Derivation of Kadane's algorithm by algebraic manipulations in the Bird-Meertens calculus. Starred lines include new function definitions (given at the bottom). See <cite style="font-style:normal">Richard S. Bird (1989). "<a rel="nofollow" class="external text" href="http://comjnl.oxfordjournals.org/content/32/2/122.full.pdf">Algebraic Identities for Program Calculation</a>". <i>Computer Journal</i> <b>32</b>: 122–126.</cite> p.126
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