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zn$O{X9UM3lqzuiP87fg7{=vju2%1?_vOgeHt%NIeEWCFa0AI)oEiwikcC@pVNEc4I z41+hR$lTBkK1~LCZGi{X14ng3R(Y93A)XuwA7@YxA?qtElpVU{`>ajq)+C1=FnYnf zZ~fVdO0I4`l3!l+@iXuT0B+_nN9Fig>7-N5`eE$vvvc>V^MwX`KxIrr1tt2*rjU9Tvea7jFY@*-0L3R_-g*s@^$;VXjlE(#i?_6sxwe0 zPQ$XL>hmiDGl5p*opJY1Itb^@mwk7L07-GXOgr7HTysJhsbw99_y}8%oW>&{YvvzE zp|hB&3AJg3u&ISkI*ptlAZ9GPBZ|OQq68`lUWyp={}u|rqZ(SAP~YKawvJXv_sl0T zepk}97^mJo9eo{U>zk1-V|n a} from prelude determines first element + \item Cross out all multiples: \verb|dropMults x ys = filter (\y -> y `mod` x /= 0) ys| + \item Repeat with recursions: \texttt{sieve xs = head xs : sieve (dropMults (head xs) (tail xs))} +\end{enumerate} + +Another example is Newton's Algorithm to find roots. + + +\paragraph{Correctness} +Lazy evaluation makes reasoning about complexity and correctness harder, as types like \texttt{[Int]} include +\begin{enumerate} + \item finite, everywhere defined lists (e.g. \texttt{[1, 3, 5]}) + \item finite lists with undefined elements like \texttt{[1, 2, undef]} + \item infinite lists with defined or undefined elements such as \texttt{[1..]} +\end{enumerate} + +However, induction is only sound for the first kind. More on this later on