We present a new version of ReLoC: a relational separation logic for proving refinements of programs with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is its refinement judgment $e \precsim e' : \tau$, which states that a program $e$ refines a program $e'$ at type $\tau$. ReLoC provides type-directed structural rules and symbolic execution rules in separation-logic style for manipulating the judgment, whereas in prior work on refinements for languages with higher-order state and concurrency, such proofs were carried out by unfolding the judgment into its definition in the model. ReLoC's abstract proof rules make it simpler to carry out refinement proofs, and enable us to generalize the notion of logically atomic specifications to the relational case, which we call logically atomic relational specifications. We build ReLoC on top of the Iris framework for separation logic in Coq, allowing us to leverage features of Iris to prove soundness of ReLoC, and to carry out refinement proofs in ReLoC. We implement tactics for interactive proofs in ReLoC, allowing us to mechanize several case studies in Coq, and thereby demonstrate the practicality of ReLoC. ReLoC Reloaded extends ReLoC (LICS'18) with various technical improvements, a new Coq mechanization, and support for Iris's prophecy variables. The latter allows us to carry out refinement proofs that involve reasoning about the program's future. We also expand ReLoC's notion of logically atomic relational specifications with a new flavor based on the HOCAP pattern by Svendsen et al.

We study different formalizations of finite sets in homotopy type theory to obtain a general definition that exhibits both the computational facilities and the proof principles expected from finite sets. We use higher inductive types to define the type K(A) of łfinite sets over type Až à la Kuratowski without assuming that A has decidable equality. We show how to define basic functions and prove basic properties after which we give two applications of our definition.On the foundational side, we use K to define the notions of łKuratowski-finite typež and łKuratowski-finite subobjectž, which we contrast with established notions, e.g., Bishop-finite types and enumerated types. We argue that Kuratowski-finiteness is the most general and flexible one of those and we define the usual operations on finite types and subobjects.From the computational perspective, we show how to use K(A) for an abstract interface for well-known finite set implementations such as tree-and list-like data structures. This implies that a function defined on a concrete finite sets implementation can be obtained from a function defined on the abstract finite sets K(A) and that correctness properties are inherited. Hence, HoTT is the ideal setting for data refinement. Beside this, we define bounded quantification, which lifts a decidable property on A to one on K(A).

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σ-and Π-types, and functional extensionality.We apply the method to the effective topos with the interval object ∇2. In the resulting model structure we identify uniform inhabited objects as contractible objects, and show that discrete objects are fibrant. Moreover, we show that the unit of the discrete reflection is a homotopy equivalence and the homotopy category of fibrant assemblies is equivalent to the category of modest sets. We compare our work with the path object category construction on the effective topos by Jaap van Oosten.

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources.

We present ReLoC: a logic for proving refinements of programs in a language with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of our logic is a judgement e ≾ e ′ : τ , which expresses that a program e refines a program e ′ at type τ. In contrast to earlier work on refinements for languages with higher-order state and concurrency, ReLoC provides type-and structure-directed rules for manipulating this judgement, whereas previously, such proofs were carried out by unfolding the judgement into its definition in the model. These more abstract proof rules make it simpler to carry out refinement proofs. Moreover, we introduce logically atomic relational specifications: a novel approach for relational specifications for compound expressions that take effect at a single instant in time. We demonstrate how to formalise and prove such relational specifications in ReLoC, allowing for more modular proofs. ReLoC is built on top of the expressive concurrent separation logic Iris, allowing us to leverage features of Iris such as invariants and ghost state. We provide a mechanisation of our logic in Coq, which does not just contain a proof of soundness, but also tactics for interactively carrying out refinements proofs. We have used these tactics to mechanise several examples, which demonstrates the practicality and modularity of our logic.

Research into C verification often ignores that the C standard leaves the evaluation order of expressions unspecified, and assigns undefined behavior to write-write or read-write conflicts in subexpressionsso called "sequence point violations". These aspects should be accounted for in verification because C compilers exploit them.We present a verification condition generator (vcgen) that enables one to semi-automatically prove the absence of undefined behavior in a given C program for any evaluation order. The key novelty of our approach is a symbolic execution algorithm that computes a frame at the same time as a postcondition. The frame is used to automatically determine how resources should be distributed among subexpressions.We prove correctness of our vcgen with respect to a new monadic definitional semantics of a subset of C. This semantics is modular and gives a concise account of non-determinism in C.We have implemented our vcgen as a tactic in the Coq interactive theorem prover, and have proved correctness of it using a separation logic for the new monadic definitional semantics of a subset of C.

Recent secure cache designs aim to mitigate sidechannel attacks by randomizing the mapping from memory addresses to cache sets. As vendors investigate deployment of these caches, it is crucial to understand their actual security.In this paper, we consolidate existing randomization-based secure caches into a generic cache model. We then comprehensively analyze the security of existing designs, including CEASER-S and SCATTERCACHE, by mapping them to instances of this model. We tailor cache attacks for randomized caches using a novel PRIME+PRUNE+PROBE technique, and optimize it using burst accesses, bootstrapping, and multi-step profiling. PRIME+ PRUNE+PROBE constructs probabilistic but reliable eviction sets, enabling attacks previously assumed to be computationally infeasible. We also simulate an end-to-end attack, leaking secrets from a vulnerable AES implementation. Finally, a case study of CEASER-S reveals that cryptographic weaknesses in the randomization algorithm can lead to a complete security subversion.Our systematic analysis yields more realistic and comparable security levels for randomized caches. As we quantify how design parameters influence the security level, our work leads to important conclusions for future work on secure cache designs.

We study different formalizations of finite sets in homotopy type theory to obtain a general definition that exhibits both the computational facilities and the proof principles expected from finite sets. We use higher inductive types to define the type K(A) of łfinite sets over type Až à la Kuratowski without assuming that A has decidable equality. We show how to define basic functions and prove basic properties after which we give two applications of our definition.On the foundational side, we use K to define the notions of łKuratowski-finite typež and łKuratowski-finite subobjectž, which we contrast with established notions, e.g., Bishop-finite types and enumerated types. We argue that Kuratowski-finiteness is the most general and flexible one of those and we define the usual operations on finite types and subobjects.From the computational perspective, we show how to use K(A) for an abstract interface for well-known finite set implementations such as tree-and list-like data structures. This implies that a function defined on a concrete finite sets implementation can be obtained from a function defined on the abstract finite sets K(A) and that correctness properties are inherited. Hence, HoTT is the ideal setting for data refinement. Beside this, we define bounded quantification, which lifts a decidable property on A to one on K(A).