Abstract
Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we investigate the compatibility of nested Hoare triples with several variations of higher-order frame rules.
The interaction of nested triples and frame rules can be subtle, and the inclusion of certain frame rules is in fact unsound. A particular combination of rules can be shown consistent by means of a Kripke model where worlds live in a recursively defined ultrametric space. The resulting logic allows us to elegantly prove programs involving stored code. In particular, it leads to natural specifications and proofs of invariants required for dealing with recursion through the store.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
America, P., Rutten, J.J.M.M.: Solving reflexive domain equations in a category of complete metric spaces. J. Comput. Syst. Sci. 39(3), 343–375 (1989)
Birkedal, L., Reus, B., Schwinghammer, J., Yang, H.: A simple model of separation logic for higher-order store. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 348–360. Springer, Heidelberg (2008)
Birkedal, L., Støvring, K., Thamsborg, J.: Realizability semantics of parametric polymorphism, general references, and recursive types. In: FOSSACS 2009. LNCS, vol. 5504, pp. 456–470. Springer, Heidelberg (2009)
Birkedal, L., Torp-Smith, N., Yang, H.: Semantics of separation-logic typing and higher-order frame rules for Algol-like languages. Log. Methods Comput. Sci. 2(5:1) (2006)
Honda, K., Yoshida, N., Berger, M.: An observationally complete program logic for imperative higher-order functions. In: LICS, pp. 270–279. IEEE Computer Society Press, Los Alamitos (2005)
Krishnaswami, N., Birkedal, L., Aldrich, J., Reynolds, J.: Idealized ML and Its Separation Logic (2007), http://www.cs.cmu.edu/~neelk/
Nanevski, A., Morrisett, G., Shinnar, A., Govereau, P., Birkedal, L.: Ynot: dependent types for imperative programs. In: ICFP, pp. 229–240. ACM Press, New York (2008)
O’Hearn, P.W., Pym, D.J.: The logic of bunched implications. B. Symb. Log. 5(2), 215–244 (1999)
Parkinson, M., Biermann, G.: Separation logic, abstraction and inheritance. In: POPL, pp. 75–86. ACM Press, New York (2008)
Pitts, A.M.: Relational properties of domains. Inf. Comput. 127, 66–90 (1996)
Pottier, F.: Hiding local state in direct style: a higher-order anti-frame rule. In: LICS, pp. 331–340. IEEE Computer Society Press, Los Alamitos (2008)
Reus, B., Schwinghammer, J.: Separation logic for higher-order store. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 575–590. Springer, Heidelberg (2006)
Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74. IEEE Computer Society Press, Los Alamitos (2002)
Smyth, M.B., Plotkin, G.D.: The category-theoretic solution of recursive domain equations. SIAM J. Comput. 11(4), 761–783 (1982)
Streicher, T.: Domain-theoretic Foundations of Functional Programming. World Scientific, Singapore (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwinghammer, J., Birkedal, L., Reus, B., Yang, H. (2009). Nested Hoare Triples and Frame Rules for Higher-Order Store. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-04027-6_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04026-9
Online ISBN: 978-3-642-04027-6
eBook Packages: Computer ScienceComputer Science (R0)