Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
CASL: the common algebraic specification language
Theoretical Computer Science
Specifying Real Numbers in CASL
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Interval arithmetic and automatic error analysis in digital computing
Interval arithmetic and automatic error analysis in digital computing
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Formal Aspects of Correctness and Optimality of Interval Computations
Formal Aspects of Computing
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This paper defines the basis for the implementation in CASL (Common Algebraic Specification Language) of an interval library such that intervals behave as real numbers endowed with an error information. To achieve that, we redefine the notion of interval local set defined in [R.H.N. Santiago. Interval local equality toward a model for real type. In Proceedings of the IV Workshop on Formal Methods, pages 54-59, Rio de Janeiro, RJ, 2001. Sociedade Brasileira de Computacao] in such a way that it can be implemented in the underlying logic of CASL. With these results, it is possible to manipulate intervals in CASL, as if they were real numbers, with equational reasoning, and get an error estimation on the obtained results for free (from the width of the resulting interval). The paper describes the CASL definition of the interval library and presents a case study on a simple example requiring handling data with ''tolerance'' margin.