Question

Although not included in appendix $B$, the standard prelude defines data Ordering $=$ LT $\mid$ EQ $\mid$ GT together with a function compare :: ord a $\Rightarrow$ a $\rightarrow$ a $->$ ordering that decides if one value in an ordered type is less than ( $\mathrm{LT})$, equal to $(\mathrm{EQ})$, or greater than (GT) another value. Using this function, redefine the function occurs :: ord $a \Rightarrow a \rightarrow$ Tree a $\rightarrow$ Bool for search trees. Why is this new definition more efficient than the original version?

   Although not included in appendix $B$, the standard prelude defines
data Ordering $=$ LT $\mid$ EQ $\mid$ GT
together with a function
compare :: ord a $\Rightarrow$ a $\rightarrow$ a $->$ ordering
that decides if one value in an ordered type is less than ( $\mathrm{LT})$, equal to $(\mathrm{EQ})$, or greater than (GT) another value. Using this function, redefine the function occurs :: ord $a \Rightarrow a \rightarrow$ Tree a $\rightarrow$ Bool for search trees. Why is this new definition more efficient than the original version?

Programming in Haskell

Graham Hutton 2nd Edition

Chapter 8, Problem 2

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Step 1

This comparison operation has a time complexity of O(1) for most types, but it can be O(n) for certain types that have a more complex equality check. In the new definition using the compare function, the comparison operation is replaced with the compare function, Show more…

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Although not included in appendix $B$, the standard prelude defines data Ordering $=$ LT $\mid$ EQ $\mid$ GT together with a function compare :: ord a $\Rightarrow$ a $\rightarrow$ a $->$ ordering that decides if one value in an ordered type is less than ( $\mathrm{LT})$, equal to $(\mathrm{EQ})$, or greater than (GT) another value. Using this function, redefine the function occurs :: ord $a \Rightarrow a \rightarrow$ Tree a $\rightarrow$ Bool for search trees. Why is this new definition more efficient than the original version?

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