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Fixities

Fixities in Juvix refer to the precedence and associativity of operators. A fixity declaration is defined using the syntax keyword followed by fixity. It specifies how an operator should be parsed in relation to other operators.

Syntax of Fixity Declaration

The syntax for a fixity declaration varies based on the operator's arity, associativity, and precedence.

Arity Declaration

For an operator with no specified precedence or associativity, the arity can be declared as follows:

syntax fixity <name> := <arity>;

In this syntax,

  • <name> represents the operator name, and
  • <arity> can either be none, unary, or binary.

This declaration is equivalent to:

syntax fixity <name> := <arity> {};

Associativity Declaration

For an operator with no specified precedence, its associativity can be declared as:

syntax fixity <name> := <arity> { assoc := <associativity> };

Here, <associativity> can either be left, right, or none.

Precedence Declaration

For an operator with no specified associativity, its precedence can be declared relative to other operators.

  • If it has equal precedence to another operator:
syntax fixity <name> := <arity> { same := otherOperatorName };
  • If it has higher precedence than other operators:
syntax fixity <name> := <arity> {
    above := [otherOperatorName1;...; otherOperatorNameN] };
  • If it has lower precedence than other operators:
syntax fixity <name> := <arity> {
    below := [otherOperatorName1;...; otherOperatorNameN] };

Associativity and Precedence Declaration

For an operator with both associativity and precedence:

syntax fixity <name> := <arity> {
    assoc := <associativity>;
    above := [otherOperatorName1;...; otherOperatorNameN]
};

Examples of Fixity Declarations

Here are some examples of common fixity declarations for operators in Juvix's standard library.

syntax fixity rapp := binary {assoc := right};

syntax fixity lapp := binary {assoc := left; same := rapp};

syntax fixity seq := binary {assoc := left; above := [lapp]};

syntax fixity functor := binary {assoc := right};

syntax fixity logical := binary {assoc := right; above := [seq]};

syntax fixity comparison := binary {assoc := none; above := [logical]};

syntax fixity pair := binary {assoc := right};

syntax fixity cons := binary {assoc := right; above := [pair]};

syntax fixity step := binary {assoc := right};

syntax fixity range := binary {assoc := right; above := [step]};

syntax fixity additive := binary {
  assoc := left;
  above := [comparison; range; cons];
};

syntax fixity multiplicative := binary {assoc := left; above := [additive]};

syntax fixity composition := binary {assoc := right; above := [multiplicative]};