HOL: Reference

new_infix

boolSyntax.new_infix : string * hol_type * int -> unit

Declares a new infix constant in the current theory.

A call new_infix ("i", ty, n) makes i a right associative infix constant in the current theory. It has binding strength of n, the larger this number, the more tightly the infix will attempt to "grab" arguments to its left and right. Note that the call to new_infix does not specify the value of the constant. The constant may have a polymorphic type, which may be arbitrarily instantiated. Like any other infix or binder, its special parse status may be suppressed by preceding it with a dollar sign.

Comments

Infixes defined with new_infix associate to the right, i.e., A <op> B <op> C is equivalent to A op (B <op> C). Some standard infixes, with their precedences and associativities in the system are:

          $,  ---> 50     RIGHT
          $=  ---> 100    NONASSOC
        $==>  ---> 200    RIGHT
         $\/  ---> 300    RIGHT
         $/\  ---> 400    RIGHT
      $>, $<  ---> 450    RIGHT
    $>=, $<=  ---> 450    RIGHT
      $+, $-  ---> 500    LEFT
    $*, $DIV  ---> 600    LEFT
        $MOD  ---> 650    LEFT
        $EXP  ---> 700    RIGHT
        $o    ---> 800    RIGHT

Note that the arithmetic operators +, -, *, DIV and MOD are left associative in hol98 releases from Taupo onwards. Non-associative infixes (= above, for example) will cause parse errors if an attempt is made to group them (e.g., x = y = z).

Failure

Fails if the name is not a valid constant name.

Example

The following shows the use of the infix and the prefix form of an infix constant. It also shows binding resolution between infixes of different precedence.

   - new_infix("orelse", Type`:bool->bool->bool`, 50);
   val it = () : unit

   - Term`T \/ T orelse F`;
   val it = `T \/ T orelse F` : term

   - “$orelse T F”;
   val it = `T orelse F` : term

   - dest_comb “T \/ T orelse F”;
   > val it = (`$orelse (T \/ T)`,  `F`) : term * term

See also

Parse.add_infix, Theory.constants, Theory.new_constant, boolSyntax.new_binder, Definition.new_definition, boolSyntax.new_binder_definition