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Proving the correctness of reactive systems using sized types
, 1996
"... { rjmh, pareto, sabry We have designed and implemented a typebased analysis for proving some baaic properties of reactive systems. The analysis manipulates rich type expressions that contain information about the sizes of recursively defined data structures. Sized types are useful for detecting d ..."
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Cited by 131 (2 self)
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{ rjmh, pareto, sabry We have designed and implemented a typebased analysis for proving some baaic properties of reactive systems. The analysis manipulates rich type expressions that contain information about the sizes of recursively defined data structures. Sized types are useful for detecting deadlocks, nontermination, and other errors in embedded programs. To establish the soundness of the analysis we have developed an appropriate semantic model of sized types. 1 Embedded Functional Programs In a reactive system, the control software must continuously react to inputs from the environment. We distinguish a class of systems where the embedded programs can be naturally expressed as functional programs manipulating streams. This class of programs appears to be large enough for many purposes [2] and is the core of more expressive formalisms that accommodate asynchronous events, nondeterminism, etc. The fundamental criterion for the correctness of programs embedded in reactive systems is Jwene.ss. Indeed, before considering the properties of the output, we must ensure that there is some output in the first place: the program must continuous] y react to the input streams by producing elements on the output streams. This latter property may fail in various ways: e the computation of a stream element may depend on itself creating a “black hole, ” or e the computation of one of the output streams may demand elements from some input stream at different rates, which requires unbounded buffering, or o the computation of a stream element may exhaust the physical resources of the machine or even diverge.
Admissible Digit Sets and a Modified Stern–Brocot Representation
"... We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “dig ..."
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We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “digit set ” yields an admissible representation of [0, +∞]. Furthermore we establish the productivity and correctness of the homographic algorithm for such “admissible” digit sets. In the second part of the paper we discuss representation of positive real numbers based on the Stern–Brocot tree. We show how we can modify the usual Stern–Brocot representation to yield a ternary admissible digit set.