Principles of parameterized programming
Software reusability: vol. 1, concepts and models
Fundamentals of algebraic specification 2: module specifications and constraints
Fundamentals of algebraic specification 2: module specifications and constraints
Category theory for computing science
Category theory for computing science
Functorial theory of parameterized specifications in a general specification framework
Theoretical Computer Science
Refinement of parameterized algebraic specifications
Proceedings of the IFIP TC 2 WG 2.1 international workshop on Algorithmic languages and calculi
Parameterized Specifications: Parameter Passing and Implementation with Respect to Observability
ACM Transactions on Programming Languages and Systems (TOPLAS)
Universal Realization, Persistent Interconnection and Implementation of Abstract Modules
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Implementation of Parameterised Specifications (Extended Abstract)
Proceedings of the 9th Colloquium on Automata, Languages and Programming
The Semantics of CLEAR, A Specification Language
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
Data type specification: Parameterization and the power of specification techniques
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Towards semantics of self-adaptive software
IWSAS' 2000 Proceedings of the first international workshop on Self-adaptive software
Composition and Refinement of Behavioral Specifications
Proceedings of the 16th IEEE international conference on Automated software engineering
Proceedings of the 2011 workshop on New security paradigms workshop
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Parametricity is one of the most effective ways to achieve compositionality and reuse in software development. Parametric specifications have been thoroughly analyzed in the algebraic setting and are by now a standard part of most software development toolkits. However, an effort towards classifying, specifying and refining algorithmic theories, rather than mere datatypes, quickly leads beyond the realm of algebra, and often to full first order theories. We extend the standard semantics of parametric specifications to this more general setting. The familiar semantic characterization of parametricity in the algebraic case is expressed in terms of the free functor, i.e. using the initial models. In the general case, initial models may not exist, and the free functor is not available. Various syntactic, semantic, and abstract definitions of parametricity have been offered, but their exact relationships are often unclear. Using the methods of categorical model theory, we establish the equivalence of two well known, yet so far unrelated, definitions of parametricity, one syntactic, one semantic. Besides providing support for both underlying views, and a way for aligning the systems based on each of them, the offered general analysis and its formalism open several avenues for future research and applications.