Many theorem provers can generate functional programs from definitions or proofs. However, this code generation needs to be trusted. Except for the HOL4 system, which has a proof producing code generator for a subset of ML. We go one step further and provide a verified compiler from Isabelle/HOL to CakeML. More precisely we combine a simple proof producing translation of recursion equations in Isabelle/HOL into a deeply embedded term language with a fully verified compilation chain to the target language CakeML.

Large systems are commonly internetworked. A security policy describes the communication relationship between the networked entities. The security policy defines rules, for example that A can connect to B, which results in a directed graph. However, this policy is often implemented in the network, for example by firewalls, such that A can establish a connection to B and all packets belonging to established connections are allowed. This stateful implementation is usually required for the network's functionality, but it introduces the backflow from B to A, which might contradict the security policy. We derive compliance criteria for a policy and its stateful implementation. In particular, we provide a criterion to verify the lack of side effects in linear time. Algorithms to automatically construct a stateful implementation of security policy rules are presented, which narrows the gap between formalization and real-world implementation. The solution scales to large networks, which is confirmed by a large real-world case study. Its correctness is guaranteed by the Isabelle/HOL theorem prover.

The security provided by a firewall for a computer network almost completely depends on the rules it enforces. For over a decade, it has been a well-known and unsolved problem that the quality of many firewall rule sets is insufficient. Therefore, there are many tools to analyze them. However, we found that none of the available tools could handle typical, real-world iptables rulesets. This is due to the complex chain model used by iptables, but also to the vast amount of possible match conditions that occur in real-world firewalls, many of which are not understood by academic and open source tools. In this paper, we provide algorithms to transform firewall rulesets. We reduce the execution model to a simple list model and use ternary logic to abstract over all unknown match conditions. These transformations enable existing tools to understand real-world firewall rules, which we demonstrate on four decently-sized rulesets. Using the Isabelle theorem prover, we formally show that all our algorithms preserve the firewall's filtering behavior.

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

This article summarizes our efforts around the formally verified static analysis of iptables rulesets using Isabelle/HOL. We build our work around a formal semantics of the behavior of iptables firewalls. This semantics is tailored to the specifics of the filter table and supports arbitrary match expressions, even new ones that may be added in the future. Around that, we organize a set of simplification procedures and their correctness proofs: we include procedures that can unfold calls to user-defined chains, simplify match expressions, and construct approximations removing unknown or unwanted match expressions. For analysis purposes, we describe a simplified model of firewalls that only supports a single list of rules with limited expressiveness. We provide and verify procedures that translate from the complex iptables language into this simple model. Based on that, we implement the verified generation of IP space partitions and minimal service matrices. An evaluation of our work on a large set of real-world firewall rulesets shows that our framework provides interesting results in many situations, and can both help and out-compete other static analysis frameworks found in related work.