Formula-Combining Operators

Formula operators combine smaller formulas to produce new formulas. Many closely resemble similar operators from programming languages, like &&, ||, and !.

List of Available Operators:

For the following <fmla> means an arbitrary formula.

Alternative syntax

Some operators have alternative syntax (marked by alt) which are equivalent. Use whichever is most natural and convenient to you.

not (alt: !)

not <fmla>

! <fmla>

true when <fmla> evaluates to false

Example

If some p.spouse is true when the person p is married, not (some p.spouse) denotes the opposite, being true whenever p is not married.

and (alt: &&)

<fmla-a> and <fmla-b>

<fmla-a> && <fmla-b>

true when both <fmla-a> and <fmla-b> evaluate to true.

Example

If some p.spouse is true when the person p is married, and p.spouse != p is true when p is not married to themselves, then some p.spouse and p.spouse != p is true exactly when p is married, but not to themselves.

Implicit and

Forge treats consecutive formulas within { ... } as implicitly combined using and. For instance, the above example could also be written as:

{
  some p.spouse
  p.spouse != p
}

or (alt: ||)

<fmla-a> or <fmla-b>

<fmla-a> || <fmla-b>

true when either <fmla-a> is true or <fmla-b> evaluates to true.

Example

If some p.spouse is true when the person p is married, and p.spouse != p is true when p is not married to themselves, then some p.spouse or p.spouse != p is true exactly when p is either:

  • married; or
  • not married to themselves (including the case where p is unmarried).

implies (alt =>)

<fmla-a> implies <fmla-b>

<fmla-a> => <fmla-b>

true when either <fmla-a> evaluates to false or <fmla-b> evaluates to true.

Example

If some p.spouse is true when the person p is married, and p.spouse != p is true when p is not married to themselves, then some p.spouse implies p.spouse != p is true exactly when p is either:

  • unmarried; or
  • not married to themselves.

implies else (alt: => else)

{<fmla-a> implies <fmla-b> else <fmla-c>}

{<fmla-a> => <fmla-b> else <fmla-c>}

takes the value of <fmla-b> when <fmla-a> evaluates to true, and takes the value of <fmla-c> otherwise.

Example

If:

  • some p.spouse is true when the person p is married,
  • p.spouse != p is true when p is not married to themselves, and
  • some p.parent1 is true when p has a parent1 in the instance,

then some p.spouse => p.spouse != p else some p.parent1 is true exactly when:

  • p is married, and not to themselves; or
  • p is not married and have a parent1 in the instance.

iff (alt: <=>)

<fmla-a> iff <fmla-b>

<fmla-a> <=> <fmla-b>

true when <fmla-a> evaluates to true exactly when <fmla-b> evaluates to true.

IFF

The term iff is short for "if and only if".

Example

If some p.spouse is true when the person p is married, and some p.parent1 is true when p has a parent1 in the instance, then some p.spouse iff some p.parent1 is true exactly when either:

  • p is married and has a parent1 in the instance; or
  • p is unmarried has no parent1 in the instance.