By Morris Rubinoff, Marshall C. Yovits
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Extra resources for Advances in Computers, Vol. 15
Suppose m transitions have been found with property ( l ) ,(2)) (3), or (4) ; then there are 2” ways of possibly assigning to these transitions their associated indexing forms, I t C or I t I C. Each of these possible feasible assignments is tried until one is found such that there is a solution to the problem of determining the values of the constants. ) Because the possible indexing instructions are so simple, the set of unknown constants can be determined by linear algebra. Returning to the above example, the proposed program now has three instructionsand three transitions (see Fig.
There are various ways to add the twenty entries properly without having to execute by hand nineteen identical add instructions in sequence. One technique involves the use of dynamic program synthesis and the continue feature. The autoprogrammer dynamically maintains a partial program at all times during execution of the example calculation, which is able to execute the portion of the trace that has been seen up to that time. 3 is constructed as the calculation proceeds, so that after the third item in X is added the partial program of Fig.
Are tested sequentially until one is found to be true. If pi(X) is the first predicate found to be true then its associated fi(X) is returned as the function result. If PI, ps, and p3 all yield false then f4(X) is returned. For this example, the required predicates are pl(X) = atom(X) p ( X ) = atom(cdr(X)) p3(X) = atom(cddr(X)) The general form of the desired program is a recursive function discovered through a process that Summers calls diferencing. Each function f i is written in terms of earlier functions fj, where j < i: fl(X) = nil fi(X) = car(X) f3(X) = fz(cdr(X)) f4(X) = fs(cdr(X)) Here we see a pattern fi(X) = fi-l(cdr(X)) for i > 2.