Proofgold is a peer to peer cryptocurrency making use of formal logic. Users can publish theories and then develop a theory by publishing documents with definitions, conjectures and proofs. The blockchain records the theories and their state of development (e.g., which theorems have been proven and when). Two of the main theories are a form of classical set theory (for formalizing mathematics) and an intuitionistic theory of higher-order abstract syntax (for reasoning about syntax with binders). We have also significantly modified the open source Proofgold Core client software to create a faster, more stable and more efficient client, Proofgold Lava. Two important changes are the cryptography code and the database code, and we discuss these improvements. We also discuss how the Proofgold network can be used to support large formalization efforts.

Abstract Multiparty session types is a typing discipline used to write specifications, known as global types, for branching and recursive message-passing systems. A necessary operation on global types is projection to abstractions of local behaviour, called local types. Typically, this is a computable partial function that given a global type and a role erases all details irrelevant to this role. Computable projection functions in the literature are either unsound or too restrictive when dealing with recursion and branching. Recent work has taken a more general approach to projection defining it as a coinductive, but not computable, relation. Our work defines a new computable projection function that is sound and complete with respect to its coinductive counterpart and, hence, equally expressive. All results have been mechanised in the Coq proof assistant.

Wadler introduced Classical Processes (CP), a calculus based on a propositions-as-types correspondence between propositions of classical linear logic and session types. Carbone et al. introduced Multiparty Classical Processes, a calculus that generalises CP to multiparty session types, by replacing the duality of classical linear logic (relating two types) with a more general notion of coherence (relating an arbitrary number of types). This paper introduces variants of CP and MCP, plus a new intermediate calculus of Globally-governed Classical Processes (GCP). We show a tight relation between these three calculi, giving semantics-preserving translations from GCP to CP and from MCP to GCP. The translation from GCP to CP interprets a coherence proof as an arbiter process that mediates communications in a session, while MCP adds annotations that permit processes to communicate directly without centralised control.

No abstract available.

Communication is a central elements in software development. As a potential typed foundation for structured communication-centered programming, session types have been studied over the past decade for a wide range of process calculi and programming languages, focusing on binary (two-party) sessions. This work extends the foregoing theories of binary session types to multiparty, asynchronous sessions, which often arise in practical communication-centered applications. Presented as a typed calculus for mobile processes, the theory introduces a new notion of types in which interactions involving multiple peers are directly abstracted as a global scenario. Global types retain the friendly type syntax of binary session types while specifying dependencies and capturing complex causal chains of multiparty asynchronous interactions. A global type plays the role of a shared agreement among communication peers and is used as a basis of efficient type-checking through its projection onto individual peers. The fundamental properties of the session type discipline, such as communication safety, progress, and session fidelity, are established for general n-party asynchronous interactions.

We propose a Curry-Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic (CLL). In this framework, propositions correspond to the local behaviour of a participant in a multiparty session type, proofs to processes, and proof normalisation to executing communications. Our key contribution is generalising duality, from CLL, to a new notion of n-ary compatibility, called coherence. Building on coherence as a principle of compositionality, we generalise the cut rule of CLL to a new rule for composing many processes communicating in a multiparty session. We prove the soundness of our model by showing the admissibility of our new rule, which entails deadlock-freedom via our correspondence.

Over the last decade, global descriptions have been successfully employed for the verification and implementation of communicating systems, respectively as protocol specifications and choreographies. In this work, we bring these two practices together by proposing a purely-global programming model. We show a novel interpretation of asynchrony and parallelism in a global setting and develop a typing discipline that verifies choreographies against protocol specifications, based on multiparty sessions. Exploiting the nature of global descriptions, our type system defines a new class of deadlock-free concurrent systems (deadlock-freedom-by-design), provides type inference, and supports session mobility. We give a notion of Endpoint Projection (EPP) which generates correct entity code (as pi-calculus terms) from a choreography. Finally, we evaluate our approach by providing a prototype implementation for a concrete programming language and by applying it to some examples from multicore and service-oriented programming.

This article relates two different paradigms of descriptions of communication behavior, one focusing on global message flows and another on end-point behaviors, using formal calculi based on session types. The global calculus, which originates from a Web service description language (W3C WS-CDL), describes an interaction scenario from a vantage viewpoint; the end-point calculus, an applied typed π -calculus, precisely identifies a local behavior of each participant. We explore a theory of end-point projection, by which we can map a global description to its end-point counterparts preserving types and dynamics. Three principles of well-structured description and the type structures play a fundamental role in the theory.

Communication is becoming one of the central elements in software development. As a potential typed foundation for structured communication-centred programming, session types have been studied over the last decade for a wide range of process calculi and programming languages, focussing on binary (two-party) sessions. This work extends the foregoing theories of binary session types to multiparty, asynchronous sessions, which often arise in practical communication-centred applications. Presented as a typed calculus for mobile processes, the theory introduces a new notion of types in which interactions involving multiple peers are directly abstracted as a global scenario. Global types retain a friendly type syntax of binary session types while capturing complex causal chains of multiparty asynchronous interactions. A global type plays the role of a shared agreement among communication peers, and is used as a basis of efficient type checking through its projection onto individual peers. The fundamental properties of the session type discipline such as communication safety, progress and session fidelity are established for generaln-party asynchronous interactions.

We propose a formal model of trust informed by the Global Computing scenario and focusing on the aspects of trust formation, evolution, and propagation. The model is based on a novel notion of trust structures which, building on concepts from trust management and domain theory, feature at the same time a trust and an information partial order.