerically and experimentally. This unusual set up is of interest because it represents a pathological case for the classical linear theory of Greenspan & Howard (J. Fluid Mech., 17, 385, 1963) since there are no closed geostrophic contours nor a denumerable set of inertial waves (even a ...

The software-defined networking language NetKAT is able to verify many useful properties of networks automatically via a PSPACE decision procedure for program equality. However, for its probabilistic extension ProbNetKAT, no such decision procedure is known. We show that several potentially useful properties of ProbNetKAT are in fact undecidable, including emptiness of support intersection and ...

Data integration involves merging two or more schemas into a global schema based on the identification of common concepts, and also the set of different concepts that are mutually related by some semantic properties. Identifying semantic relationships that exist between a set of objects in one schema and a different set of objects in another schema is crucial to the integration process. Earlier...

In a call-by-value language with first-class continuations, the usual CBV fixpoint combinator can be expressed in terms of a simpler iteration primitive. We give an informal derivation of this correspondence, together with a formal correctness proof. We also present a number of generalizations and possible applications.

The propositions-as-types correspondence [IIowSO] relates proofs in con structive logic to functional programs. The correspondence has intrigued those interested in the formal verification of programs with the possibility of developing programs from proofs of their specifications [BC85, Con86, Moh86]. However, one drawback of this approach to program development is that the programming language...

Giovanni Sirio Carmantini Dynamical Systems Theory for Transparent Symbolic Computation in Neuronal Networks In this thesis, we explore the interface between symbolic and dynamical system computation, with particular regard to dynamical system models of neuronal networks. In doing so, we adhere to a definition of computation as the physical realization of a formal system, where we say that a dy...

Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims...