By Edsger W. Dijkstra, W. H. J. Feijen, Joke Sterringa
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Extra info for A Method of Programming
And describe how to produce a program in that language that outputs its own code. ) and write a program that outputs its own code. The recursion theorem we have been discussing enabled us to write single programs that were self-referential. Our discussion now turns to more powerful forms of recursion. These more powerful forms will enable us to construct sets of self-referential programs. Cooperating self referential programming turns out to be a very powerful technique. For example, the next theorem essentially says that one can, uniformly and effectively, construct infinite sequences of self referential programs, each one of which knows its position in the sequence.
The universal RAM program is a blueprint for a stored program computer. 42: (Normal Form) There exist primitive recursive functions f, there is an i such that: f(x) = g(x, i, ILY[h(x, i, y)]). 43: Provide a proof for the above theorem. 44: Find a RAM program that takes its input (i, j) and outputs the code for a program P (P) that behaves as follows: P takes its input x and simulates program Pi on input x. If that computation converges, then P outputs the result of the computation Pj(Pi(x)). Is the function computed by your RAM program primitive recursive?
A picture representing this situation is below. 15: (Parametric recursion theorem) Suppose
A Method of Programming by Edsger W. Dijkstra, W. H. J. Feijen, Joke Sterringa