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Primitive Recursive Functions (Chapter 3)

Primitive Recursive Functions (Chapter 3). Preliminaries: partial and total functions. The domain of a partial function on set A contains the subset of A. The domain of a total function on set A contains the entire set A.

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Some Primitive Recursive Functions

Some Primitive Recursive Functions. Example 3: h(x) = x! Here are the recursion equations: h(0) = 1 h(t + 1) = h(t)  s(t) This can be rewritten as: h(0) = s(n(t)) h(t + 1) = g(t, h(t)) where g(x 1 , x 2 ) = s(x 1 )  x 2 , which can be written as:

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Homework Questions

Homework Questions. Question 1: Write a program P that computes  P (1) (r) = r-2 using no macros. Notice that we only consider natural numbers! This means that, for example, the expression 1-2 is undefined. Any program computing such an expression must never halt . Sample solution:

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