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Let f x y = x * y. We can apply this function in two ways: f 5 6, or, using infix notation, 5 `f` 6. Do the operator rules apply to this last expression? What precedence will this application have? Is it just another form of function application, and so will it also have the highest precedence?
I suppose that the compiler sees this special form (due to `` and/or the name starting with a letter(?)), and actually treats this as ordinary function application, instead of considering it an operator.
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Haskell provides special syntax to support infix notation. An operator is a function that can be applied using infix syntax (Section 3.4), or partially applied using a section (Section 3.5).
What are infix functions? In R, most of the functions are “prefix” - meaning that the function name comes before the arguments, which are put between parentheses : fun(a,b) . With infix functions, the name comes between the arguments a fun b . In fact, you use this type on a daily basis with : , + , and so on.
Functions in Haskell default to prefix syntax, meaning that the function being applied is at the beginning of the expression rather than the middle. Operators are functions which can be used in infix style. All operators are functions.
The Haskell 98 Report has a section on Operator Applications that clears it up:
An operator is either an operator symbol, such as + or $$, or is an ordinary identifier enclosed in grave accents (backquotes), such as `op`. For example, instead of writing the prefix application op x y, one can write the infix application x `op` y. If no fixity declaration is given for `op` then it defaults to highest precedence and left associativity (see Section 4.4.2).
As indicated by the other answers, the Report also has a section on Fixity Declarations that allows you to define your own fixity, for example:
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