ALGOL Program Research Articles

Modelling Local Variables: Possible Worlds and Object Spaces

Local variables in imperative languages have been given denotational semantics in at least two fundamentally different ways. One is by use of functor categories, focusing on the idea of possible worlds. The other might be termed event-based, exemplified by Reddy's object spaces and models based on game semantics. O'Hearn and Reddy have related the two approaches by giving functor category models whose worlds are object spaces, then showing that their model is fully abstract for Idealised Algol programs up to order two. But the category of object spaces is not small, and so in order to construct a functor category that is locally small, and hence Cartesian closed, they need to work with a restricted collection of object spaces. This weakens the connection between the object spaces model and the functor-category model: the Yoneda embedding no longer provides a full embedding of the original category of object spaces into the functor-category. Moreoever the choice of the restricted collection of object spaces is ad hoc. In this paper, we refine the approach by proving that the finite objects form a small dense subcategory of a simplified object-spaces model. The functor category over these finite objects is therefore locally small and Cartesian closed, and contains the object-spaces category as a full subcategory. All this work is necessarily enriched in Cpo. We further refine their full abstraction result by showing that full abstraction fails at order three.

Solution of the eigenvalue problem for the regular bundleD(λ)=λA 0−A 1 using deflated subspaces

We consider the solution of the generalized eigenvalue problem $$\left( {A_0 \Lambda - A_1 } \right)x = 0,$$ in the case where one or both of the matrices A0, A1 are degenerate but the intersection of their null spaces is empty. Using orthogonal matrices ℘ and which are independent ofλ the original problem is transformed to a simpler one in which the pencil is of smaller dimension. The construction of ℘ and Q uses the normalization process. We include an Algol program and sample runs.

Cache hit ratios with geometric task switch intervals

A simple Markov chain model is used to estimate the effect of the cache flushes. The model assumes LRU stack model of program behaviour and geometrically distributed lengths of task switch intervals. Given the LRU stack depth distribution, one may easily compute estimates of miss ratios for caches of all sizes with any desired average task switch interval. The model is validated with three reference strings recorded from simulations of large B7800 Extended Algol programs. The estimates obtained with the Markov model are within 12% error margin from the results obtained by cache simulation.

Cache hit ratios with geometric task switch intervals

A simple Markov chain model is used to estimate the effect of the cache flushes. The model assumes LRU stack model of program behaviour and geometrically distributed lengths of task switch intervals. Given the LRU stack depth distribution, one may easily compute estimates of miss ratios for caches of all sizes with any desired average task switch interval. The model is validated with three reference strings recorded from simulations of large B7800 Extended Algol programs. The estimates obtained with the Markov model are within 12% error margin from the results obtained by cache simulation.

Approximation formula and algol program of the lorentz-invariant momentum-space integral for particles of equal masses

Approximation formula and algol program of the lorentz-invariant momentum-space integral for particles of equal masses

Computation of total, differential and double-differential cross sections for compound nuclear reactions of the type (a, b), (a, b γ) and (a, b γ-γ. (III) Fortran translations of the algol programs ‘mandy’ and ‘barbara’

Computation of total, differential and double-differential cross sections for compound nuclear reactions of the type (a, b), (a, b γ) and (a, b γ-γ. (III) Fortran translations of the algol programs ‘mandy’ and ‘barbara’

Solution of the partial eigenvalue problem for a regular matrix pencilD(?) =A ? ?B

One presents the ALGOL procedures which implement the algorithm for the determination of the group of smallest (greatest) eigenvalues and their corresponding eigenvectors for a matrix pencil where A and B are real square matrices of simple structure. From the initial pencil one constructs a matrix C, whose eigenvalues are taken as the initial approximations to the eigenvalues from the group of the smallest (greatest) eigenvalues of the pencil. The refinement of the eigen-values is performed on the basis of the theory of perturbations. Then one determines the eigen-vectors and one computes the infinite norm of the residual. One gives ALGOL programs and test examples.

Solution of the eigenvalue problem for a regular pencil ?A0?A1 with singular matrices

One considers the generalized eigenvalue problem (A0λ−A1)x=0, (1) when one or both matrices A0,A1 are singular and ker A0 ∩ ker A1=φ is the empty set. With the aid of the normalized process, the solving of problem (1) reduces to the solving of the eigenvalue problem of a constant matrix of order r=min (r0,r1), where r0,r1 are the ranks of the matrices A0,A1, which are determined at the normalized decomposition of the matrices. One gives an Algol program which performs the presented algorithm and testing examples.

Solving the eigenvalue problem for matrices

One presents some algorithms related among themselves for solving the partial and the complete eigenvalue problem for an arbitrary matrix. Algorithm 1 allows us to construct the invariant subspaces and to obtain with their aid a matrix whose eigenvalues coincide with the eigenvalues of the initial matrix and belong to a given semiplane. Algorithm 2 solves the same problem for a given strip. The algorithms 3 and 4 reduces the complete eigenvalue problem of an arbitrary matrix to some problem for a quasitriangular matrix whose diagonal blocks have eigenvalues with identical real parts. Algorithm 4 finds also the unitary matrix which realizes this transformation. One gives Algol programs which realize the algorithms 1–3 for real matrices and testing examples.

An intermediate algorithm for pole placement by output feedback in linear multivariable control systems

It is known that, in the case of self-conjugate distinct eigenvalue spectra, the closed-loop eigen-structure assignable by output feedback in constrained by the requirement that the loft and right eigenvectors be in certain subspaces. In this paper an algorithm is presented which can be used to select these left and right eigenvectors in the case in which the number of inputs plus the number of outputs exceeds the number of states. The algorithm is ideally suited to digital computer implementation and an ALGOL program for this is available.

Solving a nonlinear spectral problem for a matrix

This paper examines the solving of the eigenvalue problem for a matrix M (λ) with a nonlinear occurrence of the spectral parameter. Two methods are suggested for replacing the equation dat M(λ)=0 by a scalar equationf(λ)=0. Here the functionf(λ) is not written formally, but a rule for computingf(λ) at a fixed point of the domain in which the desired roots lie is indicated. Muller's method is used to solve the equationf(λ)=0. The eigenvalue found is refined by Newton's method based on the normalized expansion of matrix M(λ), and the linearly independent vectors corresponding to it are computed. An ALGOL program and test examples are presented.

Eigenvalue problem for an irregular ?-matrix

The solution of the eigenvalue problem is examined for the polyńomial matrixD(λ)=Aoλs+A1λs−1+...+As when the matricesA 0 andA 2 (or one of them) are singular. A normalized process is used for solving the problem, permitting the determination of linearly independent eigenvectors corresponding to the zero eigenvalue of matrixD(λ) and to the zero eigenvalue of matrixA 0. The computation of the other eigenvalues ofD(λ) is reduced to the same problem for a constant matrix of lower dimension. An ALGOL program and test examples are presented.

Two-sided approximations in the LR-algorithm

An ALGOL program is derived for a modified LR-algorithm, permitting the determination of two-sided approximations to the eigenvalues of a tridiagonal symmetric matrix. Test examples are considered.

Theoretical properties and numerical tests of an efficient nonlinear decomposition algorithm

Kronsjo's nonlinear generalization (Ref. 1) of Benders' algorithm (Ref. 2) is reviewed. At each iteration, this algorithm produces upper and lower bounds to the true optimum, and the sequence of lower bounds is increasing. The algorithm is modified, so that the sequence of upper bounds is e-decreasing as well. The two versions are tested numerically using an ALGOL program originally written by Wong (Ref. 3), incorporating the SUMT method (Fiacco and McCormick, Refs. 4 and 5). The two versions are compared against each other, and the problem of the optimal degree of decomposition is considered. Finally, an attempt is made to express the computer time required to solve the test problems as a function of master problem size, number of subproblems, and average subproblem size.

P—a timesharing operating system for laboratory automation

AbstractAn operating system supporting laboratory automation and interactive use of a computer has been designed and implemented for the multiprogrammed RC4000 computer. The emphasis in the design has been to give the user interactive access to as many system resources as possible, and to facilitate writing of process control programs in a high‐level language, i.e. ALGOL. The operating system is used to run control and data collection programs for a variety of experiments in physical chemistry. Laboratory automation programs can be started and removed dynamically, and may even be restarted automatically after a system failure. The operating system is a 1500 line ALGOL program. The first version was designed, implemented and debugged in about 4 person‐months. The operating system has been running day and night for approximately 5 years without errors despite heavy use.

Normative composition and classification of lunar igneous rocks and glasses, I. Lunar igneous rocks

678 major element analyses and all available trace element determinations of lunar rocks with igneous textures were collected from the literature. Rittmann norms were calculated by an ALGOL program. The norm values, grouped according to increasing clinopyroxene contents, were plotted into quartz-plagioclase-orthopyroxene and olivine-plagioclase-orthopyroxene triangles, respectively. The plots indicate that all lunar rocks form a compositional continuum that starts from rocks very high in plagioclase and continues, with increasing clinopyroxene, to plagioclase-poorer and orthopyroxene-richer rocks containing partly quartz, partly olivine. According to apparent clusters in the plots, and taking into account lunar rock types defined by previous authors, the continuum of normative compositions was subdivided into five major rock groups (I to V). The averages of these groups can be characterized by clinopyroxene contents and plagioclase/orthopyroxene ratios (I: 3% cpx, plag/opx = 30; II: 4% cpx, plag/opx = 7; III: 8% cpx, plag/opx = 2; IV: 26% cpx, plag/opx = 0.8; V: 34% cpx, plag/opx = 1.8). According to the contents in K-feldspar, from groups III and V K-rich subgroups were separated. Average contents of major elements and trace elements were calculated for main groups and subgroups. For the normative groups of lunar igneous rocks, names are proposed which conform to the nomenclature of terrestrial rocks.

An algol program for dissimilarity analysis: a divisive-omnithetic clustering technique

Abstract Clustering techniques are used properly to generate hypotheses about patterns in data. Of the hierarchical techniques, those which are divisive and omnithetic possess many theoretically optimal properties. One such method, dissimilarity analysis, is implemented here in ALGOL 60, and determined to be competitive computationally with most other methods.

A microprogrammed virtual memory for Eclipse

The Eclipse S-200 is a Data General minicomputer available since 1975. It is a microprogrammed and microprogrammable computer: the user can buy a writable control store (WCS) to define his own specialized instructions. The Eclipse is also available with a memory allocation and protection unit (“MAP”) : so, the memory can be extended up to 128 K 16-bit words. However, the user's space is limited to 32 K words because of the address field structure in the instructions. For large programs, the user can define overlay areas or he can use chaining or swapping but these methods are sometimes not appropriate (e.g., for large recursive Algol programs). In this paper, we describe a realization of a virtual memory system that allows the user to have a working space larger than 32 K while relieving him from the management problems. Unfortunately, DG'S WCS feature is unsatisfactory: the last chapter describes some displeasing features. It should also be mentioned that Data General does not provide microutilities (microassembler or microloader), a fact which complicates the microprogramming task.

Visual demonstration of program execution

This paper describes a system which provides a visual demonstration of the structure and flow of an ALGOL program. The program is displayed on a CRT and executed interpretively, highlighting each statement prior to execution and showing the result of the statement after execution. The primary use of the system is to demonstrate program operation in a classroom environment. It has also been used as an automatic benchchecking aid.

The decomposition of a distribution into Gaussian components (Algol program)

The paper attempts to give a practical solution to the problem of decomposition of a mixture of Gaussian components. The results of an earlier paper [1] have been used and the described algorithm has been revised and improved. A complete Algol program is given with all the necessary comments and descriptions and with results of testing examples.