Struggle the First Denotational Game

Games are often complex enough that new winning strategies cannot be devised without a clear and precise knowledge of the rules of the game. This situation makes games candidate to clear speciications and denotational semantics an interesting framework to specify games. This paper introduces a new game where two programs ght against each other by alteration of their code: program errors lead to death. Programs are written in a Scheme-like language with lambda, setq, prog2, if and quote special forms. Another unusual special form fork is ooered which allows to run independent threads. Programs are interpreted in a very special way with continual references to the store which acts as the ghting arena. Data are restricted to functions (closures), symbols and dotted pairs. Primitives are only car, cdr, consp, eq, rplaca and rplacd. The two lattest primitives are the weapons that can alter the code structure of the opponent, conversely they can also be used to repair its own structure. Although very simple, these capabilities must be precisely deened since they are the rules of the game. To know, for instance, the number of steps taken by the execution of some construct as well as the semantics of threads is answered by the denotational semantics of the game. The paper is probably the rst use of denotational semantics in the realm of games and as such may be viewed as an exercise in denotation. It also ooers some insights on the meaning of the data = program equation inside interpreters. Eventually it follows the Lisp tradition and ooer a worldwide arena for cleverness. The Scientiic American Journal once introduced a game Dewdney84] named Core War which simulates the ght of two programs within a commonmemory. The way to destroy its opponent was to alter the memory where lie the code and data of the two ghters in order to place erroneous instructions in the opponent code. Instructions were written in a little assembly language (Red Code) with only eight instructions for reading and writing memory cells, performing some simple arithmetics, inconditional or conditional jumps as well as forking into two threads. All addresses are PC-relative and designate words in the memory considered cyclic. Instructions and data share an uniform size: the word. This game has some aacionados and holds an annual championship. News from Core War may regularly be found in Scientiic American. Although simply summarized this game suuers from …