That only works because Haskell can't really express it. That is, if you could write Haskell code that checked that equality, that equality wouldn't be enough, because you could write a function `mapStrange foo [x]` that is equal to `map` if `foo = id` and is something else otherwise.

But since you can't compare 2 functions for equality, and you can't compare two arbitrary values for equality, then yes - your informal requirement is enough togethet with the type to force the function to be `map`.