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Operational Semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms (denotational semantics). Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the ''individual steps'' of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics) describe how the ''overall results'' of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called ''well-formed words''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. In computer science, formal languages are used, among others, as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages, in which the words of the language represent concepts that are associated with meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algol 68
ALGOL 68 (short for ''Algorithmic Language 1968'') is an imperative programming language member of the ALGOL family that was conceived as a successor to the ALGOL 60 language, designed with the goal of a much wider scope of application and more rigorously defined syntax and semantics. The complexity of the language's definition, which runs to several hundred pages filled with non-standard terminology, made compiler implementation difficult and it was said it had "no implementations and no users". This was only partly true; ALGOL 68 did find use in several niche markets, notably in the United Kingdom where it was popular on International Computers Limited (ICL) machines, and in teaching roles. Outside these fields, use was relatively limited. Nevertheless, the contributions of ALGOL 68 to the field of computer science have been deep, wide-ranging and enduring, although many of these contributions were only publicly identified when they had reappeared in subsequently develo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation (mathematics)
In mathematics, a relation denotes some kind of ''relationship'' between two mathematical object, objects in a Set (mathematics), set, which may or may not hold. As an example, "''is less than''" is a relation on the set of natural numbers; it holds, for instance, between the values and (denoted as ), and likewise between and (denoted as ), but not between the values and nor between and , that is, and both evaluate to false. As another example, "''is sister of'' is a relation on the set of all people, it holds e.g. between Marie Curie and Bronisława Dłuska, and likewise vice versa. Set members may not be in relation "to a certain degree" – either they are in relation or they are not. Formally, a relation over a set can be seen as a set of ordered pairs of members of . The relation holds between and if is a member of . For example, the relation "''is less than''" on the natural numbers is an infinite set of pairs of natural numbers that contains both and , b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference Rule
Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure of valid arguments. If an argument with true premises follows a rule of inference then the conclusion cannot be false. ''Modus ponens'', an influential rule of inference, connects two premises of the form "if P then Q" and "P" to the conclusion "Q", as in the argument "If it rains, then the ground is wet. It rains. Therefore, the ground is wet." There are many other rules of inference for different patterns of valid arguments, such as ''modus tollens'', disjunctive syllogism, constructive dilemma, and existential generalization. Rules of inference include rules of implication, which operate only in one direction from premises to conclusions, and rules of replacement, which state that two expressions are equivalent and can be freely swapped. Rules of inference contrast with formal fallaciesinvalid argument forms involving logi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Transition System
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible. Transition systems coincide mathematically with abstract rewriting systems (as explained further in this article) and directed graphs. They differ from finite-state automata in several ways: * The set of states is not necessarily finite, or even countable. * The set of transitions is not necessarily finite, or even countable. * No "start" state or "final" states are given. Transition systems can be represented as directed graphs. Formal definition Formally, a transition system is a pair (S, T) where S is a set of states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Definition
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set ( Aczel 1977:740ff). Some examples of recursively definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function is defined by the rules :\begin & 0! = 1. \\ & (n+1)! = (n+1) \cdot n!. \end This definition is valid for each natural number , because the recursion eventually reaches the base case of 0. The definition may also be thought of as giving a procedure for computing the value of the function , starting from and proceeding onwards with etc. The recursion theorem states that such a definition indeed defines a function that is unique. The proof uses mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilles Kahn
Gilles Kahn (17 April 1946 – 9 February 2006) was a French computer scientist. He notably introduced Kahn process networks as a model for parallel processing and natural semantics for describing the operational semantics of programming languages. Gilles Kahn was born in Paris. He studied at the École polytechnique (X1964) and at Stanford. He became a member of the French Academy of Sciences in 1997. He was president and director-general of INRIA The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name French Institute for Research in Comp ... from 2004 to 2006. He died in Garches. External links Page at the French academy of sciences 1946 births 2006 deaths French computer scientists Members of the French Academy of Sciences École Polytechnique alumni {{France-compu-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matthias Felleisen
Matthias Felleisen is a German-American computer science professor and author. He grew up in Germany and immigrated to the US in his twenties. He received his PhD from Indiana University Bloomington under the direction of Daniel P. Friedman. After serving as professor for 14 years in the Computer Science Department of Rice University, Felleisen joined the Khoury College of Computer Sciences at Northeastern University in Boston, Massachusetts as Trustee Professor. Felleisen's interests include programming languages, including programming tools, program design, software contracts, and many more. In the 1990s, Felleisen launched PLT and TeachScheme! (later ProgramByDesign and eventually giving rise to the Bootstrap project ) with the goal of teaching program-design principles to beginners and to explore the use of Scheme to produce large systems. As part of this effort, he authored '' How to Design Programs'' (Massachusetts Institute of Technology Press (MIT Press), 2001) wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gordon Plotkin
Gordon David Plotkin (born 9 September 1946) is a theoretical computer scientist in the School of Informatics at the University of Edinburgh. Plotkin is probably best known for his introduction of structural operational semantics (SOS) and his work on denotational semantics. In particular, his notes on ''A Structural Approach to Operational Semantics'' were very influential. He has contributed to many other areas of computer science. Education Plotkin was educated at the University of Glasgow and the University of Edinburgh, gaining his Bachelor of Science degree in 1967 and PhD in 1972 supervised by Rod Burstall. Career and research Plotkin has remained at Edinburgh, and was, with Burstall and Robin Milner, a co-founder of the Laboratory for Foundations of Computer Science (LFCS). His former doctoral students include Luca Cardelli, Philippa Gardner, Doug Gurr, Eugenio Moggi, and Lǐ Wèi. Awards and honours Plotkin was elected a Fellow of the Royal Society (FRS) in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
