A Model of Cooperative Threads

We develop a model of concurrent imperative programming with threads. We focus on a small imperative language with cooperative threads which execute without interruption until they terminate or explicitly yield control. We define and study a trace-based denotational semantics for this language; this semantics is fully abstract but mathematically elementary. We also give an equational theory for the computational effects that underlie the language, including thread spawning. We then analyze threads in terms of the free algebra monad for this theory.Comment: 39 pages, 5 figure

Subtyping and Parametricity

In this paper we study the interaction of subtyping and parametricity. We describe a logic for a programming language with parametric polymorphism and subtyping. The logic supports the formal definition and use of relational parametricity. We give two models for it, and compare it with other formal systems for the same language. In particular, we examine the "Penn interpretation" of subtyping as implicit coercion. Without subtyping, parametricity yields, for example, an encoding of abstract types and of initial algebras, with the corresponding proof principles of simulation and induction. With subtyping, we obtain partially abstract types and certain initial order-sorted algebras, and may derive proof principles for them. 1 Introduction A function is polymorphic if it works on inputs of several types. We may distinguish various notions of polymorphism, particularly parametric polymorphism (e.g. [Rey83]) and subtype polymorphism (e.g. [CW85]). These may exist in isolation, as in ML [MT..

Reverse Derivative Categories

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.Comment: Extended version of paper to appear at CSL 202

The Ultraviolet-to-Mid-Infrared Spectral Energy Distribution of Weak Emission Line Quasars

We present Spitzer Space Telescope photometry of 18 Sloan Digital Sky Survey (SDSS) quasars at 2.7 <= z <= 5.9 which have weak or undetectable high-ionization emission lines in their rest-frame ultraviolet (UV) spectra (hereafter weak-lined quasars, or WLQs). The Spitzer data are combined with SDSS spectra and ground-based, near-infrared (IR) photometry of these sources to produce a large inventory of spectral energy distributions (SEDs) of WLQs across the rest-frame ~0.1-5 mum spectral band. The SEDs of our sources are inconsistent with those of BL Lacertae objects which are dominated by synchrotron emission due to a jet aligned close to our line-of-sight, but are consistent with the SED of ordinary quasars with similar luminosities and redshifts that exhibit a near-to-mid-IR 'bump', characteristic of hot dust emission. This indicates that broad emission lines in WLQs are intrinsically weak, rather than suffering continuum dilution from a jet, and that such sources cannot be selected efficiently from traditional photometric surveys.Comment: 10 pages (emulateapj), 4 figures. Accepted for publication in Ap

Linearization of CIF Through SOS

Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In particular, a linearization algorithm is needed for the Compositional Interchange Format (CIF), an automaton based modeling language. The problem of devising efficient linearization algorithms is not trivial, and has been already addressed in literature. However, the linearization algorithms obtained are the result of an inventive process, and the proof of correctness comes as an afterthought. Furthermore, the semantic specification of the language does not play an important role on the design of the algorithm. In this work we present a method for obtaining an efficient linearization algorithm, through a step-wise refinement of the SOS rules of CIF. As a result, we show how the semantic specification of the language can guide the implementation of such a procedure, yielding a simple proof of correctness.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Recursion does not always help

We show that adding recursion does not increase the total functions definable in the typed $\lambda\beta\eta$-calculus or the partial functions definable in the $\lambda\Omega$-calculus. As a consequence, adding recursion does not increase the class of partial or total definable functions on free algebras and so, in particular, on the natural numbers.Comment: Improved presentation a littl