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WLP for Automated Testing

WLP for Automated Testing. Wishnu Prasetya wishnu@cs.uu.nl www.cs.uu.nl/docs/vakken/pv. Testing problem. Give test-cases that would cover all 4 paths in the above program.

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WLP for Automated Testing

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  1. WLP for Automated Testing Wishnu Prasetya wishnu@cs.uu.nl www.cs.uu.nl/docs/vakken/pv

  2. Testing problem • Give test-cases that would cover all 4 paths in the above program. • Observation: any input satisfying the wlp of a post-condition Q, specifies a test-case leading a terminal state satisfying Q. • Idea : use Q to specify the target path. tax(rate, income | tax) { if(income  10000) tax := 0 ; if (income  20000) tax := income / rate.low ; tax := tax + income / rate.high ; }

  3. Wedge • A wedge is a finite path of primitive (non-composite) statements in the program, from the program’s start, where we replace guard conditions with the corresponding assert. The concept is from Tomb & Flanagan, Detecting Inconsistencies via Universal Reachability Analysis, ISSTA, 2012. They use assume. For our purpose, we need to turn them to assert. • We can use wedges to re-express coverage problem (e.g. cover this spot, or cover this path). • Then we can calculate the wlp of each wedge.

  4. Wedge & coverage cover this • a wedge covering assert income  10000 ; tax := 0 ;assertincome  20000 ; • a wedge covering without passing (unfeasible) assert income  10000 ; tax := 0 ;assertincome > 20000 ; tax(rate, income | tax) { if(income  10000) tax := 0 ; if (income  20000) tax := income / rate.low ; tax := tax + income / rate.high ; }

  5. wlp of a wedge • Let p be a target path to cover in the CFG of Pr(x). Let w(x) be a wedge such that any execution of w is also an execution of Pr that covers p. • Calculate p = wlpw true. • Check the satisfiability of p; a witness to that is basically an instance of input x for Pr that would cover p.

  6. Covering by solving wlp • if (x>9) { x := x+y ;if (x+y 0) { y := 0 ; if (x8) { cover-this ... } • a wedge to cover assert x>9 ; x := x+y ;assertx+y < 0 ; y := 0 ; assert x 8 • wlp : x>9 /\ x+2y0 /\ x+y8

  7. Concolic approach • Problems: • A long wedge has more constraints; the wlp may be difficult for your theorem prover to solve. • What to do with loops? • Combined concrete and symbolic calculation to incrementally solve the wedge. • Imagine the wedge :w(x,y) = assert p1; x:=x+y; assert p2; y:=0; assert p3 • wlp: p = p1 /\ p2[x+y/x] /\ p3[0/y][x+y/x]

  8. Concolic approach • wlp: p = p1 /\ p2[x+y/x] /\ p3[0/y][x+y/x] • Execute w, e.g. w(0,9). Suppose this manages to pass the guards p1 and p2 but fails on p3 . • Try to solve p[0/x] or p[9/y] instead. • This at least simplifies the formula to solve. • Not necessarily leads to a solution.

  9. Wedge “passing” a loop • Consider : whilegdoS ; ifhthen {  cover this } ... • A wedge to cover  has to do some iterations of S. How many iteration? • Note that arbitrarily choosing k iterations may turn out to be infeasible  leading to unsatisfiablewlp. • Run a concrete execution; suppose it iterates n times, but fails to pass h • we know that at least iterating n times is feasible • construct a wedge with n unfoldingand solve it

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