# Programming languages as mathematical objects

Invited Lectures

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## Keywords

Programming Language Partial Function Rational Theory Algebraic Theory Bottom Element
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## References

- (1973) (JAG, JWT, EGW, JBW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "A Junction between computer science and category theory: I, Basic definitions and examples," Part 1, IBM Research report RC 4526, Sept 1973.Google Scholar
- (1974) (JAG, JWT, EGW, JBW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Initial algebra semantics," Extended Abstract, IBM Research Report RC-4865, May 1974.
*Proceedings*, 15th IEEE Symposium on Switching and Automata Theory (1974) pp. 63–77. Full paper, IBM Research Report RC-5243, January 1975. (See 1975a listing.)Google Scholar - (1975) (JAG, JWT, EGW, JBW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Introduction to categories, algebraic theories and algebras," IBM Research Report RC-5369, April 1975.Google Scholar
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- (1976a) (EGW, JBW, JAG, JWT) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Some fundamentals of order-algebraic semantics,"
*Lecture Notes in Computer Science 45*(Mathematical Foundations of Computer Science 1976) pp.153–168. IBM Research Report RC-6020, May 1976.Google Scholar - (1976b) (JBW, JWT, EGW, JAG) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Rational algebraic theories and fixed-point solutions," Extended Abstract, IBM Research Report RC-6116, May 1976.
*Proceedings*, 17th IEEE Symposium on Foundations of Computing, Houston, Texas, October, 1976, pp. 147–158.Google Scholar - (1977) (JBW, EGW, JWT) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "A uniform approach to inductive posets and inductive closure."
*Lecture Notes in Computer Science 53*(Mathematical Foundations of Computer Science 1977), pp. 192–212. IBM Research Report RC-6817, October 1977. To appear,*Theoretical Computer Science*, 1978.Google Scholar - (1977a) (EGW, JWT, JBW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Free continuous theories," IBM Research Report RC-6906, December 1977.Google Scholar
- (1978a) (JWT, EGW, JBW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Many-sorted and Ordered Algebraic Theories," IBM Research Report in preparation.Google Scholar
- (1978b) (JBW, JWT, EGW) J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright "Z-Continuity, Z-Inductiveness and Products," IBM Research Report in preparation.Google Scholar
- (1978c) (EGW, JBW, JWT) "Z-inductive, Z-completions of Ordered Theories," IBM Research Report in preparation.Google Scholar
- Elgot, C. E. (1973) "Monadic computation and iterative algebraic theories," IBM Research Report RC-4564, October 1973.
*Proceedings*, Logic Colloquium '73, North Holland Publishing Company (1975) 175–230.Google Scholar - Engelfriet, J. and Schmidt, E. M. (1975) "IO and OI," Matematisk Institut, Aarhus Universitet, report DAIMI PB-47, (July 1975).Google Scholar
- Mac Lane, S. (1971)
*Categories for the Working Mathematician*, Springer-Verlag, New York, Heidelberg, Berlin (1971).Google Scholar - Maibaum, T. S. E. (1974) "A generalized approach to formal languages,"
*JCSS 8*(1974) 409–439.Google Scholar - Manes, E. G. (1976)
*Algebraic Theories*, Springer-Verlag, New York, Heidelberg, Berlin, (1975).Google Scholar - Nivat, M. (1972) "Languages algebraic sur le magma libre et semantique des schemas de programme," in
*Automata, Languages and Programming*(M. Nivat, Ed.) North Holland (1972) 293–308.Google Scholar - Scott, D. (1970)
*The lattice of flow diagrams*, Oxford University Computing Laboratory, Tech. Monograph PRG-3 (November 1970).Google Scholar - Strong, H. R., Jr. (1971) "High level languages of Maximum Power," IBM Research Report RC-3352. May 1971.Google Scholar
- Wagner, E.G. (1971) "An algebraic theory of recursive definitions and recursive languages,"
*Proceedings*, 3rd Annual ACM Symposium on Theory of Computing, Shaker Heights, Ohio (1971)Google Scholar - (1973) "From algebras to programming languages,"
*Proceedings*, th ACM Symp. on Theory of Computing, Austin, Texas (1973)Google Scholar - (1974)
*Notes on categories, algebras, and programming languages*, Lecture notes from a course given at Queen Mary College of University of London, Spring 1974.Google Scholar - Wand, M. (1973) "Mathematical foundations of formal language theory," MIT, Project Mac Report MAC TR-108. (1974)Google Scholar

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© Springer-Verlag Berlin Heidelberg 1978