We study union types and recursive types in the setting of a gradually typed lambda calculus. Our goal is to obtain a foundational account for languages that enable recursively defined data structures to be passed between static and dynamically typed regions of a program. We discuss how traditional sum types are not appropriate for this purpose and instead study a form of “true” union in the tr...

Let T be Gödel’s system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of natural numbers such that if a term A reduces to a term B and if a natural number I(A) is assigned to A then a natural number I(B) can be assigned to B such tha...

A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently...

We present a new formulation of sequential least-squares applied to scene and motion reconstruction from image features. We argue that recursive techniques will become more important both for real-time control applications and also interactive vision applications. The aim is to approximate as well as possible the result of the batch bundle adjustment method. In previously published work we desc...

It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for‐profit commercial firm or other commercial purpose without the explicit permission of the Econometric Society. For this purpose, contact Claire Sashi, General Manager, at [email protected]. This paper presents a stochastic dif...

Automatic word segmentation is a basic requirement for unsupervised learning in morphological analysis. In this paper, we formulate a novel recursive method for minimum description length (MDL) word segmentation, whose basic operation is resegmenting the corpus on a prefix (equivalently, a suffix). We derive a local expression for the change in description length under resegmentation, i.e., one...

The present paper argues that a systems theory epistemology (and particularly the notion of hierarchical recursive organization) provides the critical theoretical context within which the significance of Friston's (2010a) Free Energy Principle (FEP) for both evolution and psychoanalysis is best understood. Within this perspective, the FEP occupies a particular level of the hierarchical organiza...

This paper studies robust inference in autoregression around a polynomial trend with stable autoregressive roots under non-stationary volatility. The formulation of the volatility process is quite general including many existing deterministic and stochastic non-stationary volatility specifications. The aim of the paper is two-fold. First, it develops a limit theory for least squares estimators ...