Operator precedence ranks infix operators so an expression groups and evaluates in the intended order. Haskell combines precedence with associativity: operators at the same precedence group from the left, right, or not at all. section 7.2.3 section 11.3.3
Use fixity declarations to control custom operators:
- `infixl`, `infixr`, and `infix` select left associativity, right associativity, or no associativity. section 11.3.3
- The number following the keyword sets precedence from 0 through 9; higher-precedence operators bind more strongly. section 7.2.3 section 11.3.3
- The dollar operator is declared `infixr 0 $`, so most other operators are grouped before the function application it introduces. section 7.2.3
- Parentheses can always make the intended grouping explicit when an operator expression becomes confusing. section 7.2.3
Precedence changes the result
With `(++)` at precedence 5 and `($)` at precedence 0, `map (*10) $ [1..5] ++ [6..10]` groups as `map (*10) ([1..5] ++ [6..10])`. Without `$`, parentheses express the same intent explicitly: `map (*10) ([1..5] ++ [6..10])`. section 7.2.3
Precedence in a music DSL
A musical composition DSL gives note construction `(.|)` precedence 4, sequencing `(<~>)` precedence 3, and grouping `(<:>)` precedence 2: `infixr 4 .|`, `infixr 3 <~>`, `infixr 2 <:>`. Thus `c 4 .| wn <~> e 4 .| wn <:> g 4 .| wn` gives sequencing tighter binding than grouping. Repetition operators use precedence 1 so they wrap larger compositions. section 11.3.2 section 11.3.3
ghci> :i ($) ($) :: (a -> b) -> a -> b infixr 0 $
Inspect an operator’s type, associativity, and precedence directly in GHCi with `:i ($)`. section 7.2.3
