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In computer science, algebraic semantics is a formal approach to programming language theory that uses algebraic methods for defining, specifying, and reasoning about the behavior of programs. It is a form of axiomatic semantics that provides a mathematical framework for analyzing programs through the use of algebraic structures and equational logic.[1][2][3][4]
Algebraic semantics represents programs and data types as algebras—mathematical structures consisting of sets equipped with operations that satisfy certain equational laws. This approach enables rigorous formal verification of software by treating program properties as algebraic properties that can be proven through mathematical reasoning. A key advantage of algebraic semantics is its ability to separate the specification of what a program does from how it is implemented, supporting abstraction and modularity in software design.
- ^ J.A. Goguen; J.W. Thatcher; E.G. Wagner; J.B. Wright (1977). "Initial algebra semantics and continuous algebras". Journal of the ACM. 24 (1): 68–95. doi:10.1145/321992.321997. S2CID 11060837.
- ^ J.A. Goguen; J.W. Thatcher; E.G. Wagner (1978). "An initial algebra approach to the specification, correctness and implementation of abstract data types". In R.T. Yeh (ed.). Current Trends in Programming Methodology, Vol. IV: Data Structuring. Prentice Hall. pp. 80–149.
- ^ J.A. Goguen; C. Kirchner; H. Kirchner; A. Megrelis; J. Meseguer (1988). "An introduction to OBJ3". Proceedings of the First Workshop on Conditional Term Rewriting Systems. Lecture Notes in Computer Science. Vol. 308. Springer. pp. 258–263. doi:10.1007/3-540-19242-5_22. ISBN 978-3-540-19242-8.
- ^ J.A. Goguen; G. Malcolm (1996). Algebraic Semantics of Imperative Programs. MIT Press. ISBN 9780262071727.
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