Abstract
Manifest contracts track precise properties by refining types with predicates—e.g., {x : Int |x > 0 } denotes the positive integers. Contracts and polymorphism make a natural combination: programmers can give strong contracts to abstract types, precisely stating pre- and post-conditions while hiding implementation details— for example, an abstract type of stacks might specify that the pop operation has input type {x :α Stack |not ( empty x )} . We formalize this combination by defining FH, a polymorphic calculus with manifest contracts, and establishing fundamental properties including type soundness and relational parametricity. Our development relies on a significant technical improvement over earlier presentations of contracts: instead of introducing a denotational model to break a problematic circularity between typing, subtyping, and evaluation, we develop the metatheory of contracts in a completely syntactic fashion, omitting subtyping from the core system and recovering it post facto as a derived property.
Keywords
- contracts
- refinement types
- preconditions
- postconditions
- dynamic checking
- parametric polymorphism
- abstract datatypes
- syntactic proof
- logical relations
- subtyping
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References
PLT Racket Contracts, http://pre.plt-scheme.org/docs/html/guide/contracts.html
Ahmed, A., Findler, R.B., Matthews, J., Wadler, P.: Blame for all. In: Workshop on Script-to-Program Evolution, STOP (2009)
Ahmed, A., Findler, R.B., Siek, J., Wadler, P.: Blame for all. In: Principles of Programming Languages, POPL (2011)
Aspinall, D., Compagnoni, A.: Subtyping dependent types. Theor. Comput. Sci. 266(1-2), 273–309 (2001)
Findler, R.B., Felleisen, M.: Contracts for higher-order functions. In: International Conference on Functional Programming (ICFP), pp. 48–59 (2002)
Flanagan, C.: Hybrid type checking. In: POPL, pp. 245–256 (2006)
Greenberg, M., Pierce, B.C., Weirich, S.: Contracts made manifest. In: Principles of Programming Languages, POPL 2010 (2010)
Gronski, J., Flanagan, C.: Unifying hybrid types and contracts. In: Trends in Functional Programming, TFP (2007)
Guha, A., Matthews, J., Findler, R.B., Krishnamurthi, S.: Relationally-parametric polymorphic contracts. In: DLS, pp. 29–40 (2007)
Knowles, K., Flanagan, C.: Hybrid type checking (2010) (to appear in TOPLAS)
Matthews, J., Ahmed, A.: Parametric polymorphism through run-time sealing or, theorems for low, low prices! In: Gairing, M. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 16–31. Springer, Heidelberg (2008)
Ou, X., Tan, G., Mandelbaum, Y., Walker, D.: Dynamic typing with dependent types. In: IFIP TCS, pp. 437–450 (2004)
Pierce, B., Sumii, E.: Relating cryptography and polymorphism (July 2000)
Pitts, A.M.: Typed operational reasoning. In: Pierce, B.C. (ed.) Advanced Topics in Types and Programming Languages, ch. 7, pp. 245–289. MIT Press, Cambridge (2005)
Siek, J.G., Taha, W.: Gradual typing for functional languages. In: Scheme and Functional Programming Workshop (September 2006)
Strickland, T.S., Tobin-Hochstadt, S., Felleisen, M.: Practical variable-arity polymorphism. In: Castagna, G. (ed.) ESOP 2009. LNCS, vol. 5502, pp. 32–46. Springer, Heidelberg (2009)
Wadler, P.: Theorems for free! In: Proceedings of ACM Conference on Functional Programming and Computer Architecture (FPCA 1989), pp. 347–359, London, UK (September 1989)
Wadler, P., Findler, R.B.: Well-typed programs can’t be blamed. In: Castagna, G. (ed.) ESOP 2009. LNCS, vol. 5502, pp. 1–16. Springer, Heidelberg (2009)
Wright, A.K., Felleisen, M.: A syntactic approach to type soundness. Information and Computation 115, 38–94 (1992)
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Belo, J.F., Greenberg, M., Igarashi, A., Pierce, B.C. (2011). Polymorphic Contracts. In: Barthe, G. (eds) Programming Languages and Systems. ESOP 2011. Lecture Notes in Computer Science, vol 6602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19718-5_2
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DOI: https://doi.org/10.1007/978-3-642-19718-5_2
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