By Morris Rubinoff, Marshall C. Yovits
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Extra resources for Advances in Computers, Vol. 15
2. X1. X1. , not covered up by other objects). Having chosen a particular object, say :OBJ, it would then execute the statement (THGOAL (#PICKUP :OBJ) (THUSE TC-PICKUP) ) . 23. ’ 44 ALAN W. BIERMANN The TC-PICKUP routine would check to see whether any objects cover :OBJ, remove them if necessary, and finally pick up :OBJ. In the column sum example, the world model might be described by the following assertions: (#NUMBER 3) (#NUMBER 4) (#NUMBER 7) (#NUMBER 9) (#IN :A 4) (#IN :A 9) (#IN :A 7) (#IN :N 3) (#TYPE :A #ARRAY) That is, 3,4, 7, and 9 are numbers, 4,9, and 7 are in array A, 3 is in N, and A is an array.
Thus it is necessary to prove that VA V N 3SUM R(A,N,SUM), where R(U,Z,Z) = i x ~u (=i ) ~ true if z = false otherwise Since u will not change during the computation, it can be removed as an z ) instead of R(u,z,z) . Certain knowlargument, and we will write Ru(z, edge must be available to the theorem prover before the proof can be done. Among other things, the theorem prover must have the facts R,(O, 0) and Vz Vy (Ru(z, y) 3 R,(z 1, u ( z 1) y)). Then the proof of the basis argument 3y2R,(O, y2) yields a = 0 and the proof of the induction step VYI (3112 RY(yl,212) 3 3ysRu(y1 1, y d 1 yields g(yl, y2> = 4 9 1 1) gas So the synthesized program is as shown in Fig.
If the conclusion of such a rule resembles the problem to be solved, the rule is applied backwards and all of its premises become subgoals to be solved. Thus in the example above, the problem I(A1;AZ)G is broken into two subgoals using rule R2. The problem decomposition continues until trivial subproblems are obtained and then the solution is constructed. Besides having general programming knowledge, the system needs domain specific information, which Buchanan and Luckham call frame information.