On Constructor Rewrite Systems and the Lambda Calculus

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by- value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, each reduction in a term rewrite system can be simulated by a constant number of beta-reduction steps. This is relevant to implicit computational complexity, because the number of beta steps to normal form is polynomially related to the actual cost (that is, as performed on a Turing machine) of normalization, under weak call-by-value reduction. Orthogonal constructor term rewrite systems and lambda-calculus are thus both polynomially related to Turing machines, taking as notion of cost their natural parameters.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:0904.412

Termination of rewriting strategies: a generic approach

We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying narrowing and abstracting steps. The induction principle is applied through the abstraction mechanism, where terms are replaced by variables representing any of their normal forms. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints can be used to control the narrowing mechanism, well known to easily diverge. The generic method is then instantiated for the innermost, outermost and local strategies.Comment: 49 page

Causal Consistency for Reversible Multiparty Protocols

In programming models with a reversible semantics, computational steps can be undone. This paper addresses the integration of reversible semantics into process languages for communication-centric systems equipped with behavioral types. In prior work, we introduced a monitors-as-memories approach to seamlessly integrate reversible semantics into a process model in which concurrency is governed by session types (a class of behavioral types), covering binary (two-party) protocols with synchronous communication. The applicability and expressiveness of the binary setting, however, is limited. Here we extend our approach, and use it to define reversible semantics for an expressive process model that accounts for multiparty (n-party) protocols, asynchronous communication, decoupled rollbacks, and abstraction passing. As main result, we prove that our reversible semantics for multiparty protocols is causally-consistent. A key technical ingredient in our developments is an alternative reversible semantics with atomic rollbacks, which is conceptually simple and is shown to characterize decoupled rollbacks.Comment: Extended, revised version of a PPDP'17 paper (https://doi.org/10.1145/3131851.3131864

Developing computational thinking in the classroom: a framework

Computational thinking sits at the heart of the new statutory programme of study for Computing: “A high quality computing education equips pupils to use computational thinking and creativity to understand and change the world” (Department for Education, 2013, p. 188). This document aims to support teachers to teach computational thinking. It describes a framework that helps explain what computational thinking is, describes pedagogic approaches for teaching it and gives ways to assess it. Pupil progression with the previous ICT curriculum was often demonstrated through ‘how’ (for example, a software usage skill) or ‘what’ the pupil produced (for example, a poster). This was partly due to the needs of the business world for office skills. Such use of precious curriculum time however has several weaknesses. Firstly, the country’s economy depends on technological innovation not just on use of technology. Secondly, the pace of technology and organisational change is fast in that the ICT skills learnt are out of date before a pupil leaves school. Thirdly, technology invades all aspects of our life and the typically taught office practice is only a small part of technology use today

Geometry of abstraction in quantum computation

Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some quantum algorithms provide feasible solutions of important hard problems, such as factoring and discrete log (which are the building blocks of modern cryptography). It is of a great practical interest to precisely characterize the computational resources needed to execute such quantum algorithms. There are many ideas how to build a quantum computer. Can we prove some necessary conditions? Categorical semantics help with such questions. We show how to implement an important family of quantum algorithms using just abelian groups and relations.Comment: 29 pages, 42 figures; Clifford Lectures 2008 (main speaker Samson Abramsky); this version fixes a pstricks problem in a diagra

A Rigorous Approach to Relate Enterprise and Computational Viewpoints

Multiviewpoint approaches allow stakeholders to design a system from stakeholder-specific viewpoints. By this, a separation of concerns is achieved, which makes designs more manageable. However, to construct a consistent multiviewpoint design, the relations between viewpoints must be defined precisely, so that the consistency of designs from these viewpoints can be verified. The goal of this paper is to make the consistency rules between (a slightly adapted version of) the RM-ODP enterprise and computational viewpoints more precise and to make checking the consistency between these viewpoints practically applicable. To achieve this goal, we apply a generic framework for relating viewpoints that includes reusable consistency rules. We implemented the consistency rules in a tool to show their applicability

Insights into enzymatic halogenation from computational studies

The halogenases are a group of enzymes that have only come to the fore over the last 10 years thanks to the discovery and characterization of several novel representatives. They have revealed the fascinating variety of distinct chemical mechanisms that nature utilizes to activate halogens and introduce them into organic substrates. Computational studies using a range of approaches have already elucidated many details of the mechanisms of these enzymes, often in synergistic combination with experiment. This Review summarizes the main insights gained from these studies. It also seeks to identify open questions that are amenable to computational investigations. The studies discussed herein serve to illustrate some of the limitations of the current computational approaches and the challenges encountered in computational mechanistic enzymology