Algebraic Semantics (computer Science)

	Algebraic Semantics (computer Science) In computer science, algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program specifications in a formal manner. Syntax The syntax of an algebraic specification is formulated in two steps: (1) defining a formal signature of data types and operation symbols, and (2) interpreting the signature through sets and functions. Definition of a signature The signature of an algebraic specification defines its formal syntax. The word "signature" is used like the concept of "key signature" in musical notation. A signature consists of a set S of data types, known as sorts, together with a family \Sigma of sets, each set containing operation symbols (or simply symbols) that relate the sorts. We use \Sigma_ to denote the set of operation symbols relating the sorts s_1,~s_2,~...,~s_n \in S to the sort s \in S. For example, for the signature of integer stacks, we define two sorts, namely, int and stack, and the following famil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Computer Science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Many-sorted Logic Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive "parts of speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be done only accordingly, respecting the "sorts". There are various ways to formalize the intention mentioned above; a ''many-sorted logic'' is any package of information which fulfils it. In most cases, the following are given: * a set of sorts, ''S'' * an appropriate generalization of the notion of ''signature'' to be able to handle the additional information that comes with the sorts. The domain of discourse of any structure of that signature is then fragmented into disjoint subsets, one for every sort. Example When reasoning about biological organisms, it is useful to distinguish two sorts: \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]