Continuous predicate

Abstract: Current systems are no longer pure physical systems or information systems but tend to consist of elements from both of these areas Thus, one modelling technique which considers the behaviour of all the different system elements is elaborated within this paper Extended Predicate/Transition nets often used for information technology serve as a basis for this modelling It is shown how differential equations as used for the description of the physical elements can be modelled by this technique Linear and nonlinear systems are regarded as well as the coupling of these systems For continuous modelling of the equations a continuous Predicate/Transition net is presented

Abstract: Based on constructive type theory, we study two idealized imperative languages GC and IC and verify the correctness of a compiler from GC to IC. GC is a guarded command language with underspecified execution order defined with an axiomatic semantics. IC is a deterministic low-level language with linear sequential composition and lexically scoped gotos defined with a small-step semantics. We characterize IC with an axiomatic semantics and prove that the compiler from GC to IC preserves specifications. The axiomatic semantics we consider model total correctness and map programs to continuous predicate transformers. We define the axiomatic semantics of GC and IC with elementary inductive predicates and show that the predicate transformer described by a program can be obtained compositionally by recursion on the syntax of the program using a fixed point operator for loops and continuations. We also show that two IC programs are contextually equivalent if and only if their predicate transformers are equivalent.