Andrew Bromage:
>Pattern matching on the LHS of a function definitions looks, for all the
>world, like a set of rewrite rules.  That's because, in some sense, they
>are.
>
>In this definition:
>
>    f (x:xs) = 1 + f xs
>    f [] = []
>
>Intuitively, the first rule should only "fire" if the expression being
>evaluated conforms to the left-hand side.

But beware that even though they can be seen as rewrite rules, there is a
difference in that a term rewrite system allows all possible orders of
applying rewrite rules, whereas Haskell specifies a top-down order in which
the rules are tried. This can make a difference if patterns overlap, so
several patterns can match a given argument.

In the given example the patterns do not overlap though, so this can indeed
be seen as a little term rewriting system defining f.

Björn Lisper
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