What does :: (double colon) stand for?
You can google for haskell "double colon" or similar things; it's unfortunately a bit hard to google for syntax, but in this case you can name it.
In Haskell, your programs will often run fine without it (though you will want to use it to hone the specification of any functions you define, and it is good practice).
The idea is that you can insert a :: ... anywhere (even in the middle of an expression) to say "by the way Mr. Compiler, this expression should be of type ...". The compiler will then throw an error if it can be proved this may not be the case.
I think you can also use it to "cast" functions to the versions you want; e.g. if a function is "polymorphic" (has a general type signature) and you actually want, say an Integer, then you could do :: Integer on the resulting value perhaps; I'm a bit rusty though.
You should read:
foo :: a
as "the name foo refers to a value of type a". When you write:
run :: a -> b
this means:
-
You are declaring the name
run. -
This name will refer to a value that have type
a -> b,
The type a -> b is the type of a function which takes a value of type a and returns another value of type b.
You must really learn about types to understand Haskell. The type system is one of the most crucial feature of Haskell, and it's what makes the language so expressive.