Nicola Botta

Relation-based computations in a monadic BSP model

Abstract We propose a Haskell monadic model of bulk synchronous parallel programs and apply it to the analysis of relation-based computations. Relation-based computations are simple but general patterns found in scientific computing applications. They are easy to implement sequentially, but difficult to parallelize. We use the model to give high-level specifications of distributed relation-based algorithms and outline how to obtain testable parallel implementations from these specifications via equational reasoning. We sketch the architecture of a C++ library of components for distributed relation-based computations. We argue that the model can be used to provide a concise and consistent library documentation.

A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"

Building upon recent work of Gintis, we study evolutionary dynamics in an economy with Leontieff preferences and corner endowments for which the equilibrium is completely indeterminate. We exhibit a class of dynamics which selects, via stochastic stability, the equilibrium minimizing the quantities traded.

Contributions to a computational theory of policy advice and avoidability

We present the starting elements of a mathematical theory of policy advice and avoidability. More specifically, we formalize a cluster of notions related to policy advice, such as policy, viability, reachability, and propose a novel approach for assisting decision making, based on the concept of avoidability. We formalize avoidability as a relation between current and future states, investigate under which conditions this relation is decidable and propose a generic procedure for assessing avoidability. The formalization is constructive and makes extensive use of the correspondence between dependent types and logical propositions, decidable judgments are obtained through computations. Thus, we aim for a computational theory, and emphasize the role that computer science can play in global system science.

Type Theory as a Framework for Modelling and Programming

In the context provided by the proceedings of the UVMP track of ISoLA 2016, we propose Type Theory as a suitable framework for both modelling and programming. We show that it fits most of the requirements put forward on such frameworks by Broy et al. and discuss some of the objections that can be raised against it.

Sequential decision problems, dependent types and generic solutions

We present a computer-checked generic implementation for solving finite-horizon sequential decision problems. This is a wide class of problems, including inter-temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellmans principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research.