Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Semantics of Separation-Logic Typing and Higher-order Frame Rules for<br> Algol-like Languages

We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we provide simple sound rules for deriving higher-order frame rules, allowing for local reasoning

Research in mathematical theory of computation

Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker

A Graph Model for Imperative Computation

Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to output values. We consider a similar model based on relations whose input values are finite sequences rather than sets. This alteration means that we are taking into account the order in which observations are made. This new notion of graph gives rise to a model of affine lambda-calculus that admits an interpretation of imperative constructs including variable assignment, dereferencing and allocation. Extending this untyped model, we construct a category that provides a model of typed higher-order imperative computation with an affine type system. An appropriate language of this kind is Reynolds's Syntactic Control of Interference. Our model turns out to be fully abstract for this language. At a concrete level, it is the same as Reddy's object spaces model, which was the first "state-free" model of a higher-order imperative programming language and an important precursor of games models. The graph model can therefore be seen as a universal domain for Reddy's model

Revealing the Nature of Algol Disks through Optical and UV Spectroscopy, Synthetic Spectra, and Tomography of TT Hydrae

We have developed a systematic procedure to study the disks in Algol-type binaries using spectroscopic analysis, synthetic spectra, and tomography. We analyzed 119 H-alpha spectra of TT Hya, an Algol-type eclipsing interacting binary, collected from 1985-2001. The new radial velocities enabled us to derive reliable orbital elements, including a small non-zero eccentricity, and to improve the accuracy of the absolute dimensions of the system. High resolution IUE spectra were also analyzed to study the formation of the ultraviolet lines and continuum. Synthetic spectra of the iron curtain using our new shellspec program enabled us to derive a characteristic disk temperature of 7000K. We have demonstrated that the UV emission lines seen during total primary eclipse cannot originate from the accretion disk, but most likely arise from a hotter disk-stream interaction region. The synthetic spectra of the stars, disk, and stream allowed us to derive a lower limit to the mass transfer rate of 2e-10 solar masses per year. Doppler tomography of the observed H-alpha profiles revealed a distinct accretion disk. The difference spectra produced by subtracting the synthetic spectra of the stars resulted in an image of the disk, which virtually disappeared once the composite synthetic spectra of the stars and disk were used to calculate the difference spectra. An intensity enhancement of the resulting tomogram revealed images of the gas stream and an emission arc. We successfully modeled the gas stream using shellspec and associated the emission arc with an asymmetry in the accretion disk.Comment: 46 pages, 15 figures, 6 tables, accepted by Ap