Symbol or Macro | Meaning | Reading | Precedence | Restrictions |
---|---|---|---|---|

\c | Logical Implication | implies | 2 | |

\cond | Conditionally Existent Term | then | 3 | |

\els | Definitional Otherwise | else | 3 | |

\Iff | Logical Equivalence | if and only if | 4 | |

\And | Logical Conjunction | and | 5 | |

\Or | Logical Disjunction | or | 5 | |

\ident | Identity | is identical to | 6 | |

= | Equality | equals | 6 | |

\in | Elementhood | belongs to | 6 | |

\i | Inclusion | subset of | 6 | P |

\subset | Inclusion | subset of | 6 | L |

‹ | Inequality | less than | 6 | |

› | Inequality | greater than | 6 | |

\le | Inequality | less than or equal to | 6 | |

\ge | Inequality | greater than or equal to | 6 | |

\ne | Inequality | not equal to | 6 | |

\i \ne | Proper Inclusion | proper subset of | 6 | P |

\subset\ne | Proper Inclusion | proper subset of | 6 | L |

\notin | Non-membership | not an element of | 6 | |

\djn | Disjointness | does not intersect with | 6 | |

\orders | Order Relation | orders | 6 | |

, | Tuple Operator | comma | 6 | |

+ | Addition | plus | 9 | |

- | Subtraction | minus | 9 | |

\cdot | Multiplication | times | 13 | |

\cap | Set Intersectionintersect | 15 | ||

\cup | Set Unionunion | 15 | ||

\dsj | Disjoint Union | disjoint union | 15 | |

\cmp | Functional Composition | composed with | 15 | |

\lilx | Cartesian Product | cross | 15 | |

\symdif | Symmetric Difference symmetric difference | 17 | ||

\setdif | Set Difference | minus | 17 | |

\toThe | Exponentiation | to the power | 17 |

These operators may of course be combined to form complex expressions but they must however be used within at least one pair of parentheses.

One apparent omission from this table is mention of left vs. right associativity. The parser however does not automatically group repeated operations to the left or to the right. Repeated operations are in general left to the user to define. In the case of operations tagged as having both the associative and commutative properties however the parser removes extra parentheses and the unifier attempts to match operands irrespective of where they occur in the sequence of operands. At present conjunction is tagged in this way by the prep program and no other operators are so tagged. In time more operators will be tagged by default and more properties will be built-in, but at this stage it is helpful to keep assumptions minimal in order to better understand the behavior of the system.

Another apparent omission from the table is functional evaluation. This is omitted partly because including it would usurp adjacent-writing which is the prime location on the parse tree, partly because with outer parentheses (f(x)) is cumbersome, and partly because the non-parenthetical Morse notation using an initial dot very works well.