Friends with benefits: implementing corecursion in foundational proof assistants

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference

Computational Soundness for Dalvik Bytecode

Automatically analyzing information flow within Android applications that rely on cryptographic operations with their computational security guarantees imposes formidable challenges that existing approaches for understanding an app's behavior struggle to meet. These approaches do not distinguish cryptographic and non-cryptographic operations, and hence do not account for cryptographic protections: f(m) is considered sensitive for a sensitive message m irrespective of potential secrecy properties offered by a cryptographic operation f. These approaches consequently provide a safe approximation of the app's behavior, but they mistakenly classify a large fraction of apps as potentially insecure and consequently yield overly pessimistic results. In this paper, we show how cryptographic operations can be faithfully included into existing approaches for automated app analysis. To this end, we first show how cryptographic operations can be expressed as symbolic abstractions within the comprehensive Dalvik bytecode language. These abstractions are accessible to automated analysis, and they can be conveniently added to existing app analysis tools using minor changes in their semantics. Second, we show that our abstractions are faithful by providing the first computational soundness result for Dalvik bytecode, i.e., the absence of attacks against our symbolically abstracted program entails the absence of any attacks against a suitable cryptographic program realization. We cast our computational soundness result in the CoSP framework, which makes the result modular and composable.Comment: Technical report for the ACM CCS 2016 conference pape

Truly modular (co)datatypes for Isabelle/HOL

We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion–corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively. As a case study, we ported Isabelle’s Coinductive library to use the new commands, eliminating the need for tedious ad hoc constructions

Foundational (co)datatypes and (co)recursion for higher-order logic

We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach

Comprehending Isabelle/HOL's consistency

The proof assistant Isabelle/HOL is based on an extension of Higher-Order Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means—following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs

CoSMed: a confidentiality-verified social media platform

This paper describes progress with our agenda of formal verification of information-flow security for realistic systems. We present CoSMed, a social media platform with verified document confidentiality. The system’s kernel is implemented and verified in the proof assistant Isabelle/HOL. For verification, we employ the framework of Bounded-Deducibility (BD) Security, previously introduced for the conference system CoCon. CoSMed is a second major case study in this framework. For CoSMed, the static topology of declassification bounds and triggers that characterized previous instances of BD security has to give way to a dynamic integration of the triggers as part of the bound

A verified algorithm enumerating event structures

An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and formulas to generate, enumerate and count particular sets of their members, no algorithm or formulas are known to generate or count all the possible event structures over af inite set of events. We present an algorithm to generate such a family, along with a functional implementation verified using Isabelle/HOL. As byproducts, we obtain a verified enumeration of all possible preorders and partial orders. While the integer sequences counting preorders and partial orders are already listed on OEIS (On-line Encyclopedia of Integer Sequences), the one counting event structures is not. We therefore used our algorithm to submit a formally verified addition, which has been successfully reviewed and is now part of the OEIS.Postprin