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day11 - Recursive Functions Primitive and-Recursive Click...

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Click to edit Master subtitle style 10/4/11 Recursive Functions Primitive and ° -Recursive
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Click to edit Master subtitle style 10/4/11 Primitive Recursive An Incomplete Model
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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 33 Basis of PRFs The primitive recursive functions are defined by starting with some base set of functions and then expanding this set via rules that create new primitive recursive functions from old ones. The base functions are: Ca(x1,…,xn) = a : constant functions (x1,…,xn) = xi : identity functions : aka projection S(x) = x+1 : an increment function    i n I
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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 44 Building New Functions Composition: If G, H1, … , Hk are already known to be primitive recursive, then so is F, where F(x1,…,xn) = G(H1(x1,…,xn), … , Hk(x1, …,xn)) Iteration (aka primitive recursion): If G, H are already known to be primitive recursive, then so is F, where F(0, x1,…,xn) = G(x1,…,xn) F(y+1, x1,…,xn) = H(y, x1,…,xn, F(y, x1, …,xn))
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Dec 2, 2007/COT5310 © UCF (Charles E.
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