Trace Table: Symbolic Execution

compute symbolically
( R >= Y --> Q,R := Q+1,R-Y ) o ( R >= Y and Y > 0 --> Q,R := Q+R/Y, R mod Y )

We do this with a table for recording the effects of symbolically executing each statement of the function we are computing.

The table has one column or each variable involved in the computation. It also has one column for noting the current symbolic form of conditions when they are encountered.


  condition            Q               R             Y
  _____________________________________________________________
  R >= Y               Q+1             R-Y
  R-Y >= Y and Y > 0




The next clause of the composition is ( R >= Y and Y > 0 --> Q,R := Q+R/Y, R mod Y ).

The condition "R >= Y and Y > 0" is recorded in the table, but the current symbolic table entries are substituted in for the variable names in the condition expression. Here, this means "R" is replaced with "R-Y".