Is Inside

Is Inside is a direct subtype of Generic Trigger

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with functions Is Inside Functions, keys Is Inside keys and example object IsInside

TYPE INCLUSION RELATIONSHIPS

AVAILABLE FUNCTIONS

AVAILABLE CREATE FUNCTION KEYS

TYPICAL OBJECTS OF TYPE Is Inside

This type represents a predicate function that returns TRUE or FALSE by examining if u input variables x₁ , x₂ , ... , xᵤ are within given intervals in accordance with specified boolean transformations.

Two cases must be distinguished:

Case 1:One input variable, i.e. u == 1

If the function receives only one input variable x₁, the default output will be TRUE if x₁ is within the given interval and no boolean transformation is applied.
Note in this case the default boolean transformation is ID that is equivalent to no transformation.
But if the boolean transformation were specified as NOT, the output would change to FALSE.

Case 2:More than one input variables, i.e. u > 1

If the function processes u input variables with u > 1, then u intervals and u - 1 boolean transformations B₁ , B₂ , ... , Bᵤ₋₁ must be also specified, at least implicitly.
Concretely, if fewer than u intervals are specified, the last specified interval is deemed to apply to all remaining input variables.
Similarly if fewer than u - 1 boolean transformations are specified, the last specified boolean transformation is deemed to apply to all remaining input variables.
The exact processing is as follows:
At first, the first variable x₁ alone is tested against the corresponding interval and produces a corresponding boolean result b₁
b₁ = TRUE if x₁ lies within the interval and FALSE otherwise.
Next, the second variable x₂ alone is tested against the corresponding interval and produces a corresponding boolean result b₂
b₂ = TRUE if x₂ lies within the interval and FALSE otherwise.
Before moving to the valuation of any remaining variables, an intermediate boolean output b'₂ corresponding to the already processed x₁ and x₂ is produced by applying the first boolean transformation B₁ on b₁ and b₂:
B₂ = ƒ₁(b₁ , b₂)
b'₂ will be the final output if no other variable follows x₂
But if a variable x₃ does exist, it will be tested against the corresponding interval and produce a corresponding boolean result b₃
Then the second boolean transformation B₂ will be applied to b₃ and b'₂ to produce the boolean B'₃, which will be the cummulative result so far.
If x₃ is the last input variable, B'₃ will be the final output, otherwise the process will continue.