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I am confused as to why the 1st and 3rd versions of this functions give this error whereas the second definition works fine.

-- head and tail
third :: [a] -> a
third [a] = head (tail (tail[a]))

-- Pattern matching
third2 :: [a] -> a
third2 (_:_:x:_) = x

-- List indexing
third3 :: [a] -> a
third3 [a] = [a]!!2

Thanks in advance

BradStevenson
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2 Answers2

4

That is odd that the second one does not complain about non-exhaustive patterns, since third2 will not match lists of length zero, one, or two. The third and third3 functions complain because [a] is not a variable, it is a pattern. [a] desugars to (a:[]), so you could have written them as

third (a:[]) = head (tail (a:[]))

third3 (a:[]) = (a:[]) !! 2

Neither of which will work, as those are single element lists. I suspect what you want is

third a = head (tail a)

third3 a = a !! 2
sabauma
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1

You need to understand the syntax better.

Basically, there are 2 sub-syntaxes:

  1. syntax for types
  2. syntax for expressions and patterns

In the type syntax, [a] means list of elements of type a

In the expression/pattern syntax, [a] means the singleton list, that contains the value a. This is equivalent to (a:[]) (a prepended to the empty list).

Hence your first function, for example, checks if it gets a singleton list. Then it takes the head of the tail of the tail of a singleton list, which will fail.

The message you're getting is because there are shapes of lists you didn't cover: namely, the empty list and lists with more than 1 element.

And, of course, you should be getting a warning for third2, is it only covers lists with 3 or more elements. I am sure you're overlooking something.

Ingo
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