Unified algebras and institutions
Proceedings of the Fourth Annual Symposium on Logic in computer science
Universal algebra in higher types
Theoretical Computer Science
Membership algebra as a logical framework for equational specification
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Combining Algebraic and Set-Theoretic Specifications
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
Higher-Order Equational Logic for Specification, Simulation and Testing
HOA '95 Selected Papers from the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Specification Refinement with System F
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Hi-index | 0.00 |
In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higher-order types, interpreted set-theoretically as Cartesian products, function spaces, and power-sets. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models. It may be regarded as the basis for a Horn-clause approximation to the Z framework, and has the advantage of being amenable to prototyping and automated reasoning. Standard set-theoretic models are considered, and conditions are given for the existence of initial reducts of such models. Algebraic specifications for various set-theoretic concepts are considered.