A reference grammar of spoken Kannada by Harold F. Schiffman

By Harold F. Schiffman

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3 we want to use the quantifier (Vt)<, or (3t) < r That the theorem is still valid is clear from the relations &)·ί = x). 13. Prime(x). The predicate "x is a prime" is primitive recursive since Prime(x)ox > 1 &(Vr)^x{i = 1 v ί = x v~(i|x)}. ) Exercises 1.

The same as Exercise 2 for the empty program. 5. , x + y, x · y) giving rise to corresponding macros. Now we consider this process in general. Let / ( x l 5 . . , x„) be some partially computable function computed by the program 0. We shall assume that the variables that occur in 9 are all 5 29 More about Macros included in the list Y9 Xl9 . . 9Ah instruction of 9 of the form Zk and that the labels that occur We also assume that for each IF V Φ 0 GOTO At there is in 9 an instruction labeled A{.

Continuing: [M] [/I] [JV] S «- IS/P] GOTO JV S<^SP K <- K + 1 GOTO C 58 Chapter 4 A Universal Program 1 is subtracted or added to the value of the variable mentioned in the current instruction by dividing or multiplying S by P, respectively. The instruction counter is increased by 1 and the computation returns to process the next instruction. To conclude the program: in y - (s)i On termination, the value of Y for the program being simulated is stored as the exponent on px(= 2) in S. We have now completed our description of %„ and we put the pieces together (Fig.

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