Abstract
The theory of algebraic abstract types specified by conditional equations is extended to types with “nonstrict” operations, partial and even infinite objects based on the concept of partial interpretations. Models of such types are studied where all explicit equations have solutions. Higher order types, i.e. types comprising higher order functions are treated, too. This allows an algebraic (“equational”) specification of algebras including sorts with “infinite” objects and higher order functions (“functionals”).
(Extended Abstract)
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.A. Goguen, J.W. Thatcher, E.G. Wagner, J.B. Wright: Initial algebra semantics and continuous algebras. IBM Research Report RC-5701, November 1975, JACM 24 (1977) pp. 68–95
G. Birkhoff, J.D. Lipson: Heterogeneous algebras. J. of Combinatorial Theory 8, 115–133 (1970)
M. Broy, M. Wirsing: Programming languages as abstract data types. M. Dauchet (ed.): 5eme CAAP, Lille, February 1980, Universite de Lille 1980, 160–177
M. Broy, M. Wirsing: On the algebraic extensions of abstract data types. J. Diaz, I. Ramos (eds): International Colloquium on Formalization of Programming Concepts, Peniscola, April 1981, Lecture Notes in Computer Science 107, Berlin-Heidelberg-New York: Springer 1981, 244–251
M. Broy, M. Wirsing: Partial abstract data types. Acta Informatica 18:1, November 1982, 47–64
M. Broy, M. Wirsing: Generalized heterogeneous algebras and partial interpretations. In: Proc. CAAP 84. Lecture Notes in Computer Science 159, Berlin-Heidelberg-New York: Springer 1984, 1–34
G. Grätzer: Universal algebra. Princeton: Van Nostrand, 1968
S.C. Kleene: Introduction to metamathematics. New York: Van Nostrand 1952
Z. Manna: Mathematical theory of computation. New York: McGraw Hill 1974
B. Möller: Unendliche Objekte und Geflechte. Technische Universität München, Institut für Informatik, TUM-18213, Ph. D. Thesis 1982
D. Scott: Outline of a mathematical theory of computation. Proc. 4th Annual Princeton Conference on Information Sciences and Systems 1970, 169–176
M. Wirsing, M. Broy: Abstract data types as lattices of finitely generated models. In: Dembinski, P. (ed.): Mathematical Foundations of Computer Science — 9th Symposium, Rydzyna, Poland, Sept. 1–5, 1980. Lecture Notes in Computer Science 88. Berlin-Heidelberg-New York: Springer 1980, p. 673–685
M. Wirsing, P. Pepper, H. Partsch, W. Dosch, M. Broy: On hierarchies of abstract data types. Acta Informatica 20, 1983, 1–33.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Broy, M. (1986). Partial interpretations of higher order algebraic types. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016232
Download citation
DOI: https://doi.org/10.1007/BFb0016232
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16783-9
Online ISBN: 978-3-540-39909-4
eBook Packages: Springer Book Archive