Re: Partial recursive functions and minimization

Thank you both, I think I finally understand it. Anyway, for me it's
still unclear how can there be something like Normal Form Theorem for
partial recursive function and how can the primitive recursive
predicate T which is used in it look like.

Our professor told us we can look at the predicate T(e,x,z) in a way
that for number of program 'e', input 'x' and pair z = <y,s>, the
predicate is true if the program 'e' for input 'x' yields the value
'y' after exactly 's' steps. Ok, maybe as I'm writing this, I'm slowly
coming towards understanding it - this predicate really can be made
primitive recursive, because the decision, whether "The program 'e'
yields value 'y' on input 'x' after 's' steps." can be always answered
so the predicate is really primitive recursive. Am I right with these
speculations?

.

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