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so last time around we reviewed the idea of induction and we looked at induction on the natural numbers and we looked at induction on the type of lists in hascal we gave a number of examples of inductive proofs and we also emphasized the process of how you actually produce these kind of proofs so gave you a range of hints and tips for how to construct inductive proofs so what weamp;#39;re going to be looking at today is using induction to actually construct or to write programs not just about proving properties about programs and this is really like a secret trick which is actually not that well known so the background to todayamp;#39;s class is that many functions are naturally defined using the Plus+ or aend operator on lists but as weamp;#39;ll see the resulting functions can often be inefficient when they append or Plus+ operator is used recursively so what weamp;#39;re going to see today is how induction can be used to eliminate the append operator or to make it vanish as show
