6 research outputs found
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Algebraic specification : syntax, semantics, structure
Algebraic specification is the technique of using algebras to model properties of a system and using axioms to characterize such algebras. Algebraic specification comprises two aspects: the underlying logic used in the axioms and algebras, and the use of a small, general set of operators to build specifications in a structured manner. We describe these two aspects using the unifying notion of institutions. An institution is an abstraction of a logical system, describing the vocabulary, the kinds of axioms, the kinds of algebras, and the relation between them. Using institutions, one can define general structuring operators which are independent of the underlying logic. In this paper, we survey the different kind of logics, syntax, semantics, and structuring operators that have been used in algebraic specification
The imperative implementation of algebraic data types
The synthesis of imperative programs for hierarchical, algebraically specified abstract data types is investigated. Two aspects of the synthesis are considered: the choice of data structures for efficient implementation, and the synthesis of linked implementations for the class of ADTs which insert and access data without explicit key. The methodology is based on an analysis of the algebraic semantics of the ADT. Operators are partitioned according to the behaviour of their corresponding operations in the initial algebra. A family of relations, the storage relations of an ADT, Is defined. They depend only on the operator partition and reflect an observational view of the ADT. The storage relations are extended to storage graphs: directed graphs with a subset of nodes designated for efficient access. The data structures in our imperative language are chosen according to properties of the storage relations and storage graphs. Linked implementations are synthesised in a stepwise manner by implementing the given ADT first by its storage graphs, and then by linked data structures in the imperative language. Some circumstances under which the resulting programs have constant time complexity are discussed