Rebol is another homoiconic language that has infix operators:

  >> 1 + 2 * 3
  == 9

The Rebol interpreter see this as:

  >> multiply add 1 2 3 
  == 9

Functions in Rebol have fixed arity, both add and multiple take two arguments. You can express the above with parens if you want to make it clearer:

  >> multiply (add 1 2) 3
  == 9

Rebols infix operators have no precedence they just work left to right (like Smalltalk). Use parens where needed!

  >> 1 + (2 * 3)
  == 7