Skip to main content Accessibility help

Iris from the ground up: A modular foundation for higher-order concurrent separation logic



Iris is a framework for higher-order concurrent separation logic, which has been implemented in the Coq proof assistant and deployed very effectively in a wide variety of verification projects. Iris was designed with the express goal of simplifying and consolidating the foundations of modern separation logics, but it has evolved over time, and the design and semantic foundations of Iris itself have yet to be fully written down and explained together properly in one place. Here, we attempt to fill this gap, presenting a reasonably complete picture of the latest version of Iris (version 3.1), from first principles and in one coherent narrative.



Hide All
America, Pierre, & Rutten, Jan. (1989). Solving reflexive domain equations in a category of complete metric spaces. Journal of Computer and System Sciences, 39(3), 343375.
Appel, Andrew W. (2001). Foundational proof-carrying code. Pages 247–256 of: LICS.
Appel, Andrew W. (ed). (2014). Program Logics for Certified Compilers. Cambridge University Press.
Appel, Andrew W., & McAllester, David. (2001). An indexed model of recursive types for foundational proof-carrying code. TOPLAS, 23(5), 657683.
Appel, Andrew W., Melliès, Paul-André, Richards, Christopher, & Vouillon, Jérôme. (2007). A very modal model of a modern, major, general type system. Pages 109–122 of: POPL.
Ashcroft, Edward A. (1975). Proving assertions about parallel programs. Journal of Computer and System Sciences, 10(1), 110135.
Beringer, Lennart, Stewart, Gordon, Dockins, Robert, & Appel, Andrew W. (2014). Verified compilation for shared-memory C. Pages 107–127 of: ESOP. LNCS, vol. 8410.
Birkedal, Lars, Støvring, Kristian, & Thamsborg, Jacob. (2010). The category-theoretic solution of recursive metric-space equations. TCS, 411(47), 41024122.
Birkedal, Lars, Møgelberg, Rasmus Ejlers, Schwinghammer, Jan, & Støvring, Kristian. (2011). First steps in synthetic guarded domain theory: step-indexing in the topos of trees. Pages 55–64 of: LICS.
Bizjak, Aleš, & Birkedal, Lars. (2017). On models of higher-order separation logic. MFPS.
Bizjak, Aleš, Gratzer, Daniel, Krebbers, Robbert, & Birkedal, Lars. (2018). Iron: Managing obligations in higher-order concurrent separation logic. Draft.
Bornat, Richard, Calcagno, Cristiano, O’Hearn, Peter W., & Parkinson, Matthew J. (2005). Permission accounting in separation logic. Pages 259–270 of: POPL.
Boyland, John. (2003). Checking interference with fractional permissions. Pages 55–72 of: SAS. LNCS, vol. 2694.
Brookes, Stephen. (2007). A semantics for concurrent separation logic. TCS, 375(1–3), 227270.
Buisse, Alexandre, Birkedal, Lars, & Støvring, Kristian. (2011). Step-indexed Kripke model of separation logic for storable locks. ENTCS, 276, 121143.
Cao, Qinxiang, Cuellar, Santiago, & Appel, Andrew W. (2017). Bringing order to the separation logic jungle. Pages 190–211 of: APLAS. LNCS, vol. 10695.
Cohen, Ernie, Alkassar, Eyad, Boyarinov, Vladimir, Dahlweid, Markus, Degenbaev, Ulan, Hillebrand, Mark, Langenstein, Bruno, Leinenbach, Dirk, Moskal, Michał, Obua, Steven, Paul, Wolfgang, Pentchev, Hristo, Petrova, Elena, Santen, Thomas, Schirmer, Norbert, Schmaltz, Sabine, Schulte, Wolfram, Shadrin, Andrey, Tobies, Stephan, Tsyban, Alexandra, & Tverdyshev, Sergey. (2009). Invariants, modularity, and rights. Pages 43–55 of: PSI. LNCS, vol. 5947.
da Rocha Pinto, Pedro, Dinsdale-Young, Thomas, & Gardner, Philippa. (2014). TaDA: A logic for time and data abstraction. Pages 207–231 of: ECOOP. LNCS, vol. 8586.
Di Gianantonio, Pietro, & Miculan, Marino. (2002). A unifying approach to recursive and co-recursive definitions. Pages 148–161 of: TYPES. LNCS, vol. 2646.
Dijkstra, Edsger W. (1975). Guarded commands, nondeterminacy and formal derivation of programs. CACM, 18(8), 453457.
Dinsdale-Young, Thomas, Gardner, Philippa, & Wheelhouse, Mark J. (2010a). Abstraction and refinement for local reasoning. Pages 199–215 of: VSTTE. LNCS, vol. 6217.
Dinsdale-Young, Thomas, Dodds, Mike, Gardner, Philippa, Parkinson, Matthew J., & Vafeiadis, Viktor. (2010b). Concurrent abstract predicates. Pages 504–528 of: ECOOP. LNCS, vol. 6183.
Dinsdale-Young, Thomas, Birkedal, Lars, Gardner, Philippa, Parkinson, Matthew J., & Yang, Hongseok. (2013). Views: Compositional reasoning for concurrent programs. Pages 287–300 of: POPL.
Dockins, Robert, Hobor, Aquinas, & Appel, Andrew W. (2009). A fresh look at separation algebras and share accounting. Pages 161–177 of: APLAS. LNCS, vol. 5904.
Dodds, Mike, Feng, Xinyu, Parkinson, Matthew J., & Vafeiadis, Viktor. (2009). Deny-guarantee reasoning. Pages 363–377 of: ESOP. LNCS, vol. 5502.
Dodds, Mike, Jagannathan, Suresh, Parkinson, Matthew J., Svendsen, Kasper, & Birkedal, Lars. (2016). Verifying custom synchronization constructs using higher-order separation logic. TOPLAS, 38(2), 4:14:72.
Dreyer, Derek, Neis, Georg, Rossberg, Andreas, & Birkedal, Lars. (2010). A relational modal logic for higher-order stateful ADTs. Pages 185–198 of: POPL.
Feng, Xinyu. (2009). Local rely-guarantee reasoning. Pages 315–327 of: POPL.
Feng, Xinyu, Ferreira, Rodrigo, & Shao, Zhong. (2007). On the relationship between concurrent separation logic and assume-guarantee reasoning. Pages 173–188 of: ESOP. LNCS, vol. 4421.
Frumin, Dan, Krebbers, Robbert, & Birkedal, Lars. (2018). ReLoC: A mechanised relational logic for fine-grained concurrency. Pages 442–451 of: LICS.
Fu, Ming, Li, Yong, Feng, Xinyu, Shao, Zhong, & Zhang, Yu. (2010). Reasoning about optimistic concurrency using a program logic for history. Pages 388–402 of: CONCUR. LNCS, vol. 6269.
Garillot, François, Gonthier, Georges, Mahboubi, Assia, & Rideau, Laurence. (2009). Packaging mathematical structures. Pages 327–342 of: TPHOLs. LNCS, vol. 5674.
Gotsman, Alexey, Berdine, Josh, Cook, Byron, Rinetzky, Noam, & Sagiv, Mooly. (2007). Local reasoning about storable locks and threads. Pages 19–37 of: APLAS. LNCS, vol. 4807.
Hobor, Aquinas, Appel, Andrew W., & Zappa Nardelli, Francesco. (2008). Oracle semantics for concurrent separation logic. Pages 353–367 of: ESOP. LNCS, vol. 4960.
Hobor, Aquinas, Dockins, Robert, & Appel, Andrew W. (2010). A theory of indirection via approximation. Pages 171–184 of: POPL.
Iris Team. (2017). The Iris documentation and Coq development. Available on the Iris project website at:
Ishtiaq, Samin S., & O’Hearn, Peter W. (2001). BI as an assertion language for mutable data structures. Pages 14–26 of: POPL.
Jensen, Jonas Braband, & Birkedal, Lars. (2012). Fictional separation logic. Pages 377–396 of: ESOP. LNCS, vol. 7211.
Jung, Ralf, Swasey, David, Sieczkowski, Filip, Svendsen, Kasper, Turon, Aaron, Birkedal, Lars, & Dreyer, Derek. (2015). Iris: Monoids and invariants as an orthogonal basis for concurrent reasoning. Pages 637–650 of: POPL.
Jung, Ralf, Krebbers, Robbert, Birkedal, Lars, & Dreyer, Derek. (2016). Higher-order ghost state. Pages 256–269 of: ICFP.
Jung, Ralf, Jourdan, Jacques-Henri, Krebbers, Robbert, & Dreyer, Derek. (2018). RustBelt: Securing the foundations of the Rust programming language. PACMPL, 2(POPL), 66:166:34.
Kaiser, Jan-Oliver, Dang, Hoang-Hai, Dreyer, Derek, Lahav, Ori, & Vafeiadis, Viktor. (2017). Strong logic for weak memory: Reasoning about release-acquire consistency in Iris. Pages 17:1–17:29 of: ECOOP. LIPIcs, vol. 74.
Kock, Anders. (1970). Monads on symmetric monoidal closed categories. Archiv der Mathematik, 21(1), 110.
Kock, Anders. (1972). Strong functors and monoidal monads. Archiv der Mathematik, 23(1), 113120.
Krebbers, Robbert, Jung, Ralf, Bizjak, Aleš, Jourdan, Jacques-Henri, Dreyer, Derek, & Birkedal, Lars. (2017a). The essence of higher-order concurrent separation logic. Pages 696–723 of: ESOP. LNCS, vol. 10201.
Krebbers, Robbert, Timany, Amin, & Birkedal, Lars. (2017b). Interactive proofs in higher-order concurrent separation logic. Pages 205–217 of: POPL.
Krebbers, Robbert, Jourdan, Jacques-Henri, Jung, Ralf, Tassarotti, Joseph, Kaiser, Jan-Oliver, Timany, Amin, Charguéraud, Arthur, & Dreyer, Derek. (2018). MoSeL: A general, extensible modal framework for interactive proofs in separation logic. PACMPL, 2(ICFP), 77:116:30.
Kripke, Saul A. (1965). Semantical analysis of intuitionistic logic I. Formal systems and recursive functions, 92–130.
Krishnaswami, Neelakantan R., Turon, Aaron, Dreyer, Derek, & Garg, Deepak. (2012). Superficially substructural types. Pages 41–54 of: ICFP.
Krogh-Jespersen, Morten, Svendsen, Kasper, & Birkedal, Lars. (2017). A relational model of types-and-effects in higher-order concurrent separation logic. Pages 218–231 of: POPL.
Leino, K. Rustan, M. (2010). Dafny: An automatic program verifier for functional correctness. Pages 348–370 of: LPAR. LNCS, vol. 6355.
Leino, K. Rustan, M., Müller, Peter, & Smans, Jan. (2009). Verification of concurrent programs with Chalice. Pages 195–222 of: FOSAD. LNCS, vol. 5705.
Ley-Wild, Ruy, & Nanevski, Aleksandar. (2013). Subjective auxiliary state for coarse-grained concurrency. Pages 561–574 of: POPL.
Müller, Peter, Schwerhoff, Malte, & Summers, Alexander J. (2016). Viper: A verification infrastructure for permission-based reasoning. Pages 41–62 of: VMCAI. LNCS, vol. 9583.
Nakano, Hiroshi. (2000). A modality for recursion. Pages 255–266 of: LICS.
Nanevski, Aleksandar, Ley-Wild, Ruy, Sergey, Ilya, & Delbianco, Germán Andrés. (2014). Communicating state transition systems for fine-grained concurrent resources. Pages 290–310 of: ESOP. LNCS, vol. 8410.
O’Hearn, Peter W. (2007). Resources, concurrency, and local reasoning. TCS, 375(1), 271307.
O’Hearn, Peter W., & Pym, David J. (1999). The logic of bunched implications. Bulletin of Symbolic Logic, 5(2), 215244.
O’Hearn, Peter W., Reynolds, John C., & Yang, Hongseok. (2001). Local reasoning about programs that alter data structures. Pages 1–18 of: CSL. LNCS, vol. 2142.
Parkinson, Matthew J. (2010). The next 700 separation logics - (Invited paper). Pages 169–182 of: VSTTE. LNCS, vol. 6217.
Pilkiewicz, Alexandre, & Pottier, François. (2011). The essence of monotonic state. Pages 73–86 of: TLDI.
Pottier, François. (2013). Syntactic soundness proof of a type-and-capability system with hidden state. JFP, 23(1), 38144.
Reynolds, John C. (2000). Intuitionistic reasoning about shared mutable data structure. Pages 303–321 of: Millennial Perspectives in Computer Science.
Reynolds, John C. (2002). Separation logic: A logic for shared mutable data structures. Pages 55–74 of: LICS.
Sergey, Ilya, Nanevski, Aleksandar, & Banerjee, Anindya. (2015). Mechanized verification of fine-grained concurrent programs. Pages 77–87 of: PLDI.
Sozeau, Matthieu. (2009). A new look at generalized rewriting in type theory. Journal of formalized reasoning, 2(1), 4162.
Svendsen, Kasper, & Birkedal, Lars. (2014). Impredicative concurrent abstract predicates. Pages 149–168 of: ESOP. LNCS, vol. 8410.
Swasey, David, Garg, Deepak, & Dreyer, Derek. (2017). Robust and compositional verification of object capability patterns. PACMPL, 1(OOPSLA), 89:189:26.
Tassarotti, Joseph, & Harper, Robert. (2018). A separation logic for concurrent randomized programs. Draft.
Tassarotti, Joseph, Jung, Ralf, & Harper, Robert. (2017). A higher-order logic for concurrent termination-preserving refinement. Pages 909–936 of: ESOP. LNCS, vol. 10201.
Timany, Amin, & Birkedal, Lars. (2018). Mechanized relational verification of concurrent programs with continuations. Draft.
Timany, Amin, Stefanesco, Léo, Krogh-Jespersen, Morten, & Birkedal, Lars. (2018). A logical relation for monadic encapsulation of state: Proving contextual equivalences in the presence of runST. PACMPL, 2(POPL), 64:164:28.
Turon, Aaron, Dreyer, Derek, & Birkedal, Lars. (2013). Unifying refinement and Hoare-style reasoning in a logic for higher-order concurrency. Pages 377–390 of: ICFP.
Turon, Aaron, Vafeiadis, Viktor, & Dreyer, Derek. (2014). GPS: Navigating weak memory with ghosts, protocols, and separation. Pages 691–707 of: OOPSLA.
Vafeiadis, Viktor, & Parkinson, Matthew J. (2007). A marriage of rely/guarantee and separation logic. Pages 256–271 of: CONCUR. LNCS, vol. 4703.
Wildmoser, Martin, & Nipkow, Tobias. (2004). Certifying machine code safety: Shallow versus deep embedding. Pages 305–320 of: TPHOLs. LNCS, vol. 3223.

Iris from the ground up: A modular foundation for higher-order concurrent separation logic



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Iris from the ground up: A modular foundation for higher-order concurrent separation logic

Submit a response


No Discussions have been published for this article.


Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *