Induction Variable (orphan)
Induction variable or recursive strength reduction replaces a function of some systematically changing variable with a simpler calculation using previous values of the function. In a procedural programming language this would apply to an expression involving a loop variable and in a declarative language it would apply to the argument of a recursive function. For example,
f x = ... (2 ** x) ... (f (x + 1)) ...becomes
f x = f' x 1 where f' x z = ... z ... (f' (x + 1) (2 * z)) ...Here the expensive operation (2 ** x) has been replaced by the cheaper (2 * z) in the recursive function f'. This maintains the invariant that z = 2 ** x for any call to f'.
Read more about this topic: Strength Reduction
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