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...nd (2) either order of invocation produces the same result. The commutativity property itself is not checked by the compiler; we must rely on other forms of checking (e.g., more complex program logic =-=[52]-=- or static analysis [42, 4]) to ensure that methods declared to be commutative are really commutative. In practice, we anticipate thatcommuteswith will be used mostly by library and framework code tha...

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...lf and the programs shown in Table 1 can be downloaded from http://www.cs.kuleuven.be/~jans/vericool2. program time taken source Cell 0.1 [16, 17, 12] ArrayList and Iterator 0.8 [2, 18] LinkedList 43 =-=[19, 2]-=- Resource Pool 2.1 [17] Marriage 0.2 [20] MasterClock 0.2 [21] Subject-Observer 11 [1, 22] Recell, TCell, DCell 0.5 [15] Visitor (framing only) 127 [17] Table 1. Table showing the time taken (in secon...

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...nvariants that they can discover. At the other end, we have approaches based on verification condition generation that can be used to establish sophisticated properties of a program using SMT solvers =-=[25, 32]-=-, but require the programmer to provide all the sophisticated properties along with loop invariants, which are usually even more sophisticated. The former approach enjoys the benefit of complete autom...

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...on procedures incorporated into SMT provers [16, 6, 4] were used to verify tens of thousands of lines of imperative code [14, 3] and prove complex correctness conditions of imperative data structures =-=[67, 50]-=-. While much recent work on automation was invested into imperative languages, it is interesting (50 years after [44]) to consider the reach of such decision procedures when applied to functional prog...

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...erms Algorithms, Languages, Reliability, Verification Keywords verification, theorem prover, proof system 1. Introduction We have developed a system, Jahob, for specifying and verifying Java programs =-=[46]-=-. Because Jahob uses higher-order logic as its specification language, it can express very sophisticated correctness properties. Instead of relying on a single monolithic prover, Jahob uses integrated...

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...olvers, Gappa for reasoning about rounding, and interactive proving to prove all VCs. Improving cooperation of provers is an interesting perspective, e.g. like in the Jahob verification tool for Java =-=[31]-=- which selects the prover to call depending on the class of goal (but does not support FP).Turning the Gappa techniques for FP into some specific built-in theory for SMT solvers should be considered....

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...bility issues typically associated symbolic interpretation. Although our proposed commutativity detection algorithm leverages on random interpretation, other methods, such as verified abstract states =-=[24]-=- or fractal symbolic analysis [12], could be used as well. 6. Summary Commutative functions are a significant source of parallelism in many applications. This paper introduces a novel compiler algorit...

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...ese and the code, verification conditions (VCs) are generated whose validity implies that the code meets the specification. The VCs are then proved using automatic [13] or interactive theorem proving =-=[17, 26, 20]-=-. These approaches allow for the specification of far more expressive properties than is possible in our system. However, they require significantly more manual effort in interacting with the prover. ...