Abstract
A (commercial or financial) contract is a mutual agreement to exchange resources such as money, goods and services amongst multiple parties. It expresses which actions may, must and must not be performed by its parties at which time, location and under which other conditions.
We present a general framework for statically analyzing digital contracts, formal specifications of contracts, expressed in Contract Specification Language (CSL). Semantically, a CSL contract classifies traces of events into compliant (complete and successful) and noncompliant (incomplete or manifestly breached) ones.
Our analysis framework is based on compositional abstract interpretation, which soundly approximates the set of traces a contract denotes by an abstract value in a lattice. The framework is parameterized by a lattice and an interpretation of contract primitives and combinators, satisfying certain requirements. It treats recursion by unrestricted unfolding. Employing Schmidt’s natural semantics approach, we interpret our inference system coinductively to account for infinite derivation trees, and prove their abstract interpretation sound.
Finally, we show some example applications: participation analysis (who is possibly involved in a transfer to whom; who does definitely participate in a contract) and fairness analysis (bounds on how much is gained by each participant under any compliant execution of the contract).
The semantics of CSL, the abstract interpretation framework and its correctness theorem, and the example analyses as instances of the abstract interpretation framework have all been mechanized in the Coq proof assistant.
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Notes
- 1.
If desirable; “code is law” by contract parties fixing the association of a specific immutable contract manager is a possibility, not a necessity in this framework.
- 2.
- 3.
“Predicate” in the sense of a formula denoting a Boolean-valued function.
- 4.
- 5.
See www.deondigital.com.
- 6.
Unfair in the sense of providing unexpected gains or losses to participants. Note that under the adage of “code is law” an unfair contract is still a contract that cannot be changed: it is what it is.
- 7.
The pattern of pseudonymous parties collateralizing participation in a contract by depositing money with a trusted third party is common and practically unavoidable: The parties being pseudonymous, they could just walk away once they owe more than they are owed. This may explain why each Ethereum-style smart contract is “born” with an associated Ether account.
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Acknowledgements
We would like to thank the anonymous referees for their critical and helpful comments.
This work has been facilitated by financial support from Deon Digital and Innovation Fund Denmark for the project Formal verification for formal contracts under contract number 7092-00003B.
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Henglein, F., Larsen, C.K., Murawska, A. (2020). A Formally Verified Static Analysis Framework for Compositional Contracts. In: Bernhard, M., et al. Financial Cryptography and Data Security. FC 2020. Lecture Notes in Computer Science(), vol 12063. Springer, Cham. https://doi.org/10.1007/978-3-030-54455-3_42
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