Fixity, Associativity and Precedence
Fixity, Associativity and Precedence
With normal, prefix operators (e.g. functions), the semantics of f g h is
clear: f is a function that takes g and h as parameters. If we want
f to take the result of applying g to h we write f (g h).
In the case of infix operators (e.g. symbol operators such as + and *,
or functions surrounded by backticks, for example `elem`), it is less clear.
What does x - y - z mean? Subtracting x from y first (i.e.
(x - y) - z) generally yields different results than subtracting z from
y first (i.e. x - (y - z)). In Daml, the subtraction operator - is
defined as a left-assocative operator. That is, when we write x - y - z -
... the parser associates to the left, meaning the parser interprets this as
((x - y) - z) - ....
Some operators are right-associative. We have already encountered one:
function application! A function signature of a -> b -> c -> ... is parsed
as (a -> (b -> (c -> ...))).
Finally, some operators are non-associative. A good example are comparison
operators such as == and >. This means any ambiguous usage of these
operators (e.g. a == b == c or a > b > c) results in a parse error.
Note
Non-associative operators are not to be confused with operators that are both
left- and right-associative, such as + (since (x + y) + z = x + (y +
z))). To obtain a deterministic parser, such operators must be declared as
one of either left-associative or right-associative. In Daml the +
operator has been declared as left-associative
The precedence of operators defines, when combining different operators, which
operator is processed first. For example, in general (and in Daml),
multiplication takes precedence over addition. That is, x + y * z is
parsed as x + (y * z). Operator precedence is expressed as a number, where a
higher number indicates a higher precedence. Operators of same precedence are
associated to the left (e.g. x + y - z is parsed as (x + y) - z.
The fixity and precedence of an operator are declared using the infixl,
infix, and infixr keywords (denoting left-, non-, and
right-associativity, respectfully) that take an integer between 0 and 9
inclusive and an operator the fixity applies to. For example, infixl 6 +
declares that + is a left-associative operator with precedence 6.
These keywords can be used for user-defined operators as well. The following
table shows the fixity and precedence for operators that are built-in to the
Daml language, such as + and -:
Precedence |
Left-associative |
Non-associative |
Right-associative |
|---|---|---|---|
9 |
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8 |
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7 |
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6 |
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5 |
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4 |
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3 |
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2 |
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1 |
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0 |
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