Pattern Match(es) are Overlapped - Pattern matching on Operators

Question

I've come across a situation where I would like to pattern match on operators. However, this throws a Pattern match(es) are overlapped error with GHC. I can't figure out why. Is pattern matching on operators not allowed? I assume that since enclosing an operator symbol in parentheses converts it into an identifier, this should have worked.

test :: (Integer -> Integer -> Integer) -> String
test (+) = "plus"
test (-) = "minus"
test _ = "other"

There are other ways I can accomplish what I want to do. I'm just curious as to why this doesn't work.

Answer 1

(+) and (-) are not constructors of the type Integer -> Integer -> Integer:

• They are not constructor names
• Integer -> Integer -> Integer is not an algebraic datatype

And so your code is equivalent to using any other variable names to bind the first argument, e.g.

test foo = "plus"
test bar = "minus"
test _   = "other"

which hopefully makes it clear that all three patterns actually match anything (and the first two bind some names). In other words, there is no way for the first pattern (foo, or (+) in your example) to fall through, which is why it overlaps with the remaining two.