Basic Operators

TLA+ has a rich set of operators. Let's cover the most common ones.

Boolean Operators

The Init / Next Pattern

Almost every TLA+ spec follows this pattern:

Init — defines the initial state (conjunction of assignments)

Next — defines all possible transitions (disjunction of actions)

Init == /\ x = 0

        /\ y = 0


Next == \/ ActionA
        \/ ActionB

In Init, /\ means "and" — all conditions must hold. In Next, \/ means "or" — any one action can happen.

Actions and Primed Variables

An action describes one kind of state transition. It uses primed variables (x') to refer to the value in the next state:

Increment == /\ x' = x + 1

             /\ y' = y       ( y stays the same )

UNCHANGED

Instead of writing y' = y, you can use:

Increment == /\ x' = x + 1

             /\ UNCHANGED y

For multiple variables: UNCHANGED <>

IF / THEN / ELSE

Max(a, b) == IF a > b THEN a ELSE b

Try It

The spec demonstrates a simple traffic light with Init/Next pattern and boolean operators.