A minimal:robot,Icnown as Freddy, has been constructed with the aim of connecting a usable device online to the Department's lc L 4130, under the Multi-Pop time-sharing system, and discovering the snags. (See figure 1). Various technical problems arise when such a device runs free. It is much easier to anchor it and allow it to push its world about. Our present world is a three-foot diameter sandwich of hardboard and polystyrene which is light and rigid.

It seems most unlikely that one could in general write purely applicative Schonfmkel descriptions', like (5), of functions already known to one in some other form. Fortunately there is a general procedure -- the Schonfmkel procedure -- which, when applied to any expression written in the more intuitive lambda-calculus notation, will produce a correct translation of it into the Schonfinkel notation.

Institut Blaise Pascal, C.N.R.S., 23, Rue du Maroc, 75, Paris XIX, France We study some aspects of a general game-playing program. Such a program receives as data the rules of a game: an algorithm enumerating the moves and an algorithm indicating how to win. The program associates to each move the conditions necessary for this move to occur. It must find how to avoid a dangerous move. We describe the part of the program playing the combinatorial game in order to win: how it can find the moves which lead to victory and what are the only opponent's moves with which he does not lose. This program has been tried with various games: chess, tictac-too, etc. 1. INTRODUCTION My aim was to realize a program playing several games. The rules of the particular game which it must play are given as data. If we want to have a performing program, it must be capable of studying these rules.

"A computer program has been written which can formulate hypotheses from a given set of scientific data. The data consist of the mass spectrum and the empirical formula of an organic chemical compound. The hypotheses which are produced describe molecular structures which are plausible explanations of the data. The hypotheses are generated systematically within the program's theory of chemical stability and within limiting constraints which are inferred from the data by heuristic rules. The program excludes hypotheses inconsistent with the data and lists its candidate explanatory hypotheses in order of decreasing plausibility. The computer program is heuristic in that it searches for plausible hypotheses in a small subset of the total hypothesis space according to heuristic rules learned from chemists."In Meltzer, B., Michie, D., and Swann, M. (Eds.), Machine Intelligence 4, pp. 209-254. Edinburgh University Press

COMPUTER SOLUTION OF CALCULUS WORD PROBLEMS* Eugene Charniak Massachusetts Ins:itute of Technology Cambridge, Massachusetts SUMMARY A program was written to solve calculus word problems. The program, CARPS (CAlculus Rate Problem Solver), is restricted to rate problems. The overall plan of the program is similar to Bobrow's STUDENT, the primary difference being the introduction of "structures" as the internal model in CARPS. Structures are stored internally as trees, each structure holding the information gathered about one object. It was found that the use of structures made CARPS more powerful than STUDENT in several respects. In calculus word problems it is not uncommon to have two or three sentences providing information for one equation. For example, in a problem about a filter, ALTITUDE was interpreted as ALTITUDE OF THE FILTER because CARPS knew that since the filter was a cone and cones have altitudes the filter had an altitude. The program has solved 14 calculus problems, most taken (sometimes with slight modifications) from standard calculus texts. CARPS is written in two languages. The bulk of the coding is in LISP.

See also: Education Resources Information CenterSupplement to Proceedings of the IFIP 68 International Congress, Edinburgh, August 1968. Published in A. J. H. Morrell (ed.), Information Processing 68, Vol. II, pp. 1008-1022, Amsterdam: North-Holland, 1969.

Note: PDF of full volume downloadable by clicking on title above (26 MB). Selected individual chapters available from the links below. CONTENTSINTRODUCTION MATHEMATICAL FOUNDATIONS1 The morphology of prex—an essay in meta-algorithmics. J. LAS KS 32 Program schemata. M. S. PATE RSON 193 Language definition and compiler validation. J. J. FLORENTIN 334 Placing trees in lexicographic order. H. I.S COINS 43 THEOREM PROVING5 A new look at mathematics and its mechanization. B. M ELTZER 636 Some notes on resolution strategies. B. MELTZER 717 The generalized resolution principle. J. A. ROBINSON 778 Some tree-paring strategies for theorem proving. D.LUCKHAM 959 Automatic theorem proving with equality substitutions andmathematical induction. J. L. D ARLINGTON 113 MACHINE LEARNING AND HEURISTIC PROGRAMMING10 On representations of problems of reasoning about actions.S.AMAREL 13111 Descriptions. E.W.ELCOCK 17312 Kalah on Atlas. A.G.BELL 18113 Experiments with a pleasure-seeking automaton: J. E. DORAN 19514 Collective behaviour and control problems. V.I.VARSHAVSKY 217 MAN—MACHINE INTERACTION15 A comparison of heuristic, interactive, and unaided methods ofsolving a shortest-route problem. D.MICHIE, J. G. FLEMING andJ. V.OLDFIELD 24516 Interactive programming at Carnegie Tech. A.H.BOND 25717 Maintenance of large computer systems—the engineer's assistant.M.H.J.BAYLIS 269 COGNITIVE PROCESSES: METHODS AND MODELS18 The syntactic analysis of English by machine. J.P.THORNE,P.BRATLEY and H.DEWAR 28119 The adaptive memorization of sequences. H.C.LONOUETHIGGINSand A.ORTONY 311 PATTERN RECOGNITION20 An application of Graph Theory in pattern recognition.C.J.HILDITCH 325 PROBLEM-ORIENTED LANGUAGES21 Some semantics for data structures. D. PARK 35122 Writing search algorithms in functional form. R.M.BURSTALL 37323 Assertions: programs written without specifying unnecessaryorder. J.M.FOSTER 38724 The design philosophy of Pop-2. R.J.POPPLESTONE 393 INDEX 403 Machine Intelligence Workshop

BOXES is the name of a computer program. This is what the chess player does when he lumps together large numbers of positions as being'similar' to each other, by neglecting the strategically irrelevant features in which they differ. The resultant small game can be said to be a'model' of the large game. To give a brutally extreme example, consider a specification of chess positions so incomplete as to map from the viewpoint of White the approximately 1050 positions of the large game on to the seven shown in Figure 1. Even this simple classification may have a role in the learning of chess.

Young animals play games in order to prepare themselves for the business of serious living, without getting hurt in the training period. Game-playing on computers serves a similar function. It can teach us something about the structure of thought processes and the theory of struggle and has the advantage over economic modelling that the rules and objectives are clear-cut. If the machine wins tournaments it must be a good player. The complexity and originality of a master chess player is perhaps greater than that of a professional economist. The chess player continually pits his wits against other players and the precision of the rules makes feasible a depth of thinking comparable to that in mathematics. No program has yet been written that plays chess of even good amateur standard. A really good chess program would be a breakthrough in work on machine intelligence, and would be a great encouragement to workers in other parts of this field and to those who sponsor such work. In criticism of the writing of a chess program, Macdonald (1950) quoted a remark to the effect that a machine for smoking tobacco could be built, but would serve no useful purpose. The irony is that smoking machines have since been built in order to help research on the medical effects of smoking. This does not prove that a chess program should be written, but suggests that the arguments against it might be shallow. Many branches of science, and of pure and applied mathematics, have started with a study of apparently frivolous things such as puzzles and games. It is pertinent to ask in what way a good chess program would take us beyond the draughts program of A. The answer is related to the much greater complication of chess, the much larger number of variations and possible positions. In fact, the number of possible chess positions is about the cube or fourth power of the number of possible draughts positions (see Appendix E). Samuel was able to make considerable use of the storage of thousands of positions that had occurred in the previous experience of the machine, and this led to a very useful increase in the depth of analysis of individual positions. The value of this device depends on the probability that, at any moment in the analysis, we run into a position that has already been analysed and stored. This applies more generally to the goals and subgoals that occur to the chess player. Thus there should be'specificallydirected' as well as'routinely-directed' analysis. Another important aspect of chess thinking, also required in most other problem-solving, is what de Groot (1946, 1965) calls'progressive deepening' of an analysis. Typically an analysis of a position by a human player does not simply follow a tree formation, but contains cycles in which a piece of analysis is retraced and improved.

"The purpose of this paper is to clarify some basic issues of choice of representation for problems of reasoning about actions. The general problem of re- Presentation is concerned with the relationship between different ways of formulating a problem to a problem solving system and the efficiency with which the system can be expected to find a solution to the problem. An understanding of the relationship between problem formulation and problem solving efficiency is a prerequisite for the design of procedures that can automatically choose the most `appropriate' representation of a problem ( they can find a `point of view' of the problem that maximally simplifies the process of finding a solution).Many problems of practical importance are problems of reasoning about actions. In these problems, a course of action has to be found that satisfies a number of specified conditions. A formal definition of this class of problems is given in the next section, in the context of a general conceptual framework for formulating these problems for computers. Everyday examples of reasoning about actions include planning an airplane trip, organizing a dinner party, etc. There are many examples of industrial and military problems in this category, such as scheduling assembly and transportation processes, designing a program for a computer, planning a military operation, etc."In D.Michie (Ed.), Machine intelligence 3. New York: American Elsevier,131-171