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Is there a complete list of allowed characters somewhere, or a rule that determines what can be used in an identifier vs an operator?

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From the Haskell report, this is the syntax for allowed symbols:

a | b means a or b and

a<b> means a except b

special -> ( | ) | , | ; | [ | ] | `| { | } symbol -> ascSymbol | uniSymbol<special | _ | : | " | '> ascSymbol -> ! | # | $ | % | & | * | + | . | / | < | = | > | ? | @ \ | ^ | | | - | ~ uniSymbol -> any Unicode symbol or punctuation

So, symbols are ASCII symbols or Unicode symbols except from those in special | _ | : | " | ', which are reserved.

Meaning the following characters can't be used: ( ) | , ; [ ] ` { } _ : " '

A few paragraphs below, the report gives the complete definition for Haskell operators:

varsym -> ( symbol {symbol | :})<reservedop | dashes> consym -> (: {symbol | :})<reservedop> reservedop -> .. | : | :: | = | \ | | | <- | -> | @ | ~ | =>

Operator symbols are formed from one or more symbol characters, as defined above, and are lexically distinguished into two namespaces (Section 1.4):

  • An operator symbol starting with a colon is a constructor.
  • An operator symbol starting with any other character is an ordinary identifier.

Notice that a colon by itself, ":", is reserved solely for use as the Haskell list constructor; this makes its treatment uniform with other parts of list syntax, such as "[]" and "[a,b]".

Other than the special syntax for prefix negation, all operators are infix, although each infix operator can be used in a section to yield partially applied operators (see Section 3.5). All of the standard infix operators are just predefined symbols and may be rebound.

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Should probably be citing the haskell2010 report instead of the haskell98 report these days (although in this case they say the same thing, as far as I can see).
FWIW, tryhaskell.org currently gives a lexical error for trying to use one of the mathematical bracketing symbols, e.g. let a ⟬ b = 1
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From the Haskell 2010 Report §2.4:

Operator symbols are formed from one or more symbol characters...

§2.2 defines symbol characters as being any of !#$%&*+./<=>?@\^|-~: or "any [non-ascii] Unicode symbol or punctuation".

NOTE: User-defined operators cannot begin with a : as, quoting the language report, "An operator symbol starting with a colon is a constructor."

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Interesting that you can use arbitrary Unicode. So, for instance, λ or ⊗ would be valid Haskell operators?
No, λ is a Unicode letter, not a Unicode symbol or a Unicode punctuation character. So you can't use it as part of an operator name (but you can use it as part of an ordinary identifier).
I expect you could use ⊗ as a Haskell operator, but I don't know for sure.
You can. Its generalCategory is MathSymbol (just to make sure, I actually defined an operator (⊗) in ghci, and it was accepted).
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What I was looking for was the complete list of characters. Based on the other answers, the full list is;

Unicode Punctuation:

Unicode Symbols:

But excluding the following characters with special meaning in Haskell:

(),;[]`{}_:"'

A : is only permitted as the first character of the operator, and denotes a constructor (see An operator symbol starting with a colon is a constructor).

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This is absolutely insane! It is great that using any Unicode symbols is possible, but unfortunately they are usually very hard to type on current keyboards.
@Qqwy - Haskell is designed for use in a literate programming environment. You could be producing a document designed for typesetting with code fragments, and have those code fragments actually executable in your source document. The ability to define unicode operators is invaluable for that purpose.

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