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First Example

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Kazunori Ueda edited this page Feb 28, 2025 · 5 revisions

First Example

The following program (also called a model) describes a sawtooth function with the following shape:

INIT     <=> 0 <= f < 2.
INCREASE <=> [](f' = 1).
DROP     <=> [](f- = 2 => f = 0).
INIT, INCREASE << DROP.

The first three lines (often called rules or named constraints) define three constraints, and the final line combines those rules.

This program defines the trajectory of a variable f (whose value is a function of nonnegative time) in the following way.

  • The rule INIT defines the value of f at time 0, which takes an uncertain value between 0 and 2.
  • The rule INCREASE states that the slope of f is always 1.
  • The rule DROP states that the value of f is reset to 0 whenever the value reaches 2. (The minus sign after f means the left limit of f).
  • The final line states that
    • INIT is enabled,
    • DROP is enabled, and
    • INCREASE is enabled whenever it is consistent with DROP (that is, the priority of DROP is higher than INCREASE).

More examples can be found in the Examples page.

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