Slicing

rascal-0.40.17

We demonstrate a relational definition of program slicing based on the definitions given in :

D. Jackson & E.J. Rollins, A new model of program dependences for reverse engineering, Proceedings of the 2nd ACM SIGSOFT symposium on Foundations of software engineering Pages: 2 - 10, 1994

We need the analyses of Reaching Defs and Dominators to compute backwardSlice:

set[Use] BackwardSlice(
    set[Stat] controlstatement, 
    rel[Stat, Stat] pred,
    rel[Stat, Var] uses,
    rel[Stat, Var] defs,    
    Use criterion) {

    rel[Stat, Def] reach = reachingDefinitions(defs, pred);

    // Compute the relation between each use and corresponding definitions: ud
    rel[Use, Def] useDef = 
     {<<s1, v>, <s2, v>> | <Stat s1, Var v> <- uses, <Stat s2, v> <- reach[s1]};

    // Internal dependencies per statement
    rel[Def, Use] defUsePerStat 
        = {<<s, v1>, <s, v2>> | <Stat s, Var v1> <- defs, <s, Var v2> <- uses}
        + {<<s, v>, <s, "EXEC">> | <Stat s, Var v> <- defs}
        + {<<s, "TEST">, <s,v>> | Stat s <- controlstatement, <s, Var v> <- domainR(uses, {s})};

    // Control dependence: control-dependence
    rel[Stat, set[Stat]] controldominator = domainR(dominators(pred, 1), controlstatement);

    rel[Def, Use] controlDependence  =
       {<<s2, "EXEC">, <s1,"TEST">> | <Stat s1, set[Stat] s2s> <- controldominator, Stat s2 <- s2s};

    // Control and data dependence: use-control-def
    rel[Use, Def] useControlDef = useDef + controlDependence;
    rel[Use, Use] useUse = (useControlDef o defUsePerStat)*;

    return useUse[criterion];
}

This is an example from Frank Tip's slicing survey:

1: read(n)
2: i := 1
3: sum := 0
4: product := 1
5: while i<= n do
   begin
6:  sum := sum + i
7:  product := product * i;
8:  i := i + 1
   end
     9: write(sum)
10: write(product)

In our simplified internal program model this looks like the follow relations:

rascal>PRED = {<1,2>, <2,3>, <3,4>, <4,5>, <5,6>, <5,9>, <6,7>, <7,8>,<8,5>, <8,9>, <9,10>};
rel[int,int]: {
  <7,8>,
  <1,2>,
  <3,4>,
  <9,10>,
  <2,3>,
  <4,5>,
  <6,7>,
  <5,9>,
  <5,6>,
  <8,5>,
  <8,9>
}
rascal>DEFS = {<1, "n">, <2, "i">, <3, "sum">, <4,"product">, <6, "sum">, <7, "product">, <8, "i">};
rel[int,str]: {
  <8,"i">,
  <7,"product">,
  <1,"n">,
  <3,"sum">,
  <2,"i">,
  <4,"product">,
  <6,"sum">
}
rascal>USES = {<5, "i">, <5, "n">, <6, "sum">, <6,"i">, <7, "product">, <7, "i">, <8, "i">, <9, "sum">, <10, "product">};
rel[int,str]: {
  <10,"product">,
  <9,"sum">,
  <7,"i">,
  <7,"product">,
  <6,"i">,
  <6,"sum">,
  <8,"i">,
  <5,"i">,
  <5,"n">
}
rascal>CONTROLSTATEMENT = { 5 };
set[int]: {5}

Now we can try this out:

rascal>Example1 = BackwardSlice(CONTROLSTATEMENT, PRED, USES, DEFS, <9, "sum">);
rel[int,str]: {
  <1,"EXEC">,
  <3,"EXEC">,
  <9,"sum">,
  <2,"EXEC">,
  <6,"i">,
  <6,"sum">,
  <6,"EXEC">,
  <5,"i">,
  <5,"n">,
  <8,"i">,
  <8,"EXEC">
}
rascal>assert Example1 == { <1, "EXEC">, <2, "EXEC">,  <3, "EXEC">, <5, "i">, <5, "n">,  <6, "sum">, <6, "i">, <6, "EXEC">, <8, "i">, <8, "EXEC">, <9, "sum"> };
bool: true
rascal>Example2 = BackwardSlice(CONTROLSTATEMENT, PRED, USES, DEFS,<10, "product">);
rel[int,str]: {
  <10,"product">,
  <1,"EXEC">,
  <2,"EXEC">,
  <4,"EXEC">,
  <7,"i">,
  <7,"product">,
  <7,"EXEC">,
  <5,"i">,
  <5,"n">,
  <8,"i">,
  <8,"EXEC">
}
rascal>assert Example2 == { <1, "EXEC">,  <2, "EXEC">, <4, "EXEC">, <5, "i">, <5, "n">, <7, "i">, <7, "product">, <7, "EXEC">, <8, "i">, <8, "EXEC">, <10,  "product">  };
bool: true