Abstract
We define a framework based on dependent types for putting algebraic components together. It is defined with freely generated categories. In order to preserve initial, loose and constrained semantics of components, we introduce the notion of SPEC-categories which look like specific finitely co-complete categories. A constructive approach which includes parametrization techniques is used to define new components from basic predefined ones. The problem of the internal coding of external signature symbols is introduced.
Work supported in part by ESPRIT Project 1598 (Replay) and PRC Greco-Programmation
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Bert, R. Echahed, Design and implementation of a generic, logic and functional programming language, LNCS 213, pp.119–132 (1986).
Bergstra and al., Module Algebra, Report P8823. University of Amsterdam, (Nov. 1988).
D.Bert, J.C. Reynaud, Primitives for Algebraic Components, Esprit Project 1598, Replay/T2.3/I (July 1988).
J. Cartmell, Generalized Algebraic Theories and Contextual Categories, PhD. Thesis, Oxford (1978).
J. Cartmell, Formalizing the Network and Hierarchical Data Models. An Application of categorical logic. Symposium on Category Theory and Computer Science, LNCS 283
H. Ehrig, B. Mahr, Fundamentals of algebraic specification 1: Equations and initial semantics, Springer, (1985).
H. Ehrig, H. Weber, Programming in the large with algebraic module specifications, IFIP-Congress (1986)
K.Futatsugi, J.A. Goguen, J.P.Jouannaud, J. Meseguer, Principles of OBJ2, Proc. of the 12th ACM Symposium on Principles of Programming Languages, pp.52–66 (1985)
P. Freyd, Aspects of Topoi, Bull. Austral. Math. Soc. 7,1972.
M.C. Gaudel, A first introduction to PLUSS. Université Paris Sud, Orsay Techn. Rep., 1984.
J.A. Goguen, R.M.Burstall, Introducing institutions, Proc. Logics of Programming Workshop LNCS 164, pp.221–256 (1984).
J.Lambek, P.J. Scott, Introduction to higher order categorical logic, Cambridge University Press 1986.
S. MacLane, Categories for the working mathematician, Springer 1972.
A. Poigne, Algebra Categorically, Symposium on Category Theory and Computer Science, LNCS 283, pp.76–102.
F.Parisi-Presicce, Product and iteration of module specifications, CAAP'88, LNCS 299 (1988)
J.C. Reynaud, Semantique de LPG, RR 651 IMAG, 56 LIFIA (1987)
J.C. Reynaud, A calculus for putting Algebraic Components Together. REPLAY/T2.3/F, ESPRIT Project 1598(REPLAY), Sept. 1989.
D.T. Sannella, A. Tarlecki, Building specifications in an arbitrary institution, Proc. of the Intl. Symp. on Semantics of Data Types, LNCS 173, Springer(1984).
A. Tarlecki, On the existence of free models in abstract algebraic institutions, TCS 37 (1985) pp.269–304.
M. Wirsing, Structured algebraic specifications: a kernel language. TCS 42, 1986, 123–249.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reynaud, JC. (1990). Putting algebraic components together: A dependent type approach. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1990. Lecture Notes in Computer Science, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52531-9_133
Download citation
DOI: https://doi.org/10.1007/3-540-52531-9_133
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52531-8
Online ISBN: 978-3-540-47014-4
eBook Packages: Springer Book Archive