Refer to left limit

#### Syntax

**pre**(y)

#### Description

Returns the "left limit" y(t^{pre}) of variable y(t) at
a time instant t. At an event instant, y(t^{pre}) is the
value of y after the last event iteration at time instant t. The
**pre** operator can be applied if the following three
conditions are fulfilled simultaneously:

- variable y is a subtype of a simple type
- y is a discrete-time expression
- the operator is
**not** applied in a
**function** class

The first value of **pre**(y) is determined in the
initialization phase.

A new event is triggered if at least for one variable v
"**pre**(v) <> v" after the active model
equations are evaluated at an event instant. In this case the model
is at once reevaluated. This evaluation sequence is called
"*event iteration*". The integration is restarted, if for
all v used in **pre**-operators the following
condition holds: "**pre**(v) == v".

*[If v and ***pre**(v) are only used in when
clauses, the translator might mask event iteration for variable v
since v cannot change during event iteration. It is a "quality of
implementation" to find the minimal loops for event iteration,
i.e., not all parts of the model need to be reevaluated.

*The language allows mixed algebraic systems of equations
where the unknown variables are of type Real, Integer, Boolean, or
an enumeration. These systems of equations can be solved by a
global fix point iteration scheme, similarly to the event
iteration, by fixing the Boolean, Integer, and/or enumeration
unknowns during one iteration. Again, it is a quality of
implementation to solve these systems more efficiently, e.g., by
applying the fix point iteration scheme to a subset of the model
equations.]*

*Note that ***pre**(v) requires the argument to
be a variable and a discrete-time expression, this formulation was
chosen to allow using **pre**(v) both for
discrete-time variables and for continuous-time variables inside
when-clauses.

#### Examples

**model** Hysteresis
Real u;
Boolean y;
**equation**
u = Modelica.Math.sin(**time**);
y = u > 0.5 or **pre**(y) and u >= -0.5;
**end** Hysteresis;

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