How functional programming mattered

In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs

Algebra, coalgebra, and minimization in polynomial differential equations

We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system structure based on the concept of Lie-derivative, thus inducing a notion of L-bisimulation. We prove that two states (variables) are L-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations. A computationally less demanding approximate reduction and linearization technique is also proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape

A Refinement Calculus for Logic Programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.Comment: 36 pages, 3 figures. To be published in Theory and Practice of Logic Programming (TPLP

Finite Computational Structures and Implementations

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only partial answers to these questions. In order to make these problems more precise, we describe an abstract algebraic definition of classical computation, generalizing traditional models to semigroups. The mathematical abstraction also allows the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework. Here we summarize the main questions and recent results of the research of finite computation.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version published by IEEE Computer Societ

Canonical Abstract Syntax Trees

This paper presents Gom, a language for describing abstract syntax trees and generating a Java implementation for those trees. Gom includes features allowing the user to specify and modify the interface of the data structure. These features provide in particular the capability to maintain the internal representation of data in canonical form with respect to a rewrite system. This explicitly guarantees that the client program only manipulates normal forms for this rewrite system, a feature which is only implicitly used in many implementations

Action semantics in retrospect

This paper is a themed account of the action semantics project, which Peter Mosses has led since the 1980s. It explains his motivations for developing action semantics, the inspirations behind its design, and the foundations of action semantics based on unified algebras. It goes on to outline some applications of action semantics to describe real programming languages, and some efforts to implement programming languages using action semantics directed compiler generation. It concludes by outlining more recent developments and reflecting on the success of the action semantics project

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial