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primitive recursion


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In the study of effective computability, a particular way of defining a new function in terms of other simpler ones. The functions involved are functions over the nonnegative integers. Primitive recursion is then the process of defining a function f of n+1 variables in the following manner: f(x1,x2,…xn,0) = g(x1,x2,…xn), f(x1,x2,…xn,y+1) =h(x1,x2,…xn,y,f(x1,…xn,y) where g and h are functions of n and n+2 variables respectively. See also primitive recursive function.

f(x1,x2,…xn,0) = g(x1,x2,…xn),

f(x1,x2,…xn,y+1) =h(x1,x2,…xn,y,f(x1,…xn,y)

Subjects: Computing.


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