Safety analysis is an algorithm for determining if a term in an untyped lambda calculus with constants is safe, i.e., if it does not cause an error during evaluation. We prove that safety analysis accepts strictly more safe lambda terms than does type inference for Thatte’s partial types.

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small, ac...

A denotational semantics of simply typed lambda calculus with a basic type Dynamic, modelling values whose type is to be inspected at run-time, has been given by Abadi e.a..1]. We extend this interpretation to cover (formally contractive) recursive types as well. Soundness of typing rules and freeness of run-time type errors for well-typed programs hold. The interpretation works also for implic...

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

We study the concept of a mixed matrix in connection with linear fractional transformations of lossless and passive matrix-valued rational functions, and show that they can be parametrized by sequences of elementary chain matrices. These notions are exemplified on a model of a Surface Acoustic Wave filter for which a state-space realization is carried out in detail. The issue of optimal design ...

The lossless embedding problem, also known as the Darlington synthesis or unitary extension problem, considers the extension of a given contractive system to become the partial input-output operator of a lossless system. In the paper, the embedding problem is solved for discrete-time time-varying systems with finite but possibly time-varying state dimensions, for the strictly contractive as wel...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

A contraction analysis of risk-sensitive Riccati equations is proposed. When the state-space model is reachable and observable, a block-update implementation of the risk-sensitive filter is used to show that the N-fold composition of the Riccati map is strictly contractive with respect to the Riemannian metric of positive definite matrices, when N is larger than the number of states. The range ...

We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.