LF+ in Coq for fast-and-loose reasoning

We develop the metatheory and the implementation, in Coq, of the novel logical framework LF+ and discuss several of its applications. LF+ generalises research work, carried out by the authors over more than a decade, on Logical Frameworks conservatively extending LF and featuring lock-type constructors L-P(N:sigma)[center dot]. Lock-types capture monadically the concept of inhabitability up-to. They were originally introduced for factoring-out, postponing, or delegating to external tools the verification of time-consuming judgments, which are morally proof-irrelevant, thus allowing for integrating different sources of epistemic evidence in a unique Logical Framework. Besides introducing LF+ and its "shallow" implementation in Coq, the main novelty of the paper is to show that lock-types are also a very flexible tool for expressing in Type Theory several diverse cognitive attitudes and mental strategies used in ordinary reasoning, which essentially amount to reasoning up-to, as in e.g. Typical Ambiguity provisos or co-inductive Coq proofs. In particular we address the encoding of the emerging paradigm of fast-and-loose reasoning, which trades off efficiency for correctness. This paradigm, implicitly used normally in naive Set Theory, is producing considerable impact also in computer architecture and distributed systems, when branch prediction and optimistic concurrency control are implemented

Digital asset management via distributed ledgers

Distributed ledgers rose to prominence with the advent of Bitcoin, the first provably secure protocol to solve consensus in an open-participation setting. Following, active research and engineering efforts have proposed a multitude of applications and alternative designs, the most prominent being Proof-of-Stake (PoS). This thesis expands the scope of secure and efficient asset management over a distributed ledger around three axes: i) cryptography; ii) distributed systems; iii) game theory and economics. First, we analyze the security of various wallets. We start with a formal model of hardware wallets, followed by an analytical framework of PoS wallets, each outlining the unique properties of Proof-of-Work (PoW) and PoS respectively. The latter also provides a rigorous design to form collaborative participating entities, called stake pools. We then propose Conclave, a stake pool design which enables a group of parties to participate in a PoS system in a collaborative manner, without a central operator. Second, we focus on efficiency. Decentralized systems are aimed at thousands of users across the globe, so a rigorous design for minimizing memory and storage consumption is a prerequisite for scalability. To that end, we frame ledger maintenance as an optimization problem and design a multi-tier framework for designing wallets which ensure that updates increase the ledger’s global state only to a minimal extent, while preserving the security guarantees outlined in the security analysis. Third, we explore incentive-compatibility and analyze blockchain systems from a micro and a macroeconomic perspective. We enrich our cryptographic and systems' results by analyzing the incentives of collective pools and designing a state efficient Bitcoin fee function. We then analyze the Nash dynamics of distributed ledgers, introducing a formal model that evaluates whether rational, utility-maximizing participants are disincentivized from exhibiting undesirable infractions, and highlighting the differences between PoW and PoS-based ledgers, both in a standalone setting and under external parameters, like market price fluctuations. We conclude by introducing a macroeconomic principle, cryptocurrency egalitarianism, and then describing two mechanisms for enabling taxation in blockchain-based currency systems