Order of parameters and currying

I got really confused when reading A Gentle Introduction To Haskell, version 98 (page 10, Functions), which aim to explain currying as the first concept of describing functions.

Type definitions with -> operator is right associative.
Function calls with parameters separated by space (" ") are left associative.
Parameters are ordered from left to right both in type definitions and function calls.

For example see the type definition of div.

> :t div
:: (Integral a) => a -> a -> a

Numbering the parameters, a1 -> a2 -> a3
Using right associative rule for -> operator, a1 -> (a2 -> a3)

So the type definition roughly translates to:

A value of a1 applied to function div evaluates a function
A value of type a2 applied to this function evaluates to a value of type a3

Calling divwith parameters 10 and 2 give the result 5.

> div 10 2
=> 5

Using left associative rule for parameters in function calls, (div 10) 2

This means that the function returned by applying 10 to div translates to 10/x. 2 applied to this function evaluates to 5.
10 is of type a1, 2 of type a2 and 5 of type a3.

The infix operator of div works in the same manner.

> :t (/)
:: (Fractional a) => a -> a -> a

> (/) 10 2
=> 5.0

> 10 / 2
=> 5.0

> 10 `div` 2
=> 5

So the div can be defined as.

div a b = a / b

Note also that operators can have different priority and "associativeness". This is defined by infix, infixl and infixr functions. But functions and -> in type definitions work as explained above.

The "function application" operator, $, can be used to change the left associative rule for function argument application.

f $ x = f x

One example where you want to apply several functions at the same time and want to avoid parentheses.

Prelude> let inc = (+) 1
Prelude> inc div 10 2
    The function `inc' is applied to three arguments,
Prelude> inc $ div 10 2
6
Prelude> inc (div 10 2)

So you can make multiple function applications right associative.

References

Also see Lambda Calculus: Motivation for an mathematical example of currying.