Abstract
We present abstract refinement types which enable quantification over the refinements of data- and function-types. Our key insight is that we can avail of quantification while preserving SMT-based decidability, simply by encoding refinement parameters as uninterpreted propositions within the refinement logic. We illustrate how this mechanism yields a variety of sophisticated means for reasoning about programs, including: parametric refinements for reasoning with type classes, index-dependent refinements for reasoning about key-value maps, recursive refinements for reasoning about recursive data types, and inductive refinements for reasoning about higher-order traversal routines. We have implemented our approach in a refinement type checker for Haskell and present experiments using our tool to verify correctness invariants of various programs.
Keywords
- Type Check
- Parametric Invariant
- Input List
- Typing Judgment
- Predicate Abstraction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Belo, J.F., Greenberg, M., Igarashi, A., Pierce, B.C.: Polymorphic Contracts. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 18–37. Springer, Heidelberg (2011)
Bengtson, J., Bhargavan, K., Fournet, C., Gordon, A.D., Maffeis, S.: Refinement types for secure implementations. ACM TOPLAS 33(2), 8 (2011)
Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. Springer (2004)
Constable, R.L.: Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall (1986)
Cousot, P., Cousot, R., Logozzo, F.: A parametric segmentation functor for fully automatic and scalable array content analysis. In: POPL, pp. 105–118 (2011)
de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Dunfield, J.: A Unified System of Type Refinements. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA (2007)
Findler, R.B., Felleisen, M.: Contracts for higher-order functions. In: ICFP, pp. 48–59 (2002)
Flanagan, C., Joshi, R., Leino, K.R.M.: Annotation inference for modular checkers. Information Processing Letters (2001)
Fournet, C., Kohlweiss, M., Strub, P.-Y.: Modular code-based cryptographic verification. In: CCS, pp. 341–350 (2011)
Freeman, T., Pfenning, F.: Refinement types for ML. In: PLDI (1991)
Gopan, D., Reps, T.W., Sagiv, S.: A framework for numeric analysis of array operations. In: POPL, pp. 338–350 (2005)
Graf, S., Saïdi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Guha, A., Fredrikson, M., Livshits, B., Swamy, N.: Verified security for browser extensions. In: IEEE Symposium on Security and Privacy, pp. 115–130 (2011)
Jhala, R., McMillan, K.L.: Array Abstractions from Proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)
Kawaguchi, M., Rondon, P., Jhala, R.: Type-based data structure verification. In: PLDI, pp. 304–315 (2009)
Knowles, K.W., Flanagan, C.: Hybrid type checking. ACM TOPLAS 32(2) (2010)
Meyer, B.: Eiffel: the language. Prentice-Hall, Inc., Upper Saddle River (1992)
Nelson, G.: Techniques for program verification. Technical Report CSL81-10, Xerox Palo Alto Research Center (1981)
Norell, U.: Towards a practical programming language based on dependent type theory. PhD thesis, Chalmers, SE-412 96 Göteborg, Sweden (September 2007)
Ou, X., Tan, G., Mandelbaum, Y., Walker, D.: Dynamic Typing with Dependent Types. In: Levy, J.-J., Mayr, E.W., Mitchell, J.C. (eds.) TCS 2004. IFIP, vol. 155, pp. 437–450. Springer, Boston (2004)
Pierce, B.C.: Types and Programming Languages. MIT Press (2002)
Rondon, P., Kawaguchi, M., Jhala, R.: Liquid types. In: PLDI (2008)
Sheard, T.: Type-level computation using narrowing in omega. In: PLPV (2006)
Swamy, N., Chen, J., Fournet, C., Strub, P.-Y., Bhargavan, K., Yang, J.: Secure distributed programming with value-dependent types. In: ICFP, pp. 266–278 (2011)
Vytiniotis, D., Peyton Jones, S.L., Magalhães, J.: Equality proofs and deferred type errors: a compiler pearl. In: ICFP, pp. 341–352 (2012)
Xi, H., Pfenning, F.: Eliminating array bound checking through dependent types. In: PLDI (1998)
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Vazou, N., Rondon, P.M., Jhala, R. (2013). Abstract Refinement Types. In: Felleisen, M., Gardner, P. (eds) Programming Languages and Systems. ESOP 2013. Lecture Notes in Computer Science, vol 7792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37036-6_13
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DOI: https://doi.org/10.1007/978-3-642-37036-6_13
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