Editing Strength reduction (section)

== 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 programming language|declarative language]] it would apply to the argument of a [[recursion (computer science)|recursive function]].<ref>{{foldoc|Strength+reduction}}</ref> For example,
<syntaxhighlight lang=haskell>
 f x = ... (3 ** x) ... (f (x + 1)) ...
</syntaxhighlight>
becomes
<syntaxhighlight lang=haskell>
 f x = f' x 1
 where
   f' x z = ... z ... (f' (x + 1) (3 * z)) ...
</syntaxhighlight>
Here modified recursive function {{prime|f}} takes a second parameter z = 3 ** x, allowing the expensive computation (3 ** x) to be replaced by the cheaper (3 * z).