Abstract
Starting from an algebraic specification approach this paper presents a uniform framework for specifying data structures and configurations of systems. The framework covers (simple) algebraic specifications with higherorder functions and shallow polymorphism. The concepts of dependent types are used to define parameterised specifications and classes of specification schemata, so-called polymorphic specifications. Due to the introduction of a second level, configuration of modules can be abstractly specified; relationships between different classes of objects such as specifications, signatures or parameterised specifications can be described.
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J. Barwise: Handbook of Math. Logic, Studies in Logic, Vol. 90, North-Holland, Amsterdam 1977
CIP System Group: The Munich Project CIP. Lecture Notes in Comp. Science 292, Berlin, Springer, 1987.
J.A. Bergstra, J. Heering, P. Klint: Module algebra. J. ACM 37, 1990, 335–372.
R. Burstall, J. Goguen: Putting theories together to make specifications. Proc. 5th Internat. Joint Conf. on Artificial Intelligence, Cambridge, Mass., 1977, 1045–1058.
L. Cardelli, G. Longo: A semantic basis for Quest. DEC SRC, Palo Alto, Ca., Rep. 55, 1990.
H. Ehrig, B. Mahr: Fundamentals of Alg. Specification I and II. Berlin, Springer 1985 and 1989.
K. Futatsugi, J.A. Goguen, J.-P. Jouannaud, J. Meseguer: Principles of OBJ2. Symposium on Principles of Programming Languages 1985, 52–66.
J.V. Guttag, J.J. Horning, J.M. Wing: Larch in Five Easy Pieces. DEC SRC, Palo Alto, Cal, 1985.
M. Hanus: Horn clause programs with polymorphic types: Semantics and resolution. In: J. Diaz, F. Orejas (eds.): Tapsoft 89, Lecture Notes in Computer Science 352, Berlin, Springer, 1989, 225–240.
R. Harper, D. MacQueen, R. Milner: Standard ML report. Edinburgh Univ., 1986, ECS-LFCS-86-2.
B. Krieg-Brückner, D. Sannella: Structuring in the large and in the small: Higher-order functions, dependent types and inheritance in SPECTRAL. Draft, 1990.
Z. Luo: ECC, an extended calculus of constructions. Proc. 4th LICS, Asilomar, California, 1989.
D. MacQueen: Using dependent types to express modular structure. Proceedings of 13th ACM Symposium on Principles of Programming Languages, St. Petersberg Beach, Fla., 1986.
P. Martin-Löf: Constructive mathematics and computer programming. Sixth International Congress for Logic, Methodology and Philosophy of Science, North-Holland, Amsterdam 1982.
J.C. Mitchell: Type systems for programming languages. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science, Vol. B, Amsterdam, Elsevier, 1990, 365–458.
A. Poigné: On specifications, theories and models with higher types. Inform. and Control 68, 1986, 1–46.
D.T. Sannella, S. Sokolowski, A. Tarlecki: Toward formal development of programs from algebraic specifications: Parameterisation revisited. Draft 1990.
D.T. Sannella, A. Tarlecki: Towards a formal development of programs for algebraic specifications: Implementations revisited. Acta Informatica 25, 1988, 233–281.
D.T. Sannella, M. Wirsing: A kernel language for algebraic specification and implementation. In: M. Karpinski: FCT 83 Lecture Notes in Comp. Scie. 158. Berlin, Springer, 1983, 413–427.
G. Smolka, W. Nutt, J.A. Goguen, J. Meseguer: Order-sorted equational computation. In: H. Ait-Kaci, M. Nivat: Resolution of Equations in Algebraic Structures 2, San Diego, Acad. Press, 1989, 297–367.
T. Streicher: A general scheme for specification languages. Draft, University of Passau, 1990.
T. Streicher, M. Wirsing: Dependent types considered necessary for specification languages. Draft 1990.
M. Wirsing: Structured algebraic specifications: A kernel language. Theor. Comp. Sci. 42, 1986.
M. Wirsing: Algebraic Specification. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science, Vol. B, Amsterdam, Elsevier, 1990, 677–788.
M. Wirsing, M. Broy: A modular framework for algebraic specification and implementation. In: J. Diaz, F. Orejas: TAPSOFT 89, Lecture Notes in Computer Science 351, Berlin, Springer, 42–73.
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Leszczylowski, J., Wirsing, M. (1991). Polymorphism, parameterization and typing: An algebraic specification perspective. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020783
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DOI: https://doi.org/10.1007/BFb0020783
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