http://stackoverflow.com/questions/6364409/why-does-haskells-head-crash-on-an-empty-list-or-why-doesnt-it-return-an

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Is polymorphism lost by allowing empty list handling? If so, how so, and why? 
Are there particular cases which would make this obvious?
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The free theorem for head states that

f . head = head . $map f

Applying this theorem to [] implies that

f (head []) = head (map f []) = head []

This theorem must hold for every f, so in particular it must hold for const True and const False. 
This implies

True = const True (head []) = head [] = const False (head []) = False

Thus if head is properly polymorphic and head [] were a total value, then True would equal False.