Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree. The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".
Andrew D. Gordon is a British computer scientist employed by Microsoft Research. His research interests include programming language design, formal methods, concurrency, cryptography, and access control.
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements, places and transitions. Place elements are depicted as white circles and transition elements are depicted as rectangles. A place can contain any number of tokens, depicted as black circles. A transition is enabled if all places connected to it as inputs contain at least one token. Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.
In computer science, communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi, based on message passing via channels. CSP was highly influential in the design of the occam programming language and also influenced the design of programming languages such as Limbo, RaftLib, Erlang, Go, Crystal, and Clojure's core.async.
The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. Its actions model indivisible communications between exactly two participants. The formal language includes primitives for describing parallel composition, choice between actions and scope restriction. CCS is useful for evaluating the qualitative correctness of properties of a system such as deadlock or livelock.
In theoretical computer science, the π-calculus is a process calculus. The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation.
Solid modeling is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid modeling is distinguished from related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. Together, the principles of geometric and solid modeling form the foundation of 3D-computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.
In computer science, the process calculi are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes. Leading examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus.
The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though it is not convenient for writing software. Instead, it is important in the mathematical theory of algorithms because it is an extremely simple Turing complete language. It can be likened to a reduced version of the untyped lambda calculus. It was introduced by Moses Schönfinkel and Haskell Curry.
The actor model in computer science is a mathematical model of concurrent computation that treats an actor as the basic building block of concurrent computation. In response to a message it receives, an actor can: make local decisions, create more actors, send more messages, and determine how to respond to the next message received. Actors may modify their own private state, but can only affect each other indirectly through messaging.
In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation. See Actor model and process calculi history.
Concurrent computing is a form of computing in which several computations are executed concurrently—during overlapping time periods—instead of sequentially—with one completing before the next starts.
The actor model and process calculi share an interesting history and co-evolution.
The denotational semantics of the Actor model is the subject of denotational domain theory for Actors. The historical development of this subject is recounted in [Hewitt 2008b].
Interaction nets are a graphical model of computation devised by Yves Lafont in 1990 as a generalisation of the proof structures of linear logic. An interaction net system is specified by a set of agent types and a set of interaction rules. Interaction nets are an inherently distributed model of computation in the sense that computations can take place simultaneously in many parts of an interaction net, and no synchronisation is needed. The latter is guaranteed by the strong confluence property of reduction in this model of computation. Thus interaction nets provide a natural language for massive parallelism. Interaction nets are at the heart of many implementations of the lambda calculus, such as efficient closed reduction and optimal, in Lévy's sense, Lambdascope.
Operational transformation (OT) is a technology for supporting a range of collaboration functionalities in advanced collaborative software systems. OT was originally invented for consistency maintenance and concurrency control in collaborative editing of plain text documents. Its capabilities have been extended and its applications expanded to include group undo, locking, conflict resolution, operation notification and compression, group-awareness, HTML/XML and tree-structured document editing, collaborative office productivity tools, application-sharing, and collaborative computer-aided media design tools. In 2009 OT was adopted as a core technique behind the collaboration features in Apache Wave and Google Docs.
Reo is a domain-specific language for programming and analyzing coordination protocols that compose individual processes into full systems, broadly construed. Examples of classes of systems that can be composed with Reo include component-based systems, service-oriented systems, multithreading systems, biological systems, and cryptographic protocols. Reo has a graphical syntax in which every Reo program, called a connector or circuit, is a labeled directed hypergraph. Such a graph represents the data-flow among the processes in the system. Reo has formal semantics, which stand at the basis of its various formal verification techniques and compilation tools.
Membrane systems have been inspired from the structure and the functioning of the living cells. They were introduced and studied by Gh.Paun under the name of P systems [24]; some applications of the membrane systems are presented in [15]. Membrane systems are essentially models of distributed, parallel and nondeterministic systems. Here we motivate and present the mobile membranes. Mobile membranes represent a variant of membrane systems inspired by the biological movements given by endocytosis and exocytosis. They have the expressive power of both P systems and process calculi with mobility such as mobile ambients [11] and brane calculi [10]. Computations with mobile membranes can be defined over specific configurations, while they represent also a rule-based formalism.
Join-patterns provides a way to write concurrent, parallel and distributed computer programs by message passing. Compared to the use of threads and locks, this is a high level programming model using communication constructs model to abstract the complexity of concurrent environment and to allow scalability. Its focus is on the execution of a chord between messages atomically consumed from a group of channels.
