Mark B. Wells

MADCAP: a scientific compiler for a displayed formula textbook language

A discussion is presented of some of the unique features of a compiler for scientific problems which was designed at Los Alamos for the MANIAC II computer. The compiler, MADCAP, is an attempt to eliminate the disparity between the textbook presentation of a problem and that presentation which serves as input for a compiler. (T.R.H.)

The unified data structure capability in Madcap VI

The data structures which form an integral part of the Madcap VI programming language are described. The initialization (declarationand constructor) expressions and selector expressions of these structures are defined and their implementation using “codewords” is discussed. Structures, since they can contain references to other structures (including themselves), have the form of directed trees (graphs). Variables of primitive data type (real, complex, etc.) are naturally considered as degenerate graphs, merely single nodes. The possibility for both multiword and fractional-word representation of structures is evident, but the language itself is implementation-independent. Thus a “field” is simply a substructure. The Madcap VI data structures are compared to data structure concepts in PL/I.

Aspects of Language Design for Combinatorial Computing

Experience in the area of combinatorial computing acquired by the Maniac group at Los Alamos has motivated language development in this direction. Features incorporated into the MADCAP language to aid in programming combinatorial calculations include notation for set synthesis and analysis, notation for variably nested iterations (backtracking) and notation for complex conditional statements. The paper also examines the relationship of such combinatorial language design to machine design. Prominent in this discussion are the bit manipulation (shifting, counting and searching) facilities of Maniac II.

Recent improvements in MADCAP

MADCAP is a programming language admitting subscripts, superscripts and certain forms of displayed formulas. The basic implementation of this language was described in a previous paper [MADCAP: A scientific compiler for a displayed formula textbook language, Comm. ACM 4 (Jan. 61), 31-36]. This paper discusses recent improvements in the language in three areas: complex display, logical control, and subprogramming. In the area of complex display, the most prominent improvements are a notation for integration and for the binomial coefficients. In the area of logical control the chief new feature is a notation for variably nested looping. The discussion of subprogramming is focused on MADCAPs notation for and use of “procedures.”

A review of two-dimensional programming languages

Everyday mathematical language, as it appears on the printed page for instance, non-trivially makes use of two dimensions. This paper discusses various technical aspects of programming languages which utilize such natural symbolism. First, some terminology which is and can be useful in describing these systems is presented. Then, the man-machine interface in relation to two-dimensional languages in general is examined. This is followed by an historical survey of particular languages, including a brief description of their two-dimensional characteristics. Finally, a review of the analysis problem for such languages is given.

Lower bound for the connective constant of a self-avoiding walk on a square lattice

Abstract It is shown that 2.58105 lim k→∞ c k 1 k , where ck is the number of self-avoiding walks on the square lattice of k steps which start at the origin; this is the best lower bound so far calculated. The bound is obtained by use of a theorem of Kesten and computer enumeration of walks.

Reflections on the Evolution of Algorithmic Language

Publisher Summary This chapter focuses on the interpretation of the existing history regarding algorithmic languages. Algorithmic language before computers was essentially textual with a liberal sprinkling of examples and three dots. There are four areas of language in which structure plays a prominent role: (1) program organization, (2) program control, (3) data, and (4) expression notation. Progress toward common algorithmic language has been made in all four areas, with particular signs of convergence relative to program control and, to a lesser extent, to data. In regard to abstraction, there are three areas mentioned in the chapter: (1) subroutines and procedures, (2) set-theoretic symbolism, and (3) algorithm-data-representation independence. It is observe that in spite of the seeming proliferation of programming languages at present, the various features are being sorted out, and in fact general-purpose languages are converging toward everyday algorithmic language. The chapter discusses that progress has been made relative to the design and use of procedures, while set-theoretic notation and data abstraction are just beginning to come into prominence.

Preprocessing of typed two-dimensional mathematical expressions

An algorithm is discussed which translates two-dimensional mathematical expressions such as subscripting and displayed division, that have been prepared using a keyboard input device, into a string form suitable for input to a classical compiler. The algorithm allows reasonably general forms, yet is sufficiently simple to be practically applicable today. It may be used as a preprocessor to an existing compiler in order to improve the readability of an existing language.

Use of symbolic and numeric methods in an algorithm for the approximation of multivariate functions

In this paper, we discuss aspects of a particular algorithm, namely that of finding an approximation to a real function of n variables, that uses both symbolic and numeric manipulations. Development of this algorithm was motivated in part by an actual application; it is being used in a study of the optimal design of a geothermal energy extraction plant [4]. Our experience here with the extensible language Madcap [6], in which the approximation algorithm was developed, certainly corroborates the importance of very high level, general-purpose languages for the design of involved algorithms.

GENERATION OF ELEMENTARY CONFIGURATIONS

This chapter discusses the practical schemes for generating the basic elementary combinatorial configurations. Most of these algorithms are given explicitly as generation procedures, that is, the procedures designed to produce one configuration after another until all admissible configurations have been formed. However, it is frequently not the generated configurations themselves, but the structure of the generating program that is of primary importance, as programs to generate points of an object-space form the basis of many combinatorial algorithms. Thus, various procedures for accomplishing the same generation are useful, one scheme rather than another being more adaptable to a particular application. Nevertheless, the controlling factor in the practicality of most generation programs is still the number of configurations being generated.