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Weakest Precondition for General Recursive Programs Formalized in Coq
, 2002
"... This paper describes a formalization of the weakest precondition, wp, for general recursive programs using the typetheoretical proof assistant Coq. The formalization is a deep embedding using the computational power intrinsic to type theory. Since Coq accepts only structural recursive functions, th ..."
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This paper describes a formalization of the weakest precondition, wp, for general recursive programs using the typetheoretical proof assistant Coq. The formalization is a deep embedding using the computational power intrinsic to type theory. Since Coq accepts only structural recursive functions, the computational embedding of general recursive programs is nontrivial. To justify the embedding, an operational semantics is defined and the equivalence between wp and the operational semantics is proved. Three major healthiness conditions, namely: Strictness, Monotonicity and Conjunctivity are proved as well.
Symbolic Simulation of HybridSystems RalphJohan BackCristina Cerschi Seceleanu Jan Westerholm
"... TUCS LaboratorySoftware Construction Laboratory 1 Introduction Hybrid systems fall on the borderline between Computer Science and ControlTheory, requiring techniques from both areas. These systems can be quite hard to build, due to the many different ways in which the continuous system behaviorneeds ..."
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TUCS LaboratorySoftware Construction Laboratory 1 Introduction Hybrid systems fall on the borderline between Computer Science and ControlTheory, requiring techniques from both areas. These systems can be quite hard to build, due to the many different ways in which the continuous system behaviorneeds to interact with the discrete controller. Modeling hybrid systems is therefore of great help, allowing one to analyze the properties of the system to be builtbeforehand, to find out potential trouble spots, and to convince oneself of the correctness of the controller.A formal approach to modeling hybrid systems, especially safetycritical control systems has the advantage of providing a precise model of the system, onwhich wellestablished formal verification methods may be applied to prove that any behavior of the system satisfies the properties that are verified.Discrete concurrent systems can be modeled as action systems [4], where a state (described by a collection of state variables) is manipulated by a collectionof actions.