Tutorial Debugging Well-Definedness and Transition Errors

We assume that you have grasped the way that ProB setups up the initial states of a B machine as outlined in Tutorial Setup Phases, and have understood why animation is difficult as outlined in Tutorial Understanding the Complexity of B Animation. You may also want to have a look at the explanation of well-definedness in B.

A simple example

Let us use the following B machine as starting point:

MACHINE WhileLoopInvariantError
VARIABLES xx
INVARIANT
 xx:NATURAL
INITIALISATION xx:=1
OPERATIONS
  Set(c) = PRE c:1..10 & xx<=c THEN
    WHILE xx < c DO xx := xx+1
    INVARIANT
      xx <= c & xx:NATURAL &
      xx<10 /* this is wrong */
    VARIANT c-xx
    END
  END;
  r <-- Get = BEGIN r:= xx END
END

After loading and initialising the machine you see that ProB has found a so-called "transition error", i.e., an error that occured while computing enabled operations (which correspond to a transition from one state to the B machine to another). These errors are displayed in red in the State Properties pane:

When you click on the red transition error you get presented with more details about the error:

Sometimes you can also have the possibility to click on a "Visualise" button, which in this case will give you a graphical visualisation of the invariant violation:

The same technique applies for inspecting other transition errors, such as:

• well-definedness errors of expressions such as:
  • arithmetic well-definedness errors (division by 0, modulo by 0, modulo for negative numbers, min or max of empty set)
  • functional well-definedness errors (function applied outside of domain or applied to relation,...)
  • sequence well-definedness errors (first, last, tail, front of empt sequence,...)
• PRE condition errors (not for outermost preconditions, which are treated specially)
• ASSERT condition violations