Wetherell recently described an algebra of error values that could be added to the ordinary arithmetic of a programming language. Along with ordinary arithmetic values, error values were included in the set of computational quantities. The error values could participate in all arithmetic operations and return meaningful results. Unfortunately, the definitions of the error values were not precise enough. Using Brown's model of computer arithmetic, we supply precise definitions for the error values, define the fundamental arithmetic operations on the new values, comment on their properties, and discuss briefly how they might be used and implemented. We also compare our model to the error handling features of the proposed IEEE floating point standard.

The data-flow architecture is intended to support large scientific computations, and VAL is an algebraic, procedural language for use on a data-flow computer.VAL is apt for numerical computations but requires an error monitoring feature that can be used to diagnose and correct errors arising during program execution.Traditional monitoring methods (software traps and condition codes} are inappropriate for VAL; instead, VAL includes a set of error data values and an algebra for their manipulation.The error data values and their algebra are described and assessed; the conclusion is that error values provide a clean way for a high-level language to handle numeric (and some other) errors.

LR is an LR(1) parser generation system. It is written entirely in portable ANS1 standard Fortran 66 and has been successfully operated on a number of computers. LR uses a powerful algorithm of Pager's to generate a space efficient parser for any LR(1) grammar. Generated parsers have been used in a variety of compilers, utility programs, and applications packages.

Abstract The Department of Energy (DoE) has a long history of large‐scale scientific calculation on the most advanced ‘number‐crunching’ computers. Recently, an effort to improve communications and software sharing among DoE laboratories has been underway. One result of this sharing is a project to design and implement a common language. That language turns out to be FORTRAN 77 significantly extended with new data structures, control structures and array processing. The data used to design the array processing feature is surprising and likely to be of use to others working in scientific language design; it is reported here so that others may profit from DoE's experience.

Trees are extremely common data structures, both as internal objects and as models for program output. But it is unusual to see a program actually draw trees for visual inspection. Although part of the difficulty lies in programming graphics devices, most of the problem arises because naive algorithms to draw trees use too much drawing space and sophisticated algorithms are not obvious. We survey two naive tree drawers, formalize aesthetics for tidy trees, and descnbe two algorithms which draw tidy trees. One of the algorithms may be shown to require the minimum possible paper width. Along with the algorithms proper, we discuss the reasoning behind the algorithm development.

Chess is a warlike game descended from a long line of games with military overtones.However, many chess players feel that the element of complete information in chess is incompatible with a realistic model of war.Kriegspiel introduces an explicit element of incomplete information into chess without the use of a chance device.This is accomplished by screening each player's men from the opponent's view.Because the legality of a move in chess depends on the positions of all 32 men, neither player in a game of Kriegspiel can determine if a given move is legal.Thus a third participant is necessary.This third participant, the direct or §, enforces the rules of Kriegspiel, keeps a record of the game, and controls communications between the players.(In addition, the director controls the kibitzers, who are an important part of the Kriegspiel atmosphere.)These tasks are normally accomplished with a chess board, pencil and paper, and a commanding voice.This paper describes a pair of computer programs which act as director for Kriegspiel.The programs are implemented on a time-shared graphics-oriented computer.In this environment, a large portion of the director's task is communication, either between the players or between the director and one player.This aspect of the director is not intimately connected with Kriegspiel-the problems and solutions we discuss apply to many gaming situations.We have separated communications from the strictly rules-enforcing portion of the programs; communications are handled by the Kriegspiel monitor, which calls a referee subprogram when there are rules decisions to be made.The referee never communicates directly with the players.Kriegspiel has been the subject of at least one previous paper, Burger (1967), which describes a considerably more primitive director.The rules for Kriegspiel are not standardised, but there is a large measure of agreement on them.Both Harkness (1967) and Gollon (1968) give rules.A surge of Kriegspiel activity occurred within the scientific community after a memorandum by Williams (1950).We were encouraged to publish by an article of Bell (1970) which describes a referee for chess.Our referee in the Kriegspiel director is more powerful than that of Bell and may be used to control either chess or Kriegspiel.The details of the referee are described in a separate paper (Buckholtz and Wetherell, 1970).