Comparing the expressive power of the Synchronous and the Asynchronous pi-calculus

The Asynchronous pi-calculus, as recently proposed by Boudol and, independently, by Honda and Tokoro, is a subset of the pi-calculus which contains no explicit operators for choice and output-prefixing. The communication mechanism of this calculus, however, is powerful enough to simulate output-prefixing, as shown by Boudol, and input-guarded choice, as shown recently by Nestmann and Pierce. A natural question arises, then, whether or not it is possible to embed in it the full pi-calculus. We show that this is not possible, i.e. there does not exist any uniform, parallel-preserving, translation from the pi-calculus into the asynchronous pi-calculus, up to any ``reasonable'' notion of equivalence. This result is based on the incapablity of the asynchronous pi-calculus of breaking certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the pi-calculus and CCS.Comment: 10 pages. Proc. of the POPL'97 symposiu

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

Towards a GPU-based implementation of interaction nets

We present ingpu, a GPU-based evaluator for interaction nets that heavily utilizes their potential for parallel evaluation. We discuss advantages and challenges of the ongoing implementation of ingpu and compare its performance to existing interaction nets evaluators.Comment: In Proceedings DCM 2012, arXiv:1403.757

The debris flow occurred at ru secco creek, venetian dolomites, on 4 august 2015: Analysis of the phenomenon, its characteristics and reproduction by models

On 4 August 2015, a very high intensity storm, 31.5 mm in 20 min (94.5 mm/h), hit the massif of Mount Antelao on the Venetian Dolomites triggering three stony debris \ufb02ows characterized by high magnitude. Two of them occurred in the historical sites of Rovina di Cancia and Rudan Creek and were stopped by the retaining works upstream the inhabited areas, while the third routed along the Ru Secco Creek and progressively reached the resort area and the village of San Vito di Cadore, causing fatalities and damages. The main triggering factor of the Ru Secco debris \ufb02ow was a large rock collapse on the northern cliffs of Mount Antelao occurred the previous autumn. The fallen debris material deposited on the Vallon d\u2019Antrimoia inclined plateau at the base of the collapsed cliffs and, below it, on the Ru Salvela Creek, covering it from the head to the con\ufb02uence with the Ru Secco Creek. The abundant runoff, caused by the high intensity rainfall on 4 August 2015, entrained about 52,500 m3 of the debris material laying on the Vallon d\u2019Antrimoia forming a debris \ufb02ow surge that hit and eroded the debris deposit covering the downstream Ru Salvela Creek, increasing its volume, about 110,000 m3 of mobilized sediments. This debris \ufb02ow routed downstream the con\ufb02uence, \ufb02ooding the parking of a resort area where three people died, and reached the village downstream damaging some buildings. A geomorphological analysis was initially carried out after surveying the whole basin. All liquid and solid-liquid contributions to the phenomenon were recognized together with the areas subjected to erosion and deposition. The elaboration of pre and post-event topographical surveys provided the map of deposition-erosion depths. Using the rainfall estimated by weather radar and corrected by the nearest rain gauge, about 0.8 km far, we estimated runoff by using a rainfall-runoff model designed for the headwater rocky basins of Dolomites. A triggering model provided the debris \ufb02ow hydrographs in the initiation areas, after using the simulated runoff. The initial solid-liquid surge hydrographs were, then, routed downstream by means of a cell model. The comparison between the simulated and estimated deposition-erosion pattern resulted satisfactory. The results of the simulation captured, in fact, the main features of the occurred phenomenon

Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators

The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them, analogous to normal form and head normal form equivalence in the lambda-calculus. Then, we prove a full abstraction result for each of the two equivalences. This is obtained by interpreting nets as certain subsets of the Cantor space, called edifices, which play the same role as Boehm trees in the theory of the lambda-calculus

Probabilistic Rewriting: On Normalization, Termination, and Unique Normal Forms

While a mature body of work supports the study of rewriting systems, even infinitary ones, abstract tools for Probabilistic Rewriting are still limited. Here, we investigate questions such as uniqueness of the result (unique limit distribution) and we develop a set of proof techniques to analyze and compare reduction strategies. The goal is to have tools to support the operational analysis of probabilistic calculi (such as probabilistic lambda-calculi) whose evaluation is also non-deterministic, in the sense that different reductions are possible. In particular, we investigate how the behavior of different rewrite sequences starting from the same term compare w.r.t. normal forms, and propose a robust analogue of the notion of "unique normal form". Our approach is that of Abstract Rewrite Systems, i.e. we search for general properties of probabilistic rewriting, which hold independently of the specific structure of the objects.Comment: Extended version of the paper in FSCD 2019, International Conference on Formal Structures for Computation and Deductio

Observational equivalences for linear logic CC languages

Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the problem of program equivalence for this programming framework. For this purpose, we present a structural operational semantics for LCC based on a label transition system and investigate different notions of observational equivalences inspired by the state of art of process algebras. Then, we demonstrate that the asynchronous \pi-calculus can be viewed as simple syntactical restrictions of LCC. Finally we show LCC observational equivalences can be transposed straightforwardly to classical Concurrent Constraint languages and Constraint Handling Rules, and investigate the resulting equivalences.Comment: 17 page